0.23226 ± 0.00031 *
0.23272 + 0.00079
-*
0.2324 ± 0 . 0 0 1 2 0.23152 + 0.00017
Average
X2/d.o.f.: 12.8/5
-0.1110'
68.3 95.5 99.5 % CL -0.12 -0.45 -0.44 -0.43 -0.42
-0.41
>
-0.40
CD
o
9Lb
X E
Figure 11. LEP and SLD measurements of gm, versus gu, compared to the Standard Model prediction.
SSSH Actff^ 0.02761 ± 0.00036 as? IYV= 91.1875 ±0.0021 GeV E^mj= 174.3 ± 5 . 1 GeV
10 20.23
0.232
0.234
sin 0 eff sin29^F. as determined from lepton and quark data is presented in Fig. 12. While the lepton data prefer a small value of sin2Ql^fl and thereby a small Higgs mass the quark asymmetries tend to larger sin29leeFf and m # values. Evaluating the average from the lepton data alone yields: sin26leeff(leptons)
= 0.23113 ± 0.00021. (15) The corresponding average from the quark asymmetries is: sin2O^fj {quarks) = 0.23230 ± 0.00029. (16) The two values differ by 3.3 standard deviations. Presently this deviation is unexplained. It could either be due to a statistical fluctuation (the error of the most precise quark asymmetry ApB is completely dominated by statistics), or due to unknown sources of systematic errors (this is unlikely due to the small systematic uncertainty correlated between the different measurements of ApB) or due to completely unexpected new physics. However, one has to keep in
Figure 12. The effective electroweak mixing angle sin26^Fr derived from d a t a depending on lepton couplings only (top) and from data depending on lepton and quark couplings (bottom). Also shown is the prediction of the Standard Model as a function of mn • The band indicates the uncertainty of t h e SM prediction due to the uncertainty of our knowledge on (5) AQS'J, mz,
and
mt.
mind that four of the nine ApB measurements shown in Fig. 9 are still preliminary. One should note that only the average of lepton and quark sin2 9^ measurements is consistent with a Higgs mass of 0(100) GeV. 3
Two Fermion Production above the Z
Two fermion production at high energies provides a beautiful laboratory for searching for new physics. Compared to other processes the cross-section for qq production is still high as shown in Fig. 13 prepared by the L3 Collaboration 23 , where the energy dependences of cross-sections for various final states in e+e~ annihilation are collected. At
356
J. Drees
Review of Final LEP Results or A Tribute to LEP The combined cross-sections and asymmetries and the results on b and c quark production have been used to study models with an additional heavy neutral Z' boson. Limits for the Z' mass have been obtained, for instance, for an E(6) x model mz1 > 0.68 TeV or for the left-right symmetric model mZ' > 0.80 TeV. In both cases the 95% confidence level lower limits are quoted and zero mixing with the Z boson is assumed. It should be remarked that the LEP2 data alone are not sufficient to constrain the mixing angle. But fits including the LEP1 data of a single experiment are consistent with zero mixing, see e.g. 26 .
Figure 13. Energy dependence of cross-sections in e + e _ annihilation. The data are from the L3 Collaboration. The cross-sections for e + e - —> qq are shown for the inclusive sample (full squares) and the non-radiative sample (open squares).
energies above the Z radiative processes are important. Due to the large cross-section for radiative return to the Z resonance only a fraction of the detected events have large s', the square of the centre-of-mass energy transferred to the / / final state. The Electroweak Working Group defines the interesting non-radiative cross-section by y/s'/s > 0.85 24 . For this cut the cross-sections for hadron, fi+fi~, T+T~ , bb, cc production have been combined. Some results are shown in Fig. 14. The lower part of the figure presents the ratio of the data divided by the SM prediction. Obviously the data are in agreement with the prediction but one should notice that the hadronic cross-section is 1.8 a high. The combined measurements of forward-backward asymmetries for /i+/x~ and T+T~ final states are collected in Fig. 15.
357
Many models for physics beyond the SM can be investigated in the general framework of four-fermion contact interactions (analogous to the low energy approximation of the weak force by Fermi theory). Using the combined data, constraints have been placed on the characteristic high energy scale A describing the low energy phenomenology of hypothetical new interactions. Limits for contact interactions between leptons range from V&rA/g > 8.5 to 26 TeV depending on the helicity coupling between initial and final state fermions and on the sign of the interference with the SM. Here g is the coupling of the new interaction. The corresponding limits for contact interactions between leptons and b quarks are \/4nA/g > 2.2 to 15 TeV, for leptons and c quarks ^/4nA/g > 1.4 to 7.2 TeV. Constraints have further been placed on the energy scale of quantum gravity in compactified extra dimensions. Including data from the Bhabha channel the typical result from the analysis of a single experiment is Ms > 1 TeV. Furthermore limits have been set on the masses of leptoquarks. The 7 — Z interference has been investigated in terms of the S-Matrix framework. In all cases no deviations from the SM expectation have been observed. Details on the two fermion analyses can be found m25>26>27>28>29. For a more
J. Drees
Review of Final LEP Results or A Tribute to LEP
preliminary
preliminary
LEP
10 zl
g o CD
10
w CO CO
o
o
a e+e_-^hadrons(Y) * eV-»u + u_ (y)
* e*e_->|iV(y) « e e ->x x (y)
O LL
* e e ^ n (y)
0
1.2 1.1
hh¥\^~
1 0.9
LL.
™ E
CO LL
<
0.2 0-
t*
•Hftjft-
< -0.2-
0.8 120
CO
140
160
180
200
220
120
Vs(GeV)
140
160
180
200
220
Vs(GeV)
Figure 14. Combined LEP measurements of the cross-sections for gc>, fJ.+fi~, T+T~ production. The curves show the SM expectation evaluated with ZFITTER. The lower part shows the ratio data to SM prediction.
Figure 15. Combined L E P results for the forwardbackward asymmetries for n+/J.~ and T+T~ final states. The curves represent the SM expectation. The lower part shows the differences between measurements and SM prediction.
complete recent summary of the two fermion data and their interpretation see 30 .
lected about 10000 W+W~ events which are analysed in terms of five decay classes: fully hadronic events where both W's decay into quarks, three semileptonic decays and fully leptonic decays. In the SM the branching ratio for the four quark class is 45.5%, for each semileptonic class 14.6%, and for the fully leptonic class 10.6%. Powerful tools to separate the four fermion events originating from W production from the background have been developed involving, for instance, neural networks. The efficiency for WW selection is high, typically around 85%, at very high purity.
4
W+W~
Production
Experimental studies of W-pair production have been a focus of the LEP2 physics programme with two main goals: the measurements of the W mass and the investigation of the structure of triple gauge boson couplings. In e+e~ annihilation double resonant W pairs are produced via the so-called CC03 diagrams shown in Fig. 16. Near threshold the cross-section is dominated by the neutrino t-channel exchange. Contributions from the more interesting s-channel exchange of a Z boson or a photon have been measured at centre-of-mass energies from 172 to 209 GeV. Each LEP experiment has finally col-
The total CC03 cross-sections measured by the four collaborations have been combined 31 , the results are summarised in Fig. 17. All experiments have published their final results for centre-of-mass energies up to
358
J. Drees
Review of Final LEP Results or A Tribute to LEP 08/07/2001
Preliminary
LEP
4
•
# '
#
*
Figure 16. CC03 diagrams for W+W production with subsequent decay into ud and /iP^.
189 GeV 32>33.34>35. The results for energies up to 207 GeV are still preliminary 36>37.38>28. Inspection of Fig. 17 immediately shows that all t- and s-channel contributions are needed to understand the data. More subtle is the comparison with predictions of the new four fermion generators Racoon WW 3 9 and YFSWW 40 with improved radiative corrections. The calculations of both programmes are based on the so-called double pole approximation for virtual 0{a) corrections in resonant W-pair production plus all other QED corrections needed for a 0.5% accuracy. It is quite remarkable that for y/s > 180 GeV:
^measured!VRacoonWW
= 1.000 ± 0 . 0 0 9 .
(17) A very similar result is obtained for the calculation with YFSWW. 4-1
Measurements of the W mass
Even before crossing the W-pair threshold a precise value of the W mass was evaluated from the LEP1 measurement of mz using SM relations. The updated indirect value obtained from a fit to all data excluding the direct W mass measurements but including the measured value of the top mass is mw = 80.368 ±0.023 GeV 4 . The small error sets the scale for all direct measurements. In the SM mw depends on electroweak loop corrections. A recent complete two-loop calculation yields the dependence on the top mass, the Higgs mass, and the QED induced shift of
359
RacoonWW / YFSWW 1.14 no ZWW vertex (Gentle 2.1) only v, exchange (Gentle 2.1)
Figure 17. The W-pair production cross-section as a function of the centre-of-mass energy compared to the predictions of the Monte Carlo generators RacoonWW and Y F S W W .
the fine structure constant Aa as expressed in Eq. (18). In the Eq. (18) only the numerically most important terms are shown, all masses are in GeV. For the complete expression see 41 . An increase of mt will increase, an increase of m # or A a will decrease the SM prediction for mw • A significant deviation of a direct measurement from the indirect value would indicate new physics and the existence of new fundamental particles. At LEP 2 two independent and complementary methods have been used to measure mw- The first is based on the measurement of the cross-section near threshold, which depends strongly on mw- Combining the measurements at a centre-of-mass energy of 161 GeV the LEP groups obtain 4 mw = 80.40±0.22 GeV, where the largest contribution to the total error is due to the low event statistics. One should remark, however, that in principle the threshold method can give a precise result, the estimated error for a GigaZ Linear Collider42 is Amw = 0.006 GeV,
J. Drees
mw
Review of Final LEP Results or A Tribute to LEP
mt = 80.3767 + 0.5235((—j-)^ - 1)
0.05613Zn(^)-1.081(
I300 K
250 200 7 150
-
Aa 0.05924
1)±....
(18)
b— 1 Signal
qqqq
E H Combi
OPAL 183-209 GeV
H i Other 1
I L d t = 677pb"'
100 50
SS^?-V-r.i^rr^.KtesK''«filc?'JSE&;i-iJ.y«£i
50
55
60
65
70
75
80
85
90 M
w
95
Figure 19. Reconstructed W mass distribution for all OPAL W+W~ -> qqqq data from y/s = 183 to 209 GeV. The histogram shows the SM expectation for Mw = 80.42 GeV.
100
(GeV/c2)
Figure 18. Reconstructed invariant mass distribution from the ALEPH experiment for the qqfiV/j, channel.
supposing that radiative corrections are controlled to this level. At higher energies the W mass is directly reconstructed from the invariant mass distribution of the decay products of the two W's. Using constraints set by energy and momentum conservation clean reconstructed mass distributions for the semileptonic and hadronic decay channels are obtained. An example from the semileptonic data taken at y/s > 202 GeV 4 3 is reproduced in Fig. 18. Note that there is practically no background in the [iv^qq channel. This also holds for eveqq channel, the background in the rvrqq and 4q channels is small. The statistical power of the data is illustrated in Fig. 19, where the mass distribution for the fully hadronic channel as reconstructed by the OPAL Collaboration is shown for all data taken at ^fs above 183 GeV 2 8 . The data are compared to the Monte Carlo prediction for mw = 80.42 GeV. From the measured masses in each event the final value of the W mass is extracted by means of sophisticated analysis techniques,
which are somewhat different for the four experiments and in each case require the comparison with a large number of Monte Carlo events. ALEPH, L3, and OPAL use a reweighting technique to determine the W mass, DELPHI uses a convolution technique. Details on the analysis of the four experiments can be found in the final publications for the data taken up to v ^ = 189 GeV 44 - 45 ' 47 or up to ^ = 183 GeV 4 6 and in more recent analyses contributed to this conference43 >48 >49. At present the precision of the combined result is limited by systematic uncertainties. They are smallest for the mass values extracted from semileptonic events. Here the total systematic uncertainty is 29 MeV with the largest contributions due to fragmentation effects, beam energy uncertainty, detector systematics, initial and final state photon radiation. The mass determination from the fully hadronic events contains additional uncertainties due to possible final state interactions between quarks originating from the decay of different W's (colour reconnection) or between hadrons (Bose-Einstein correlations). Both effects may lead to distortions in the invariant mass distribution, they
360
J. Drees
Review of Final LEP Results or A Tribute to LEP the SM prediction.
W-Boson Mass [GeV] —i —
80.454 ± 0.060
4-2
LEP2
—!
80.450 + 0.039
Average
-( i -
80.451 ± 0.033
Measuring the specific form of the nonAbelian triple gauge boson self-coupling •yWW or ZWW has been the second main goal of W physics at LEP. Assuming electromagnetic gauge invariance, charge conjugation and parity conservation and using also constraints from low energy data reduces the number of couplings from 14 in the most general case to three 51 : gf,K 7 ,A 7 which have been most intensively studied. Within the SM model these are given by 1,1,0 at tree level. They are related to the magnetic dipole moment fiw and the electric quadrupole moment qw of the W+:
pp-colliders
X2/DoF: 0.0/1
NuTeV/CCFR
— * ——
LEP-l/SLD/vN/APV
-A-
LEP1/SLD/vN/APV/mt 80
80.2
-A-
80.4
80.25 ±0.11 80.363 + 0.032 80.373 ± 0.023 80.6
m w [GeV ]
Figure 20. Direct and indirect W mass measurements.
are under study. Including such uncertainties in a conservative way, a total systematic uncertainty of 54 MeV is quoted for mw from fully hadronic events. The difference in the masses obtained from the semileptonic and fully hadronic WW decay channels is: Amw(qqqq-qqlD)
= +9 ±44 MeV.
(19)
Combining all LEP measurements 50 yields the nearly final result: mw = 80.450±0.026(stai.)±0.030(s2/st.)GeV. (20) Here the weight of the fully hadronic channel in the combined fit is only 26%. All direct and indirect W mass measurements are summarised in Fig. 20. Since not all LEP data are included yet and studies of the final state interaction effects continue it is hoped that the final LEP error will decrease to about 35 MeV. There is still agreement between the indirect determination from a fit including the measured top mass and the direct measurements of mw, but this year only within 1.9 a. The width of the W boson has also been measured at LEP: Yw = 2.150 ± 0.091 GeV. Within error there is good agreement with 361
Charged Gauge Couplings
Hw =
2mw
- ( 1 + K7
+ A 7 ),
(21) mw A deviation of K 7 or A7 from their SM values would therefore prove the presence of anomalous electromagnetic moments of the W boson and thus indicate completely new physics in the boson sector. Results have been derived using all available information from the total WW production cross-section, the polar angular distribution of the W~, the W± helicities analysed via the fermion decay angles, single W production e + e~ —> evW, and vv~i production. Within errors the measurements agree with the SM expectation with the following precision evaluated from one parameter fits to the combined data 5 2 :
<5#f = ±0.026, O~K7 = ±0.066, <5A7 = ±0.028. (22) Considering higher order effects the SM predicts small deviations from the tree level values, e.g. A K 7 ~ 0.005. Such small effects, however, are outside the scope of present experimental verification. In a more general approach the CP violating couplings have been studied by
J. Drees
Review of Final LEP Results or A Tribute to LEP
ALEPH 53 and OPAL 54 . Within errors no deviation from the SM has been observed. One should mention that limits for the quartic charged gauge couplings have been presented by ALEPH 55 , L3 5 6 , and OPAL 57 albeit with large errors. All results can be summarised by stating: no evidence has been found for any anomalous W boson coupling.
08/07/2001
LEP
]5
xm ±2.0% uncertainty •--- YFSZZ ZZTO
0.5
4-3
Preliminary
-
ZZ production
Measurements of ZZ production at T/S > 183 GeV allow an investigation of a sector of the SM not tested before. Deviations from the SM production cross-section, which is defined by the NC02 diagrams involving only t- and u-channel electron exchange, would be an indication for the existence of anomalous neutral gauge couplings absent in the SM at tree level. The ability to understand this process is also essential for the Higgs boson search, where ZZ production forms an irreducible background. All experiments have analysed ZZ decays into qqqq (4 jets), qqvv (2 jets plus missing energy), qql+l" (2 jets plus 2 isolated leptons), and l+l~l+l~. New results have been submitted to this conference 58 ' 59 ' 60 ' 28 . Since the cross-section is only about 1 pb, a factor ~ 17 smaller than the WW crosssection, the statistics is very limited. The comparison of the energy dependence of the LEP combined data to the SM prediction in Fig. 21 31 proves the agreement within the large errors of the data. The coupling of a virtual photon or Z boson to ZZ or Z7 final states is not forbidden by fundamental principles. Non SM contributions from the -y*ZZ or Z*ZZ vertex are described by j?'2 (i = 4, 5) couplings, from the 7*^7 or Z*Zy vertex by h]'Z (2 = 1,4) couplings. Experimental tools to search for such anomalous neutral triple gauge couplings are the measurement of the total ZZ or 7Z crosssection (increase at high energies?), the polar angle distribution of the produced Z or 7 (deviations at large #?), and the 7 energy dis-
, 170
\ZZ11^—,—,—I—,—,—,—,—I—,—,—,—,—L_ 180 190 200
Figure 21. LEP combined NC02 cross-sections. The curve shows the SM expectation, the band corresponds to the ± 2 % uncertainty of the prediction.
tribution. New results submitted by all LEP collaborations 61 ' 62,63 ' 64 have been combined by the Electroweak Working Group 5 2 . For CP conserving anomalous amplitudes a large interference with the SM amplitude could arise. However, no evidence for anomalous neutral couplings has been found. To give a few examples, the 95% confidence level limits for the CP conserving couplings f£, hf and /ig a r e :
fi hg hi 4-4
[-0.36, +0.39], [-0.20, +0.07], [-0.049, +0.008].
Consistency test of the SM
A consistency test of the SM can be performed by comparing the indirect and the direct measurements of the W and the top quark masses. In Fig. 22 the indirect contour has been obtained from an SM fit to the data from LEP1, SLD, neutrino nucleon scattering, and from atomic parity violation experiments 4 . Both the direct and the indirect data favour a low Higgs mass. The di-
362
Review of Final LEP Results or A Tribute to LEP
J. Drees
80.6
80.6
i
i
|
i
i
i
r
- L E P 1 . S L D , vN. APVData - L E P 2 , pp'.i?-.!:.
80.5
68% CL
80.4
3 E
>
80.3
CD
S 80.4 5
80.2
E
150
170
190
210
m. [ G e V ]
80.3
80.2
130
150
170
190
210
Figure 23. Same as Fig. 22 but with the data from summer 2000. T h e indirect result is obtained from an SM fit to the L E P 1 , SLD, and neutrino nucleon data.
mt [GeV]
Figure 22. Comparison of the indirect (full line) and the direct (dotted line) measurements of m w and mt- The diagonal band shows the SM prediction for various values of the Higgs mass ranging from 114 GeV to 1000 GeV, mH < 114 GeV has been excluded by direct searches.
rect and the indirect measurements still agree with each other though not as excellently as last year (Fig. 23). The experimental results of the direct searches for the Higgs boson are discussed by G. Hanson 65 , the theoretical aspects by F. Zwirner 66 . With no significant Higgs signal being observed, an indirect mass evaluation becomes again important. Fig. 24 presents the updated version of the traditional plot in form of a Ax 2 versus mu curve. The solid curve shows the result of the SM fit to all data from LEP and SLD, the world data on mw and mt, sin29w from the neutrino experiments CCFR and NUTEV, the measurements of atomic parity violation parameters, and also to the new direct determination of Aa^d(mz) (the contribution of the 5 quarks to the running of the fine structure constant a) from 67 . The fit confirms the preference for a low Higgs mass. The 95% confidence level
363
upper limit for rag is now 196 GeV. The dashed curve in Fig. 24 is the result of a fit with Aa^ 'rf from68 but otherwise unchanged input data and indicates the sensitivity of the rriH prediction; for details see 4 . As discussed before the b quark forwardbackward asymmetry deviates by about 3 a from its SM expectation. One may therefore ask: what is the relative importance of including A0pbB in the SM fit. The answer is given in Fig. 25, where the dotted contour line presents the 68% probability of the SM fit to all data except ApB. The preference for a low Higgs mass is even stronger, the one a contour is then completely excluded by the direct Higgs search. 5
Contributions to the C K M Matrix
LEP was part of the world wide effort to explore the structure of the CabibboKobayashi-Maskawa quark-mixing matrix. From the measurement of the W leptonic branching ratio one can determine Vcs • More important, the determination of the CKM elements Vub,Vcb, and of the ratio Vtd/Vts has been a central part of the LEP B-physics programme. Strong points of the LEP b quark studies are:
Review of Final LEP Results or A Tribute to LEP
J. Drees
- Large statistics, in total about 4 million Z —> bb decays, - fast moving B hadrons, the B hadron decay particles are well separated from the QCD rest, - tools for particle identification including K±, - experience of 12 years of data analysis. In the following only a few examples can be mentioned. A detailed summary of combined B-physics results including the data from the four LEP collaborations, from CDF and from SLD is available 69 .
CM
< 2-
Excluded
Preliminary
mH
5.1
10 [GeV]
Figure 24. A x 2 = X2 ~Xmin a s f u n c t i ° n of the Higgs mass. The solid curve presents the result of the SM fit, the band indicates the theoretical uncertainty. Also shown is the Higgs mass 95% CL exclusion limit from the direct search. The dashed curve shows an SM fit assuming a lower value of Aa^d(mz).
0.11
-
. - - All except Aj, 68% CL
0.105
\VCS\ from BR(W -> lv)
The leptonic branching fraction of the W boson is directly related to the squares of the six CKM matrix elements not depending on the t quark: = 1+[1+Mmvl}
1 3BR{W
^
lVij]2
->W) j=
d,a,b
(23) Taking the LEP average branching fraction as determined under the assumption of lepton universality yields 31 :
J2\Vij\2 = 2.039 ±0.025 ••-..
_ consistent with the value of 2 expected from unitarity. With the world average values for the other five CKM elements:
0.1
BmmmmKMttm 0.095
Excluded 10
10
10
mH [GeV] Figure 25. 68% probability contour curve in the (ApB, mu) plane obtained from an SM fit to all data except ApB. The direct measurement of A£B is shown as horizontal band of width ± 1 a. Also shown is the exclusion limit from the direct Higgs search.
(24)
V,. 1=0.996 ±0.013.
Preliminary
5.2
Inclusive measurement of \Vub
At LEP the measurement of \Vut\ relies on the inclusive reconstruction of the b —> ulv fraction:
2
\Vub\
_ BR(B -> XUW) —
> ibn
364
l^OJ
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Review of Final LEP Results or A Tribute to LEP
r
ALEPH DELPHI
44+
L3
Here the error includes all theoretical uncertainties. The LEP value of Eq. (26) agrees very well with the most recent measurement of the CLEO Collaboration 75 . It should be mentioned that the accuracy of \Vut,\ achieved at LEP is far beyond of what was originally hoped for.
1.73 ±0.56 ±0.55
l.S7± 0.51 ±0.49 3 3 + 1 . 3 + 1.5
1
1
i
OPAL
1.63+0.57 ±0.52
i
ft
LEP Average 1
I . I2
1.67 ±0.31 ±0.42 3
4
5.3
5
B R ( B ^ X„ 1 l>) x 103
Figure 26. Measurements of the branching ratio B —> Xulv by the four LEP experiments and the resulting average. The first error is due to statistics and experimental systematics uncorrelated between experiments, the second due to all other systematic uncertainties.
where u is the average b lifetime and jb includes QCD corrections and b quark mass effects. Much progress has been made during the last years as a consequence of both, improved understanding of the theoretical uncertainties of 7t and improved experimental analysis techniques 69 . Obviously it is very difficult to separate charmless b decays from the dominant b -> c background. Several techniques have been applied in earlier publications 70 ' 71,72 based, for instance, on inclusive analysis of semileptonic decays. In a new analysis submitted to this conference the OPAL Collaboration uses 7 kinematic variables as neural net input in order to enrich the B -> Xuli> sample 73 . All measurements of the four collaborations are collected in Fig. 26. With the average branching ratio as determined by the LEP Vu\, Group: BR(B ->• Xun>i)
= (1.67 ± 0.52) x 1(T 3
and taking the world average B hadron lifetime n = (1.564 ± 0.014) ps one finds: |K*| = (4.04 t ° J 9 ) x KT 3 .
(26) 365
B° - B°
oscillations
Much progress has also been made recently in the search for £?° oscillations. The main impact on the determination of the CKM elements is explained in Eq. (27): Am. Amd
Wu mB, mBd " \Vtd\2'
e
(27)
In the ratio of the £?° and B°d mass differences Ams to Arrid many uncertainties cancel (see e.g.76) and the remaining nonperturbative quantity £2 is well known from lattice gauge theory: £2 = 1.16 ± 0.05 7 7 . No measurement of Ams has been performed yet, but upper limits have been set by each experiment applying the so-called amplitude method. The idea of the method is to replace the expression for the time dependent probability that a produced 5 ° is detected as B° by P(B°S -> B°s) = - (1 - Acos{Am s t)) e
-t/r
o
(28) and then fit the amplitude A to the data for various fixed values of Ams. Fig. 27 shows the amplitude spectrum resulting from the combination of the spectra of all LEP The combined spectrum experiments 69,78 includes the new results from DELPHI 79 ' 80 and from OPAL 81 . From the LEP data in Fig. 27 a 95% confidence level lower limit of Ams > 14.3 p s - 1 is derived. Including the data from SLD and CDF the present world limit increases to 8 2 : Ams > 14.6ps" 1 at 95% CL.
(29)
Review of Final LEP Results or A Tribute to LEP
J. Drees
Figure 27. Combined B° oscillation amplitude A as a function of A m , . The 95% CL limit derived from this spectrum is marked by the small solid triangle.
With the measured B® and B° masses and the world average value of A m j the limit for the ratio of the CKM elements is now: \Vtd\/\Vu\ < 0.22. 6
Contributions to Q C D
An important point to remember is that electroweak precision quantities depend on the strong coupling as. One of the best known examples is the ratio of the Z partial decay widths Riept, which is known to O(al) as given in Eq.(30). With the final value R°lept = 20.767 ± 0.025 (derived by assuming lepton universality) one gets the result of Eq. (31). The advantage of evaluating as from Eq. (30) is that nonperturbative corrections are suppressed and the dependence on the renormalization scale /i (which is often responsible for the dominant uncertainty of as measurements) is small. All theoretical uncertainties including the renormalization scale uncertainty amount to only +0.003, —0.001, for details see 83 . Varying mt within ± 5 GeV and ran from 100 to 1000 GeV leads to the additional small uncertainty of ±0.002. A fit
to all electroweak Z pole data from LEP and SLD and to the direct measurements of mt and mw yields: as(mz) = 0.1183 ±0.0027 4 . One may wonder whether these are the most reliable evaluations of as(mz) using the LEP data. The problem is, however, that the quoted results fully rely on the validity of the electroweak sector of the SM. Small deviations can lead to large changes. It is therefore necessary to measure as from infrared safe hadronic event shape variables like jet rates, thrust, jet mass, jet broadenings, etc. not depending on the electroweak theory. Such studies have been performed by all LEP experiments, for more recent publications see84>85>86>87. Measurements extracted by using resummed calculations in next-to-leading logarithmic approximation (NLLA) matched to 0{a2s) calculations have been combined by the LEP QCD Working Group 8 8 . As an example Fig. 28 shows as values from fits to event shape distributions at all LEP energies including measurements of the JADE Collaboration at lower energies. A fit to the combined data results in as{mz) = 0.1195 ±0.0047, where the error is almost entirely due to theoretical uncertainties (renormalization scale). The figure also indicates to which extent the running of as can be tested. All LEP as measurements using a multitude of analysis methods are collected in Fig. 29 8 9 . The three entries at the top present inclusive measurements for which perturbative calculations are known in 0(a3s). One of the most precise measurements is obtained from the ratio of the r partial decay widths RT = T(T —» hadrons + VT)/T(T —> ei>evT), the quoted value is from 90 . The figure also includes the average values from each of five different methods to extract as from hadronic event shape distributions: four jet rates, 3 jet like observables analysed in 0{a2s) using either power corrections or hadronic Monte Carlo generators for evaluating hadronisation effects, three jet like observables analysed in
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Review of Final LEP Results or A Tribute to LEP
i?!L, = TJ:adrons- = 19.934 {1 + 1 . 0 4.<Xs 5^ + 0.94(^)2 - 1 5 ( ^ ) 3 } Hept Ti eptons
as{mz)
6 0.15 8
7T
= 0.124 ± 0.004(ea;p.) ± 0.002{mH,mt)
LEP/Jade 35...207GeV
7T
(30)
IT
ig;gg?(QC7D).
(31)
EWfit(5 Param. to LEP data)
NLLA+0(a2) log(R)
Miaif'lepc
R
0.14
,
4-jets O(o^) 3-jet like 0(a^)+PC
0.13
3-jet like O(a^)+Models 3-jet like NLLA i 3-jet like NLLA+0(a^) log(R)
0.12 PDG 2001
0.11
0.1
0.11 0.115 0.12 0.125 0.13 afM 7 )
A Jade T L3
• DLO (preliminary) • ADLO (preliminary) 50
0.1181±0.OO2O
100
150
Figure 29. Summary of as measurements at L E P compared t o the world average. T h e theoretical uncertainty for all 5 measurements from event shapes (ES) is evaluated by changing the renormalization scale /j, by a factor of 2.
200
E cm [GeV] Figure 28. Energy dependence of as- The d a t a are extracted from the analysis of infrared safe hadronic event shape distributions in the next-to-leading logarithmic approximation. T h e dotted curve presents the expected running of as.
pure NLLA and in matched NLLA as mentioned above. All measurements agree well with each other and with the world average. Studying QCD at LEP has several advantages: the centre-of-mass energy is high and well denned, jets are collimated, the environment is clean, statistics is high enough to investigate even rare topologies. In consequence more than 200 QCD papers have been published till now including detailed investigations of perturbation theory, hadronisation models, power corrections, quark and gluon jet fragmentation, local parton-hadron duality, soft gluon coherence etc. The exper-
367
imental aspects are reviewed, e.g. in91>92>93. Of the many new QCD studies contributed by the LEP Collaborations to this conference only few can be briefly mentioned, for instance, measurements of the colour factors and/or of as based on 4-jet events 94 ' 95 ' 96 , studies of the energy evolution of event shape distributions and of inclusive charged particle production including measurements at the highest energies compared to the prediction of hadronisation models 97 ' 98 ' 99 ' 100 ' 28 , measurements of the b quark mass at the Z mass scale 101 . As the outcome of the work at LEP one can conclude that the understanding of QCD phenomenology has much improved and even rather subtle measurements are all consistent with QCD predictions.
Review of Final LEP Results or A Tribute to LEP
J. Drees 7
Conclusion and Reflection
Table 1. Expected and achieved precision at LEP.
It is appropriate now to recall what was known in summer 1989, when LEP started and what was expected from LEP for the future. Some examples of what was known are given below:
Quantity
mz = 91.12 ±0.16 GeV, mw = 80.0 ± 0.36 GeV, sin2ew = 0.227 ± 0.006, Nv = 3.0 ± 0.9.
Achieved
50 to 20 MeV
2.1 MeV
mw
100 MeV
39 MeV
Nv
0.3
0.008
FB
0.0035
0.0013
A°'b FB
0.0050
0.0017
AT
0.0110
0.0043
A
Why was LEP so successful? Many fortunate facts had to come together: - A highly dedicated machine group responsible for the excellent performance of LEP, - low background in the detectors, - good performance of all detectors from the pilot run in August 1989 till the end of data taking, - effective division of work between CERN and the outside laboratories, - close cooperation between the 4 collaborations and also between LEP and SLD (without avoiding competition), - close cooperation between experiments and the machine group, - and, very important, close cooperation with theory groups. Many analyses are continuing and still more can be expected in the future.
error
mz
A
It was expected, of course, that LEP would improve the accuracy substantially. Looking back at the review talks presented by G. Altarelli 102 at the Lepton Photon Symposium 1989 in Stanford and by R. Barbieri 103 at the EPS Conference 1989 in Madrid one finds the expected experimental errors compared in Table 1 with those actually achieved. I should remark that the error for Nv quoted as expected is from the answer which was given by the DELPHI Collaboration to the LEPC in 1982. In the end, all measurements turned out to be much more precise than expected. Despite this precision the SM continues to be in good shape.
Expected
Acknowledgments First I would like to thank the organizing committee for giving me the opportunity to present this summary talk. Preparing such a talk is not possible without numerous communications with colleagues from the LEP Collaborations. In particular I profited much from discussions and mail exchanges with P. Antilogus, E. Barberio, R. Chierici, M. Elsing, P. Gagnon, F. Glege, M. Griinewald, J. Holt, R. Jones, M. Kienzle, N. Kjaer, W. Liebig, K. Monig, S. Myers, C. Parkes, A. Stocchi, H. Voss, Ch. Weiser and D. Wicke. I am very grateful to G. Myatt for many helpful suggestions and also for carefully reading the manuscript. I thank S. Braccini for his assistance during the conference and during finalising the manuscript.
References
368
1. S. Myers, "The LEP Machine", talk presented at the LEP Fest October 2000, http://cern.web.cern.ch/CERN/ Divisions/SL/publications/talks/. 2. Design Study of a 22 to 130 GeV e + e~ Colliding Beam Machine (LEP), CERN/ISR-LEP/79-33, CERN (1979). 3. Precision Electroweak Measurements on the Z Resonance; The ALEPH, DELPHI, L3, OPAL and SLD Collaborations, the LEP Electroweak Working
J. Drees
4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21.
Review of Final LEP Results or A Tribute to LEP
Group, and the SLD Electroweak and Heavy Flavor Groups, Review article in preparation. The LEP Collaborations ALEPH, DELPHI, L3, OPAL, the LEP Electroweak Working Group and the SLD Electroweak and Heavy Flavor Groups, CERN-EP/2001-021, February 2001, updates are available on website: http://lepewwg.web.cern.ch/LEPEWWG. ALEPH Collaboration, R. Barate et al., Euro. Phys. J. C 14 (2000) 1. DELPHI Collaboration, P. Abreu et al., Euro. Phys. J. C 16 (2000) 371. L3 Collaboration, M. Acciarri et al., Euro. Phys. J. C 16 (2000) 1. OPAL Collaboration, G. Abbiendi et al., Euro. Phys. J. C19 (2001) 587. ALEPH Collaboration, A. Heister et al., Eur. Phys. J. C20 (2001) 401. DELPHI Collaboration, P. Abreu et al., Euro. Phys. J. C 14 (2000) 585. L3 Collaboration, M. Acciarri et al., Phys. Lett. B 429 (1998) 387. OPAL Collaboration, G. Abbiendi et al., Euro. Phys. J. C21 (2001) 1. SLD Collaboration, K. Abe et al., Phys. Rev. Lett. 84 (2000) 5945. SLD Collaboration, K. Abe et al., Phys. Rev. Lett. 86 (2001) 1162. ALEPH Collaboration, R. Barate et al., Phys. Lett. B 401 (1997) 163. DELPHI Collaboration, P. Abreu et al., Euro. Phys. J. C 10 (1999) 415. L3 Collaboration, M. Acciarri et al., Euro. Phys. J. C13 (2000) 47. OPAL Collaboration, G. Abbiendi et al., Euro. Phys. J. C 8 (1999) 217. M. Con very, "Recent Results from SLD", SLAC-PUB-8781 (2001). ALEPH Collaboration, H.Heister et al., "Measurement of AbFB using Inclusive b-hadron Decays", CERN-EP/2001-047, LP01 paper 217. DELPHI Collaboration, K. Munich et al., "Determination of AbFB using inclu-
369
22.
23. 24.
25.
26.
27.
28.
29.
30.
31.
sive charge reconstruction and lifetime tagging at LEP1", DELPHI 2001-048 CONF 476, LP01 paper 198. M. L. Swartz, "Precision Electroweak Physics at the Z", Proceedings of the XIX International Symposium on Lepton and Photon Interactions at High Energies, Stanford (1999) 307. L3 Annual Report to CERN (2000) LepEWWG / / S u b g r o u p , G. Geweniger et al., "Combination of the LEP II / / Results", LEP2FF/01-02 September (2001); updates can be found under http://www.cern.ch/LEPEWWG/lep2/. ALEPH Collaboration, "Fermion Pair Production in e + e~ Collisions at high energy and Limits on Physics beyond the Standard Model", ALEPH 2001-019 CONF 2001-016, LP01 paper 252. DELPHI Collaboration, A.Behrmann et al., "Results on Fermion-Pair Production at LEP running in 2000", DELPHI 2001-094 CONF 522, LP01 paper 151. L3 Collaboration, "Preliminary L3 Results on Fermion-Pair Production in 2000", L3 Note 2648, LP01 paper 673; and "Search for New Physics Phenomena in Fermion-Pair Production in e + e~ Collisions at Centre-of-Mass Energies up to 209 GeV", L3 Note 2647, LP01 paper 672. OPAL Collaboration, "Measurement of Standard Model Processes in e+e~ Collisions at v ^ ~ 203 - 209 GeV", OPAL Physics Note PN469 (2001), LP01 paper 28. OPAL Collaboration, "Limits on Low Scale Quantum Gravity in Extra Spatial Dimensions from Measurements of e+e" -+ e+e~ at LEP2", OPAL Physics Note PN471 (2001), LP01 paper 33. J. Holt, "Fermion Production above the Z resonance", Proceedings of the International Europhysics Conference on High Energy Physics, Budapest 2001. The LEP Collaborations ALEPH, DEL-
J. Drees
32. 33. 34. 35. 36.
37.
38.
39.
40.
41. 42.
Review of Final LEP Results or A Tribute to LEP
PHI, L3, OPAL, and the LEP WW Working Group, "LEP W-pair, Zpair and Single W Cross-Section Results for the Summer 2001 Conferences" , LEPEWWG/XSEC/2001-03, August 2001, updates are available on website: http://lepewwg.web.cern.ch /LEPEWWG/lepww/4f/. ALEPH Collaboration, R. Barate et al., Phys. Lett. B484 (2000) 205. DELPHI Collaboration, P. Abreu et al., Phys. Lett. B479 (2000) 89. L3 Collaboration, M. Acciarri et al., Phys. Lett. B496 (2000) 19. OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B493 (2000) 249. ALEPH Collaboration, "Measurement of W-pair production and W branching ratios in e + e~ collisions up to 208 GeV", ALEPH 2001-013 CONF 2001010, LP01 paper 257. DELPHI Collaboration, P.Buschmann et al.,"Measurement of the W-Pair Production Cross Section and W Branching Ratios at y/s = 205 and 207 GeV", DELPHI 2001-104 CONF 532, LP01 paper 161. L3 Collaboration, "Preliminary Results on the Measurement of the W-Pair Cross Sections in e+e~ Interactions at yfs — 205 and 208 GeV and W-Decay Branching Fractions", L3 Note 2638 (2001), LP01 paper 664. A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Phys. Lett. B475 (2000) 127. S. Jadach, W. Placzek, M. Skrzypek, B.F.L. Ward, Z. Was, "The Monte Carlo Event Generator YFSWW3 version 1.16 for W-Pair Production and Decay at LEP2/LC Energies", CERN-TH/2001017 (2001), and refences quoted therein. A. Freitas, W. Hollik, W. Walter, and G. Weiglein, Phys. Lett. B495 (2000) 338. J.A. Aguilar-Saavedra et al., TESLA Technical Design Report, Part III,
43.
44. 45. 46. 47. 48.
49.
50.
51.
52.
370
DESY 2001-011, ECFA 2001-209, March 2001. ALEPH Collaboration, "Preliminary Measurement of the W Mass and Width in e+e~ Collisions at ^fs between 192 and 208 GeV", ALEPH 2001-020 CONF 2001-017, LP01 paper 256. ALEPH Collaboration, R. Barate et al., Eur. Phys. J. C17 (2000) 241. DELPHI Collaboration, P. Abreu et al., Phys. Lett. B511 (2001) 159. L3 Collaboration, M. Acciarri et al., Phys. Lett. B454 (1999) 386. OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B507 (2001) 29. DELPHI Collaboration, D. Bloch et al., "Measurement of the mass and width of the W Boson in e + e~ collisions at V^ ~ 192 - 209 GeV", DELPHI 2001103 CONF 531, LP01 paper 160. L3 Collaboration, "Preliminary results on the Measurement of Mass and Width of the W Boson at LEP", L3 Note 2637 (2001), LP01 paper 665. The LEP Collaborations ALEPH, DELPHI, L3, OPAL and the LEP W Working Group, "Combined Preliminary Results on the Mass and Width of the W Boson Measured by the LEP Experiments", LEPEWWG/MASS/200101 (2001), updates are available under http://lepewwg.web.cern.ch/LEPEWWG /lepww/mw/. G. Gounaris et al., "Physics at LEP2", CERN 96-01, eds. G. Altarelli, T. Sjostrand, F. Zwirner, Vol. 1(1996) 525. The LEP Collaborations ALEPH, DELPHI, L3, OPAL and the LEP GC Working Group, "Combined Results for Electroweak Gauge Boson Couplings Measured on the LEP Experiments", LEPEWWG/TGC/2001-02 (2001), see also LEPEWWG/TGC/200002 (2000), updates are available under http://lepewwg.web.cern.ch/LEPEWWG /lepww/tgc/.
J. Drees
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53. ALEPH Collaboration, "Measurement of Triple Gauge-Boson Couplings in e+e~ collisions up to 208 GeV", ALEPH 2001-027 CONF 2001-021, LP01 paper 265. 54. OPAL Collaboration, G.Abbiendi et al., " Measurement of W boson polarisations and CP-violating triple gauge couplings from W+W~ production at LEP", CERN-EP/2000-113 (2000), LP01 paper 39. 55. ALEPH Collaboration, "Constraints on Anomalous Quartic Gauge boson Couplings from photon pair events at 189202 GeV", LP01 paper 262. 56. L3 Collaboration, "Measurement of the W+W~/y Cross Section and Direct Limits on Anomalous Quartic Gauge Boson Couplings at LEP", L3 Note 2675 (2001), LP01 paper 668. 57. OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B471 (1999) 293. 58. ALEPH Collaboration, "Measurement of e+e~ -¥ ZZ Production Cross Section", ALEPH 2001-006 CONF 2001003, LP01 paper 258. 59. DELPHI Collaboration, G. Borisov et al., "Update of the ZZ cross-section measurement in e+e~ interactions using data collected in 2000", DELPHI 2001105 CONF 533 (2001), LP01 paper 162. 60. L3 Collaboration, "Z Boson Pair Production at LEP", L3 Note 2696 (2001), LP01 paper 675. 61. ALEPH Collaboration, "Constraints on anomalous neutral gauge boson couplings using data fromm ZZ production between 183 and 207 GeV", ALEPH 2001-014 CONF 2001-011, LP01 paper 261. 62. DELPHI Collaboration, P.Bambade et al., "Study of Trilinear Gauge Boson Couplings ZZZ, ZZ 7 and Z77", DELPHI 2001-097 CONF 525, LP01 paper 154. 63. L3 Collaboration, "Search for Anomalous ZZ7 and Z77 couplings in the pro-
371
64. 65. 66. 67. 68. 69.
70. 71. 72. 73.
74. 75. 76.
77. 78. 79.
80.
cess e+e" -> Z-y at LEP", L3 Note 2672 (2001), LP01 paper 676. OPAL Collaboration, G.Abbiendi et al., Eur. Phys. J. C I 7 (2000) 553. G. Hanson, "Searches for new particles", these proceedings. F. Zwirner, "The Higgs puzzle: experiment and theory", these proceedings. H. Burkhardt and B. Pietrzyk, Phys. Lett. B513 (2001) 46. A. D. Martin, J. Outhwaite, and M. G. Ryskin, Phys. Lett. B492 (2000) 69. ALEPH, CDF, DELPHI, L3, OPAL, SLD Collaborations, "Combined results on b-hadron production rates and decay properties", CERN-EP/2001-050 (2001), updates are available under http://lephfs.web.cern.ch/LEPHFS/. ALEPH Collaboration, R. Barate et al., Eur. Phys. J. C6 (1999) 555. DELPHI Collaboration, P. Abreu et al., Phys. Lett. B478 (2000) 14. L3 Collaboration, M. Acciarri et al., Phys. Lett. B436 (1998) 174. OPAL Collaboration, G. Abbiendi et al., "Measurement of |Vuf,| using b hadron semileptonic decay", CERN-EP/2001044 (2001), LP01 paper 53. http://battagl.home.cern.ch /battagl/vub/vub.html D. Cassel, "CLEO results: B decays, CP violation", these proceedings. Particle Data Group, Review of Particle Physics, D.E. Groom et al., Eur. Phys. J. C15 (2000) 1. C.T. Sachrajda, "Phenomenology from lattice QCD", these proceedings. Working Group on B oscillations, http://lepbosc.web.cern.ch/LEPBOSC/. DELPHI Collaboration, T. Allmendinger et al., "Search for B°s - B° oscillations in inclusive samples", DELPHI 2001-054 CONF 482, LP01 paper 204. DELPHI Collaboration, P. Kluit et al., "Search for B°s - B°s oscillations in DELPHI using high pt leptons", DELPHI
J. Drees
81.
82.
83. 84. 85. 86. 87. 88.
89.
90.
91. 92.
93.
94.
Review of Final LEP Results or A Tribute to LEP
2001-055 CONF 483, LPOl paper 205. OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C19 (2001) 241, LPOl paper 50. All references on B° and £?° oscillation analyses can be found under http://lepbosc.web.cern.ch /LEPB OSC /references/. S. Bethke, "Determination of the QCD Coupling a s ", / . Phys. G26 (2000) R27. ALEPH Collaboration, R. Barate et al. Phys. Rep. 294 (1998) 1. DELPHI Collaboration, P. Abreu et al., Eur. Phys. J. C14 (2000) 557. L3 Collaboration, M. Acciarri et al., Phys. Lett. B489 (2000) 65. OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C16 (2000) 185. The LEP QCD Working Group, "Preliminary Combination of as Values derived from Event Shape Variables at LEP", ALEPH 01-038 Physic 01-012, DELPHI 2001-043 PHYS 893, L3 Note 2661, OPAL TN689, 30.April 2001. D. Wicke, "Event shape studies at LEP", Proceedings of the International Europhysics Conference on High Energy Physics, Budapest 2001. A. Pich, "Tau Physics", Proceedings of the XIX International Symposium on Lepton and Photon Interactions at High Energies, Stanford (1999) 157. O. Biebel, Phys. Rep. 340 (2001) 165. S. Bethke, "QCD at LEP", talk presented at the LEP Fest October 2000, http://opal.web.cern.ch/OPAL/ talks / siggi Jepfest. D. Duchesneau, "Experimental Aspects of QCD in e+e~ Collisions", Proceedings of the 29th International Copnference on High Energy Physics, Vancouver (1998) 263. ALEPH Collaboration, "Simultaneous Measurement of the Strong Coupling Constant and the QCD Coulor Factors from 4-jet hadronic Z decays", ALEPH
2001-042 CONF 2001-026, LPOl paper 208. 95. DELPHI Collaboration, U. Flagmeyer et al., "Measurement of the strong coupling as and its energy dependence from the four jet rate of hadronic events with the DELPHI detector", DELPHI 2001-059 CONF 487, LPOl paper 164. 96. OPAL Collaboration, G. Abbiendi et al., "A Simultaneous Measurement of QCD Colour Factors and the Strong Coupling", CERN EP-2001-001, LPOl paper 24. 97. ALEPH Collaboration, "QCD Measurements in e+e~ Annihilations at 206 GeV", ALEPH 2001-007 CONF 2001004, LPOl paper 210. 98. DELPHI Collaboration, R. Reinhardt et al., "A study of the energy evolution of event shape distributions and their means with the DELPHI Detector at LEP", DELPHI 2001-062 CONF 490, LPOl paper 166. 99. DELPHI Collaboration, O. Passon et al., "QCD Results from the DELPHI Measurements of Event Shape and Inclusive Particle Distributions at the highest LEP energies", DELPHI 2001-065 CONF 493, LPOl paper 168. 100. L3 Collaboration, "QCD Results at 192 < Js < 208 GeV", LPOl paper 682. 101. OPAL Collaboration, G. Abbiendi et al., "Determination of the b Quark Mass at the Z Mass Scale", CERN-EP-2001034, LPOl paper 188. 102. G. Altarelli, "Theory of Precision Electroweak Experiments" Proceedings of the 1989 International Symposium on Lepton and Photon Interactions at High Energies, Stanford University (1989) 286. 103. R. Barbieri, "Electroweak Physics", Nucl. Phys. B (Proc. Suppl.) 16 (1990) 71.
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Discussion Alberto Sirlin, New York University: I have an observation and a question, i) With respect to the evidence for genuine electroweak corrections, I think there is a very simple argument that shows a very large signal. It consists of measuring the radiative correction Ar by using the experimental results for raw and mz, and comparing with the value Ar would have if the only contribution arose from the running of a. Last time I did this, about a year ago, I found a difference amounting to many standard deviations, ii) The question is: what is the \ 2 per degrees of freedom of the most recent electroweak global fit? J. Drees: The most recent MSM fit to all electroweak data including the direct measurements of mw and mt has X2 /ndf = 22.9/15 corresponding to the still reasonable probability of 8.6%.
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DECLINE A N D FALL OF T H E S T A N D A R D MODEL? JOHN ELLIS Theoretical Physics Division, CERN, CH-1211 Geneva 23 E-mail: [email protected] Motivations for physics beyond the Standard Model are reviewed, with particular emphasis on supersymmetry at the TeV scale. Constraints on the minimal supersyymetric extension of the Standard Model with universal soft supersymmetry-breaking terms (CMSSM) are discussed. These are also combined with the supersymmetric interpretation of the anomalous magnetic moment of the muon. The prospects for observing supersymmetry at accelerators are reviewed using benchmark scenarios to focus the discussion. Prospects for other experiments including the detection of cold dark matter, ji —> e-y and related processes, as well as proton decay are also discussed.
1
Introduction
The empire of the Standard Model has resisted all attacks by accelerator data. Nevertheless, we theorists are driven to overcome our ignorance of the barbarian territory beyond its frontiers. In the gauge sector, the Standard Model has three independent gauge couplings and (potentially) a CP-violating phase in QCD. In the Yukawa sector, it has six random-seeming quark masses, three charged-lepton masses, three weak mixing angles and the Kobayashi-Maskawa phase. Finally, the symmetry-breaking sector has at least two free parameters. Moreover, this list of 19 parameters in the Standard Model begs the more fundamental questions of the origins of the particle quantum numbers. As if this were not enough, non-accelerator neutrino experiments x now convince us that we need three neutrino mass parameters, three neutrino mixing angles and three CP-violating phases in the neutrino sector: one observable in oscillation experiments and two that affect PPov experiments, without even talking about the mechanism of neutrino mass generation. Moreover, we should not forget about gravity, with at least two parameters to understand: Newton's constant Gjv = nip1 ~ (10 19 G e V ) - 2 and the cosmological 'constant', which recent data suggest is non-
zero 2 , and may not even be constant. Talking of cosmology, we would need at least one extra parameter to produce an inflationary potential, and at least one other to generate the baryon asymmetry, which cannot be explained within the Standard Model. Confronted by our ignorance of so much barbarian territory, we legions of theorists organize our explorations on three main fronts: unification - the quest for a single framework for all gauge interactions, flavour - the quest for explanations of the proliferation of quark and lepton types, their mixings and CP violating phases, and mass - the quest for the origin of particle masses and an explanation why they are so much smaller than the Planck mass mp ~ 10 19 GeV. Beyond all these beyonds, other scouting parties of theorists seek a Theory of Everything that includes gravity, reconciles it with quantum mechanics, explains the origin of space-time and why we live in four dimensions (if we do so). Physics beyond the Standard Model is therefore a very broad subject. However, many aspects are discussed here by other speakers: electroweak flavour physics 3 , CP violation 4 , the Higgs sector 5 , g^ — 2 6 , searches for new particles 7 , neutrinos 8 , dark matter 9 , strings and extra dimensions 10 . Therefore, in this talk I seek a complemen-
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tary approach. For reasons that I describe in Section 2, many theorists believe that supersymmetry is the inescapable framework for discussing physics at the TeV scale and beyond. In the rest of this talk, I first discuss the constraints imposed on (the simplest) supersymmetric models by the available experimental and cosmological constraints, then address the prospects for understanding
2
The Electroweak Vacuum
Figure 1. Predictions for the radiative corrections £j in the Standard Model and a minimal one-generation m o d e l 1 4 are compared with the precision electroweak data 1 3 .
The generation of particle masses requires the breaking of gauge symmetry in the vacuum:
consistent with the data, but for now we focus on elementary Higgs models.
mw,z / 0 « < 0|X J i / s |0 > ^ 0
Within this framework, the data favour a relatively light Higgs boson, with m # ~ 115 GeV, just above the exclusion unit provided by direct searches at LEP, being the 'mostprobable' 15 . This is one reason why many theorists were excited by the possible sighting during the last days of LEP of a Higgs boson, with a preferred mass of 115.6 GeV 7 . If this were to be confirmed, it would suggest that the Standard Model breaks down at some relatively low energy ^ 10 3 TeV 16 . As seen in Fig. 2, above this scale the effective Higgs potential of the Standard Model becomes unstable as the quartic Higgs self-coupling is driven negative by radiative corrections due to the relatively heavy top quark 17 . This is not necessarily a disaster, and it is possible that the present electroweak vacuum might be metastable, provided that its lifetime is longer than the age of the Universe 18 . However, we would surely feel more secure if such instability could be avoided.
(1)
for some field X with isospin I and third component 73. The measured ratio P=
m
\ Q ^1 (2) mz cosz o\y tells us that X mainly has I = 1/2 n , which is also what is needed to generate fermion masses. The key question is the nature of the field X: is it elementary or composite? A fermion-antifermion condensate v = < 0|X|0 > = < 0\FF\0 > ^ 0 would be analogous to what we know from QCD, where < 0|gqjO >^= 0, and conventional superconductivity, where < 0|e~e~|0 >^= 0. However, analogous 'technicolour' models of electroweak symmetry breaking 12 fail to fit the values of the radiative corrections e^ to p and other quantities extracted from the precision electroweak data provided by LEP and other experiments, as seen in Fig. 1 13 . One cannot exclude the possibility that some calculable variant of technicolour might emerge that is 2
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This may be done by introducing new
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Decline and Fall of the Standard Model?
u I—,—1—.—1—^J_i—,—1—,—1—,—1—,—1—.—I 10 2 10 6 10" 10» 10'° 10' 2 10" 10'e 10'8 |i (GeV) 5
Figure 2. T h e range allowed for t h e mass of t h e Higgs boson if the Standard Model is to remain valid up to a given scale A. In the upper p a r t of the plane, the effective potential blows up, whereas in the lower part the present electroweak vacuum is unstable i r .
bosons (f> coupled to the Higgs field \22\H\2 \4>\2 : M2=X22v2
16
1—i—,—1—1—1—1—1—1—1—1—'—r—'—1—•—1-7-
102
10 4
106
10 s
10 10 10' 2 (L (GeV)
10"
10 i e
10 1S
Figure 3. (a) If the quartic coupling Mo (3) is too large, the effective potential blows up (solid line), whereas it is unstable if Mo is too small (dotted line), indicating a need for fine tuning, (b) This occurs naturally in a supersymmetric model (solid line) but not if the H are omitted (dotted line) 1 6 .
: (3)
As seen in Fig. 3a, the effective potential is very sensitive to the coupling parameter M 0 : for M0 < 70.9 GeV in this example, the potential still collapses, whereas for Mo > 71.0 GeV the potential blows up instead. Thus the bosonic coupling (3) must be finely tuned 16 . This occurs naturally in supersymmetry, in which the Higgs bosons are accompanied by fermionic partners H. As seen in Fig. 3b, again the Higgs coupling blows up in the absence of the H, whereas it is well behaved in the minimal supersymmetric extension of the Standard Model (MSSM). The avoidance of fine tuning has long been the primary motivation for supersymmetry at the TeV scale 19 . This issue is normally formulated in connection with the hierarchy problem: why/how is mw "C mp, or equivalently why is Gp ~ 1 / m ^ » GN = 1/rrip, or equivalently why does the Coulomb potential in an atom dominate over the Newton potential, e 2 ^> G^mvme ~ (m/mp)2, where the proton and electron masses? One might think naively
that it would be sufficient to set mw -C mp by hand. However, radiative corrections tend to destroy this hierarchy. For example, oneloop diagrams generate 5m2w = O ( £ ) A2 » m2w
(4)
where A is a cut-off representing the appearance of new physics, and the inequality in (4) applies if A ~ 10 3 TeV, and even more so if A ~ triGUT ~ 10 16 GeV or ~ rnp ~ 10 19 GeV. If the radiative corrections to a physical quantity are much larger than its measured values, obtaining the latter requires strong cancellations, which in general require fine tuning of the bare input parameters. However, the necessary cancellations are natural in supersymmetry, where one has equal numbers of bosons B and fermions F with equal couplings, so that (4) is replaced by 6m2w = O ( ^ )
\m% - m%\ .
(5)
The residual radiative correction is naturally
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small if 2
\m% - m F\ < 1 TeV
2
(6)
Note that this argument is logically distinct from that in the previous paragraph. There supersymmetry was motivated by the control of logarithmic divergences, and here by the absence of quadratic divergences.
3
The M S S M
The MSSM has the same gauge interactions as the Standard Model, and similar Yukawa couplings. A key difference is the necessity of two Higgs doublets, in order t o give masses to all the quarks and leptons, and to cancel triangle anomalies. This duplication is important for phenomenology: it means that there are five physical Higgs bosons, two charged H± and three neutral h, H, A. Their quartic self-interactions are determined by the gauge interactions, solving the vacuum instability problem mentioned above and limiting the possible mass of the lightest neutral Higgs boson. However, the doubling of the Higgs multiplets introduces two new parameters: tan /3, the ratio of Higgs vacuum expectation values and /i, a parameter mixing the two Higgs doublets. There are two key experimental hints in favour of supersymmetry. One is provided by the LEP measurements of the gauge couplings, that are in very good agreement with supersymmetric GUTs 20 if sparticles weigh ~ 1 TeV. This agreement appears completely fortuitous in composite Higgs models 12, and is difficult (though not impossible 21 ) to reproduce accurately in models with large extra dimensions 22 . The other experimental hint is provided by the preference of the precision electroweak data for a relatively light Higgs boson 15 . In the MSSM, one predicts nih ^ 130 GeV 23,5 , right in the preferred range, whereas composite Higgs model generally predict heavier effective Higgs masses.
377
The gauge symmetries of the MSSM would permit the inclusion of interactions that violate baryon number and/or lepton number 24 : XLLEC + X'QDCL + A" UCDCDC
(7)
where the L(Q) are left-handed lepton (quark) doublets and the EC(DC, Ud) are conjugates of the right-handed lepton (quark) singlets. Their possible appearance is ignored in this talk, in which case the lightest supersymmetric particle is stable, and hence a candidate for dark matter 25 . In the following this is assumed to be a neutralino, i.e., a mixture of the 7, H and Z. The final ingredient in the MSSM is the soft supersymmetry breaking, in the form of scalar masses mo, gaugino masses m ^ and trilinear couplings A 2 6 . These are presumed to be inputs from physics at some high-energy scale, e.g., from some supergravity or superstring theory, which then evolve down to lower energy scale according to well-known renormalization-group equations. In the case of the Higgs multiplets, this renormalization can drive the effective mass-squared negative, triggering electroweak symmetry weaking 27 . In this talk, it is assumed that the TOO are universal at the input scale a , as are the rn\j2 and A parameters. In this case the free parameters are mo,mi/2,A
and
tan/3 ,
(8)
with pi being determined by the electroweak vacuum conditions, up to a sign. This constrained MSSM (CMSSM) serves as the basis for the subsequent discussion. It has the merit of being sufficiently specific that the different phenomenological constraints can be combined meaningfully. On "Universality between the squarks and sleptons of different generations is motivated by upper limits on flavour-changing neutral interactions 2 8 , but universality between the soft masses of the L, EC,QC, Dc and Uc is not so well motivated.
Decline and Fall of the Standard Model?
John Ellis the other hand, it is just one of the phenomenological possibilities offered by supersymmetry 29 .
200
4
tan p=10. u > 0
C o n s t r a i n t s on t h e C M S S M > O
Important constraints on the CMSSM parameter space are provided by direct searches at LEP and the Tevatron collider 7 , as seen in Fig. 4. One of these is the limit mx± ^ 103 GeV provided by chargino searches at LEP, where the third significant figure depends on other CMSSM parameters. LEP has also provided lower limits on slepton masses, of which the strongest is mj <; 99 GeV, again depending only sightly on the other CMSSM parameters, as long as m^ — mx ^ 10 GeV. The most important constraints on the u,d,s,c,b squarks and gluinos are provided by the Tevatron collider: for equal masses rrig = rrig ^ 300 GeV. In the case of the i, LEP provides the most stringent limit when m^ — mx is small, and the Tevatron for larger mj — mx. Their effect is almost to exclude the range of parameter space where electroweak baryogenesis is possible 30 . Another important constraint is provided by the LEP limit on the Higgs mass: mH > 114.1 GeV. This holds in the Standard Model, for the lightest Higgs boson h in the general MSSM for tan/3 ^ 5, and in the CMSSM for all tan /?, at least as long as CP is conserved b. Since rrih is sensitive to sparticle masses, particularly m^, via loop corrections: 5m\ oc
+
(9)
the Higgs limit also imposes important constraints on the CMSSM parameters, principally mi/2 as seen in Fig. 4.
III
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Figure 4. Compilations of phenomenological constraints on the CMSSM for tan j3 = 10 and (a) fj, > 0, (b) n < 0. Representative contours of the selectron, chargino and Higgs masses are indicated, as is the likely physics reach of Run II of the Tevatron Collider in (a). The dark shaded regions are excluded because the LSP is charged, whereas a neutralino LSP has acceptable relic density (10) in the lightshaded regions 3 1 . The medium-shaded region in (b) is excluded by b —* sf 3 2 .
The lower bound on the lightest MSSM Higgs boson may be relaxed significantly if C P violation feeds into the MSSM Higgs sector 3 3 .
378
John Ellis
Decline and Fall of the Standard Model?
Also shown in Fig. 4 is the constraint imposed by measurements of b —> sj 3 2 . These agree with the Standard Model, and therefore provide bounds on chargino and charged Higgs masses, for example. For moderate tan/3, the b —> S7 constraint is more important for n < 0, as seen in Fig. 4b, but it is also significant for /z > 0 when tan /? is large.
500 400
300
Fig. 4 also displays the regions where the supersymmetric relic density px = £lxpCriticai falls within the preferred range 0.1 < Q,xh2 < 0.3
(10)
The upper limit is rigorous, since astrophysics and cosmology tell us that the total matter density f2TO ^ 0.4, and the Hubble expansion rate h ~ l / v 2 to within about 10 % (in units of km/s/Mpc). On the other hand, the lower limit in (10) is optional, since there could be other important contributions to the overall matter density. As is seen in Fig. 4, there are generic regions of the CMSSM parameter space where the relic density falls within the preferred range (10). What goes into the calculation of the relic density? It is controlled by the annihilation rate 25 : Px = mxnx
• nx ~ ~
1
/
7——
"ann\XX
T
x
(11)
' • • •)
and the typical annihilation rate 1/m2 For this reason, the relic density typically increases with the relic mass, and this combined with the upper bound in (10) then leads to the common expectation that mx ^ 1 TeV. However, there are various ways in which the generic upper bound on m x can be increased along filaments in the (mi/2, mo) plane. For example, if the next-to-lightest sparticle (NLSP) is not much heavier than X- Am/mx ^j 0.1, the relic density may be suppressed by coannihilation: <j(x+NLSP—> ...) 34 . In this way, the allowed CMSSM region may acquire a 'tail' extending to large ' X ' as in the case where the NLSP is the lighter stau: fi and m^j m v as seen in 379
500
1000
1500
2000
m 1/2
Figure 5. The large-mi/2 'tail' of the x — fi coannihilation region for tan/? = 10 and fi < 0 3 5 .
Fig. 5 35 . Another mechanism for extending the allowed CMSSM region to large mx is rapid annihilation via a direct-channel pole when mx ~ \mHiggs,z 36 ' 37 . This may yield a 'funnel' extending to large m y 2 and mo at large tan/3, as seen in Fig. 6 3 7 . Another allowed region at large m y 2 and mo is the 'focus-point' region 3 8 , which is adjacent to the boundary of the region where electroweak symmetry breaking is possible, as seen in Fig. 7. However, in this region mx is not particularly large. These filaments extending the preferred CMSSM parameter space are clearly exceptional, in some sense, so it is important to understand the sensitivity of the relic density to input parameters, unknown higher-order effects, etc. One proposal is the relic-density fine-tuning measure 39 d\n(flxh2) din at
(12)
where the sum runs over the input parameters, which might include (relatively) poorlyknown Standard Model quantities such as mt
John Ellis
Decline and Fall of the Standard Model? and nib, as well as the CMSSM parameters mo,mi/2, etc. As seen in Fig. 7, the sensitivity A Q (12) is relatively small in the 'bulk' region at low mi/2, mo, and tan/3. However, it is somewhat higher in the x ~ ^i coannihilation 'tail', and at large tan/3 in general. The sensitivity measure A n (12) is particularly high in the rapid-annihilation 'funnel' and in the 'focus-point' region. This explains why published relic-density calculations may differ in these regions 40 , whereas they agree well when A n is small: differences may arise because of small differences in the treatments of the inputs.
tanp=50. »>o
It is important to note that the relicdensity fine-tuning measure (12) is distinct from the traditional measure of the finetuning of the electroweak scale 41 :
m1/2 (GeV)
Figure 6. The region where the cosmological relic density is in the preferred range (10) for tan/3 = 50 and [i > 0. Note the rapid-annihilation 'funnel' at intermediate m o / m j / 2 37 -
This electroweak fine-tuning is a completely different issue, and values of the Aj are not necessarily related to values of A n . Electroweak fine-tuning is sometimes used as a criterion for restricting the CMSSM parameters. However, the interpretation of the A, (13) is unclear. How large a value of Aj is tolerable? Different physicists may well have different pain thresholds. Moreover, correlations between input parameters may reduce its value in specific models.
5
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mi /2 (GeV) Figure 7. The ml/2,™>0 plane for tan/3 = 10 and /i > 0, including the 'focus-point' region 3 8 at large moi close to the boundary of the shaded region where electroweak symmetry breaking occurs, and exhibiting contours of the cosmological sensitivity (12) 3 9 .
Muon Anomalous Magnetic Moment
As reported at this meeting 6 , the BNL E821 experiment has recently reported a 2.6-a deviation of aM = TJ((?M — 2) from the Standard Model prediction 42 : a^P - af = (43 ± 16) x 1CT10
(14)
The largest contribution to the error in (14) is the statistical error of the experiment, which will soon be significantly reduced, as 380
Decline and Fall of the Standard Model?
John Ellis many more data have already been recorded. The next-largest error is that due to stronginteraction uncertainties in the Standard Model prediction. Recent estimates converge on an estimate of about 7x 10~ 10 for the error in the hadronic vacuum polarization contribution to (14) 43 , and the error in the hadron light-by-light scattering contribution is generally thought to be smaller 44 . Therefore, if the central value in (14) does not change substantially with the new data, this would be strong evidence for new physics at the TeV scale. 45
As many authors have pointed out , the discrepancy (14) could well be explained by supersymmetry if \i > 0 and tan (3 is not too small, as exemplified in Fig. 8. Good consistency with all the experimental and cosmological constraints on the CMSSM is found for tan/3 < 10 and m x ~ 150 to 350 GeV. Already before the measurement (14), the LHC was thought to have a good chance of discovering supersymmetry 46 . If the result (14) were to be confirmed, this would be almost guaranteed, as we now discuss.
tan p = 10, \l > 0 m
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Figure 8. The medium-shaded region is that compatible with the BNL E821 measurement of g^ — 2 at the 2-CT level 6 ' 4 2 , the light-shaded region has a relic density in the preferred range (10), and the dark-shaded region does not have a neutralino LSP. Good compatibility is found between g^ — 2 and the other phenomenological constraints for tan /3 ~ 5 or more 4 5 .
• ; • » • • • • • • .
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Prospects for Observing Supersymmetry at Accelerators
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As an aid to the assessment of the prospects for detecting sparticles at different accelerators, benchmark sets of supersymmetric parameters have often been found useful 4 7 , since they provide a focus for concentrated discussion. A set of post-LEP benchmark scenarios in the CMSSM has recently been proposed 48 , and are illustrated schematically in Fig. 9. They take into account the direct searches for sparticles and Higgs bosons, b —> s"f and the preferred cosmological density range (10). About a half of the proposed benchmark points are consistent with
381
: 'i^\ j-w na Figure 9. Schematic overview of the benchmark points proposed in 4 8 . They were chosen to be compatible with the indicated experimental constraints, as well as have a relic density in the preferred range (10). The points are intended to illustrate the range of available possibilities.
John Ellis
Decline and Fall of the Standard Model?
The proposed points were chosen not to provide an 'unbiased' statistical sampling of the CMSSM parameter space, whatever that means in the absence of a plausible a priori measure, but rather are intended to illustrate the different possibilities that are still allowed by the present constraints 48 . Five of the chosen points are in the 'bulk' region at small mi/2 and mo, four are spread along the coannihilation 'tail' at larger m\/2 for various values of tan/?, two are in the 'focus-point' region at large mo, and two are in rapidannihilation 'funnels' at large m-i/2 and moThe proposed points range over the allowed values of tan/? between 5 and 50. Most of them have \i > 0, as favoured by gM - 2, but there are two points with \i < 0. Various derived quantities in these supersymmetric benchmark scenarios, including the relic density, g^ — 2,b —* S7, electroweak fine-tuning A and the relic-density sensitivity A n , are given in 4 8 . These enable the reader to see at a glance which models would be excluded by which refinement of the experimental value of g^ — 2. Likewise, if you find some amount of fine-tuning uncomfortably large, then you are free to discard the corresponding models. The LHC collaborations have analyzed their reach for sparticle detection in both generic studies and specific benchmark scenarios proposed previously 4 6 . Based on these studies, Fig. 10 displays estimates how many different sparticles may be seen at the LHC in each of the newly-proposed benchmark scenarios 4 8 . The lightest Higgs boson is always found, and squarks and gluinos are usually found, though there are some scenarios where no sparticles are found at the LHC. The LHC often misses heavier weaklyinteracting sparticles such as charginos, neutralinos, sleptons and the other Higgs bosons. The physics capabilities of linear e+e~ colliders are amply documented in various
gluino • •
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design studies 4 9 . Not only is the lightest MSSM Higgs boson observed, but its major decay modes can be measured with high accuracy, as seen in Fig. 11. Moreover, if sparticles are light enough to be produced, their masses and other properties can be measured very precisely, enabling models of supersymmetry breaking to be tested ° 2 . As seen in Fig. 10, the sparticles visible at an e + e~ collider largely complement those visible at the LHC 4 8 . In most of benchmark scenarios proposed, a 1-TeV linear collider would be able to discover and measure precisely several weakly-interacting sparticles that are invisible or difficult to detect at the LHC. However, there are some benchmark scenarios where the linear collider (as well as the LHC) fails to discover supersymmetry. Only a linear collider with a higher centre-of-mass energy appears sure to cover all the allowed CMSSM parameter space, as
382
John Ellis
Decline and Fall of the Standard Model? fi —» e7 and related processes
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— ~ »c a
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seen in the lower panels of Fig. 12, which illustrate the physics reach of a higher-energy lepton collider, such as CLIC 50 or a multiTeV muon collider 51 .
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Fig. 12 shows rates for the elastic spinindependent scattering of supersymmetric relics 54 , including upper limits from the UKDMC, CDMS and Heidelberg experiments 9 , as well as the range suggested by the DAM A collaboration 55 . Also shown are the rates calculated in the proposed benchmark scenarios discussed in the previous section, which are considerably below the DAMA range, but may be within reach of future projects. Indirect searches for supersymmetric dark matter via the products of annihilations in the galactic halo or inside the Sun also have prospects in some of the benchmark scenarios
54
383
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.
.
.
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John Ellis
Decline and Fall of the Standard Model? can (B = 30 , u > 0
100
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m„ 2 (GeV) Figure 13. Illustration in one particular leptonflavour texture model, for tan/3 = 30 and /i > 0, indicating that n —• e~t decay may occur at a rate close to the present experimental upper limit, in the CMSSM with parameters chosen 5 7 to match the measured value of o > - 2 6 ' 4 2 .
possible to measure CP violation in // —> 3e decay. This may provide another interesting interface with neutrino physics and cosmology 58 . The minimal supersymmetric seesaw model has six CP-violating phases: the MNS phase 6, two light-neutrino Majorana phases, and three phases arising from neutrino Dirac Yukawa couplings, which may be responsible for our existence via leptogenesis in the early Universe 8 . The CP-violating neutrino phases induce phases in slepton mass matrices, which may show up in fi —* 3e decay, T —• 3e//x decays and leptonic electric dipole moments. In principle, the leptogenesis phases might be obtainable by comparing CP-violating measurements in the chargedlepton and neutrino sectors 58 . Proton decay
This could be within reach, with r ( p —• e+7r°) via a dimension-six operator possibly ~ 1035y if TUGUT ~ 10 16 GeV as expected in a minimal supersymmetric GUT. Such a The BNL E821 report of a possible de- model also suggests that r ( p —» vK+) < viation from the Standard Model suggests 10322/ via dimension-five operators 59 , unless that a non-trivial \i — /j, — 7 vertex is gen- measures are taken to suppress them 6 0 . This erated at a scale ^ 1 TeV. Neutrino oscilla- provides motivation for a next-generation tions indicate that there are A£ M 7^ 0 pro- megaton experiment that could detect processes 8 , so it is natural to expect that there ton decay as well as explore new horizons in might also be a non-trivial /i — e — 7 vertex. neutrino physics 6 1 . This is indeed the case in a generic supersymmetric GUT, where neutrino mixing induces slepton mixing 5 6 . Within this framework, the measurement of #M - 2 fixes the sparticle 8 Conclusions scale, and Y[p, —» e~/) may then be calculated within any given flavour texture. Very approximately, if Qy. - 2 is within one or two a As we have seen, future colliders such as of the present central value, one may expect the LHC and a TeV-scale linear e+e~ colB(fi —» ey) with one or two orders of magni- lider have good prospects of discovering sutude of the present experimental upper limit, persymmetry and making detailed measureas illustrated in Fig. 13 57 . ments. In parallel, B and v factories have good prospects of making inroads on the The decay /z —> 3e and \i —* e conversion flavour and unification problems. Searches on nuclei are expected to occur with branch- for dark matter, stopped-muon experiments ing ratios within two or three orders of mag- and searches for proton decay also have innitude of B(n —• e-y), and it is in principle teresting prospects. 384
Decline and Fall of the Standard Model?
John Ellis Looking further beyond the Standard Model, how can one hope to test a Theory of Everything, including quantum gravity? This should be our long-term ambition, our analogue of the 'faint blue dot' towards which exoplanetary science is directed, and which motivates much of their funding. Testing a quantum theory of gravity will be relatively easy if there are large extra dimensions 10 ' 62 . Much more challenging would be the search for observable effects if the gravitational scale turns out, after all, to be of the same order as the Planck mass ~ 10 19 GeV. Perhaps the only way to reconcile relativity with quantum mechanics is to modify one or the other, or both 63 ? Testing the Theory of Everything may require thinking beyond the standard 'Beyond the Standard Model' box.
References 1. S. Aoki, J. Goodman, C. K. Jung and J. Klein, talks at this conference. 2. M. S. Turner, talk at this conference. 3. R. Barbieri, talk at this conference. 4. M. Neubert, talk at this conference. 5. F. Zwirner, talk at this conference. 6. L. Robertson, talk at this conference. 7. G. Hanson, talk at this conference. 8. H. Murayama, talk at this conference. 9. H. Klapdor-Kleingrothaus, talk at this conference. 10. L. Randall, talk at this conference. 11. D. A. Ross and M. J. Veltman, Nucl. Phys. B 95 (1975) 135. 12. For a classic review,see: E. Farhi and L. Susskind, Phys. Rept. 74 (1981) 277; for a recent review and references, see: K. D. Lane, Technicolor 2000, arXiv: hep-ph/0007304. 13. See, for example: G. Altarelli, arXiv:hep-ph/0011078, as updated in G. Altarelli, F. Caravaglios, G. F. Giudice, P. Gambino and G. Ridolfi, JHEP 0106 (2001) 018 [arXiv:hep-
385
ph/0106029]. 14. J. R. Ellis, G. L. Fogli and E. Lisi, Phys. Lett. B 343 (1995) 282. 15. J. Drees, talk at this conference. See the LEP Collaborations, ALEPH, DELPHI, L3, OPAL, the LEP Electroweak Working Group and the SLD Heavy Flavour and Electroweak Groups, LEPEWWG/2001-01, available from http://lepewwg.web.cern.ch/LEPEWWG/ Welcome.html. 16. J. R. Ellis and D. Ross, Phys. Lett. B 506 (2001) 331 [arXiv:hep-ph/0012067]. 17. For a review, see: T. Hambye and K. Riesselmann, arXiv:hep-ph/9708416. 18. G. Isidori, G. Ridolfi and A. Strumia, Nucl. Phys. B 609 (2001) 387 [arXiv:hep-ph/0104016]. 19. L. Maiani, Proceedings of the 1979 Gifsur-Yvette Summer School On Particle Physics, 1; G. 't Hooft, in Recent Developments in Gauge Theories, Proceedings of the Nato Advanced Study Institute, Cargese, 1979, eds. G. 't Hooft et al., (Plenum Press, NY, 1980); E. Witten, Phys. Lett. B 105 (1981) 267. 20. J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B 260 (1991) 131; U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B 260 (1991) 447; C. Giunti, C. W. Kim and U. W. Lee, Mod. Phys. Lett. A 6 (1991) 1745. 21. K. R. Dienes, E. Dudas and T. Gherghetta, Phys. Lett. B 436 (1998) 55 [arXiv:hep-ph/9803466] and Nucl. Phys. B 537 (1999) 47 [arXiv:hepph/9806292]. 22. D. M. Ghilencea and G. G. Ross, Nucl. Phys. B 606 (2001) 101 [arXiv:hepph/0102306]. 23. J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257 (1991) 83; M.S. Berger, Phys. Rev. D 41 (1990) 225; Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1; Phys. Lett. B 262 (1991) 54; H.E. Haber and R.
John Ellis Hempfling, Phys. Rev. Lett. 66 (1991) 1815; R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B 258 (1991) 167; P.H. Chankowski, S. Pokorski and J. Rosiek, Phys. Lett. B 274 (1992) 191; J.R. Espinosa and M. Quiros, Phys. Lett. B 266 (1991) 389; J.L. Lopez and D.V. Nanopoulos, Phys. Lett. B 266 (1991) 397; M. Carena, K. Sasaki and C.E.M. Wagner, Nucl. Phys. B 381 (1992) 66; P.H. Chankowski, S. Pokorski and J. Rosiek, Phys. Lett. B 281 (1992) 100; Nucl. Phys. B 423 (1994) 437; D.M. Pierce, A. Papadopoulos and S.B. Johnson, Phys. Rev. Lett. 68 (1992) 3678; A. Brignole, Phys. Lett. B 281 (1992) 284; M. Drees and M.M. Nojiri, Phys. Rev. D 45 (1992) 2482; V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 49 (1994) 4908; G.L. Kane, C. Kolda, L. Roszkowski and J.D. Wells, Phys. Rev. D 49 (1994) 6173; R. Hempfling and A.H. Hoang, Phys. Lett. B 331 (1994) 99; P. Langacker and N. Polonsky, Phys. Rev. D 50 (1994) 2199; H.E. Haber, R. Hempfling and A.H. Hoang, Zeit. fur Phys. C 75 (1997) 539; S. Heinemeyer, W. Hollik and G. Weiglein, Comput. Phys. Commun. 124, 76 (2000) [hepph/9812320]. 24. For a review, see: H. Dreiner, arXiv:hepph/9707435. 25. J. Ellis, J.S. Hagelin, D.V. Nanopoulos, K.A. Olive and M. Srednicki, Nucl. Phys. B 238 (1984) 453; see also H. Goldberg, Phys. Rev. Lett. 50 (1983) 1419. 26. S. Dimopoulos and H. Georgi, Nucl. Phys. B 193 (1981) 150; N. Sakai, Z. Phys. C 11 (1981) 153. 27. K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Prog. Theor. Phys. 68 (1982) 927 [Erratum-ibid. 70 (1982) 330]; L.E. Ibafiez and G.G. Ross, Phys. Lett. B 110 (1982) 215; L.E. Ibafiez, Phys. Lett. B 118 (1982) 73; J. El-
Decline and Fall of the Standard Model?
28.
29.
30.
31.
32.
386
lis, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 121 (1983) 123; J. Ellis, J. Hagelin, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 125 (1983) 275; L. Alvarez-Gaume, J. Polchinski, and M. Wise, Nucl. Phys. B 221 (1983) 495. J. R. Ellis and D. V. Nanopoulos, Phys. Lett. B 110 (1982) 44; R. Barbieri and R. Gatto, Phys. Lett. B 110 (1982) 211. M. Dine and A. E. Nelson, Phys. Rev. D 48, 1277 (1993) [hep-ph/9303230]; M. Dine, A. E. Nelson and Y. Shirman, Phys. Rev. D 51, 1362 (1995) [hep-ph/9408384]; M. Dine, A. E. Nelson, Y. Nir and Y. Shirman, Phys. Rev. D 53, 2658 (1996) [hep-ph/9507378]. D. E. Kaplan, G. D. Kribs and M. Schmaltz, Phys. Rev. D 62, 035010 (2000) [hep-ph/9911293]; Z. Chacko, M. A. Luty, A. E. Nelson and E. Ponton, JHEP 0001, 003 (2000) [hep-ph/9911323]. L. Randall and R. Sundrum, Nucl. Phys. B 557, 79 (1999) [hep-th/9810155]; G. F. Giudice, M. A. Luty, H. Murayama and R. Rattazzi, JHEP 9812, 027 (1998) [hepph/9810442]. M. Fukugita and T. Yanagida, Phys. Lett. B 174 (1986) 45; for a recent review, see: W. Buchmuller, arXiv:hepph/0107153. J. R. Ellis, G. Ganis, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B 502 (2001) 171 [arXiv:hep-ph/0009355]. M.S. Alam et al., [CLEO Collaboration], Phys. Rev. Lett. 74 (1995) 2885 as updated in S. Ahmed et al., CLEO CONF 99-10; BELLE Collaboration, BELLECONF-0003, contribution to the 30th International conference on High-Energy Physics, Osaka, 2000. See also K. Abe et al., [Belle Collaboration], [arXiv:hepex/0107065]; L. Lista [BaBar Collaboration], [arXiv:hep-ex/0110010]; C. Degrassi, P. Gambino and G. F. Giudice, JHEP 0012 (2000) 009; M. Carena,
John Ellis
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34.
35.
36.
37.
38.
39.
Decline and Fall of the Standard Model?
D. Garcia, U. Nierste and C. E. Wagner, hep-ph/0010003; G. Isidori, talk at this conference. M. Carena, J. R. Ellis, A. Pilaftsis and C. E. Wagner, Nucl. Phys. B 586 (2000) 92 [arXiv:hep-ph/O0O318O], Phys. Lett. B 495 (2000) 155 [arXiv:hepph/0009212]; and references therein. S. Mizuta and M. Yamaguchi, Phys. Lett. B 298 (1993) 120 [arXiv:hepph/9208251]; J. Edsjo and P. Gondolo, Phys. Rev. D 56 (1997) 1879 [arXiv:hepph/9704361]. C. Boehm, A. Djouadi and M. Drees, Phys. Rev. D 62 (2000) 035012 [arXiv:hep-ph/9911496]. J. Ellis, T. Falk and K. A. Olive, Phys. Lett. B 444, 367 (1998); J. Ellis, T. Falk, K. A. Olive and M. Srednicki, Astropart. Phys. 13 (2000) 181; M. E. Gomez, G. Lazarides and C. Pallis, Phys. Rev. D 61, 123512 (2000) [hep-ph/9907261] and Phys. Lett. B 487, 313 (2000) [hepph/0004028]; R. Arnowitt, B. Dutta and Y. Santoso, hep-ph/0102181. M. Drees and M. M. Nojiri, Phys. Rev. D 47, 376 (1993); H. Baer and M. Brhlik, Phys. Rev. D 53 (1996) 597 and Phys. Rev. D 57 (1998) 567; H. Baer, M. Brhlik, M. A. Diaz, J. Ferrandis, P. Mercadante, P. Quintana and X. Tata, Phys. Rev. D 63 (2001) 015007; A. B. Lahanas, D. V. Nanopoulos and V. C. Spanos, hep-ph/0009065. J. R. Ellis, T. Falk, G. Ganis, K. A. Olive and M. Srednicki, Phys. Lett. B 510 (2001) 236 [arXiv:hep-ph/0102098]. J. L. Feng, K. T. Matchev and T. Moroi, Phys. Rev. Lett. 84, 2322 (2000) [hep-ph/9908309]; J. L. Feng, K. T. Matchev and T. Moroi, Phys. Rev. D 61, 075005 (2000) [hep-ph/9909334]; J. L. Feng, K. T. Matchev and F. Wilczek, Phys. Lett. B 482, 388 (2000) [hep-ph/0004043]. J. R. Ellis and K. A. Olive, Phys. Lett. B 514 (2001) 114 [arXiv:hep-ph/0105004].
387
40. For other recent calculations, see, for example: A. B. Lahanas, D. V. Nanopoulos and V. C. Spanos, Phys. Lett. B 518 (2001) 94 [arXiv:hep-ph/0107151]; L. Roszkowski, R. Ruiz de Austri and T. Nihei, JHEP 0108, 024 (2001) [arXiv:hep-ph/0106334]. 41. J. Ellis, K. Enqvist, D. V. Nanopoulos and F. Zwirner, Mod. Phys. Lett. A 1, 57 (1986); R. Barbieri and G. F. Giudice, Nucl. Phys. B 306 (1988) 63. 42. H. N. Brown et al. [Muon g-2 Collaboration], Phys. Rev. Lett. 86, 2227 (2001) [hep-ex/0102017]. 43. R. Alemany, M. Davier and A. Hocker, Eur. Phys. J. C 2 (1998) 123 [arXivrhepph/9703220]; M. Davier and A. Hocker, Phys. Lett. B 419 (1998) 419 [arXivrhepph/9711308]; M. Davier and A. Hocker, Phys. Lett. B 435 (1998) 427 [arXivrhepph/9805470]; S. Narison, Phys. Lett. B 513 (2001) 53 [arXiv:hep-ph/0103199]; J. F. De Troconiz and F. J. Yndurain, arXiv:hep-ph/0106025. 44. J. Bijnens, talk at this conference, arXiv:hep-ph/0108111. See also J. Bijnens, E. Pallante and J. Prades, Nucl. Phys. B 474 (1996) 379 [arXiv:hepph/9511388]; M. Hayakawa and T. Kinoshita, Phys. Rev. D 57 (1998) 465 [arXiv:hep-ph/9708227]. 45. L. L. Everett, G. L. Kane, S. Rigolin and L. Wang, Phys. Rev. Lett. 86, 3484 (2001) [arXiv:hep-ph/0102145]; J. L. Feng and K. T. Matchev, Phys. Rev. Lett. 86, 3480 (2001) [arXiv:hepph/0102146]; E. A. Baltz and P. Gondolo, Phys. Rev. Lett. 86, 5004 (2001) [arXiv:hep-ph/0102147]; U. Chattopadhyay and P. Nath, Phys. Rev. Lett. 86, 5854 (2001) [arXiv:hep-ph/0102157]; S. Komine, T. Moroi and M. Yamaguchi, Phys. Lett. B 506, 93 (2001) [arXiv:hep-ph/0102204]; S. P. Martin and J. D. Wells, Phys. Rev. D 64, 035003 (2001) [arXiv:hep-ph/0103067];
John Ellis
Decline and Fall of the Standard Model?
H. Baer, C. Balazs, J. Ferrandis and X. Tata, Phys. Rev. D 64, 035004 (2001) [arXiv:hep-ph/0103280]; J. Ellis, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B 508 (2001) 65 [arXiv:hepph/0102331]; R. Arnowitt, B. Dutta, B. Hu and Y. Santoso, Phys. Lett. B 505 (2001) 177 [arXiv:hep-ph/0102344]. 46. ATLAS Collaboration, ATLAS detector and physics performance Technical Design Report, CERN/LHCC 9914/15 (1999); S. Abdullin et al. [CMS Collaboration], hep-ph/9806366; S. Abdullin and F. Charles, Nucl. Phys. B 547 (1999) 60; CMS Collaboration, Technical Proposal, CERN/LHCC 94-38 (1994).
51.
52.
53. 54.
47. See, for example: I. Hinchliffe, F. E. Paige, M. D. Shapiro, J. Soderqvist and W. Yao, Phys. Rev. D 55 (1997) 5520; TESLA Technical Design Report, DESY-01-011, Part III, Physics at an e+e~ Linear Collider (March 2001). 48. M. Battaglia et al., arXiv:hep-ph/0106204. 49. S. Matsumoto et al. [JLC Group], JLC1, KEK Report 92-16 (1992); J. Bagger et al. [American Linear Collider Working Group], The Case for a 500-GeV e+e~ Linear Collider, SLAC-PUB-8495, BNL-67545, FERMILAB-PUB-00-152, LBNL-46299, UCRL-ID-139524, LBL46299,Jul 2000,hep-ex/0007022; T. Abe et al. [American Linear Collider Working Group Collaboration], Linear Collider Physics Resource Book for Snowmass 2001, SLAC-570, hep-ex/0106055, hep-ex/0106056, hep-ex/0106057 and hep-ex/0106058; TESLA Technical Design Report, DESY-01-011, Part III, Physics at an e+e~~ Linear Collider (March 2001). 50. R. W. Assmann et al. [CLIC Study Team], A 3-TeV e+e~ Linear Collider Based on CLIC Technology, ed. G. Guignard, CERN
55. 56.
2000-08; CLIC Physics Study Group, http://clicphysics.web.cern.ch/ CLICphysics/. Neutrino Factory and Muon Collider Collaboration, http://www.cap.bnl.gov/mumu/ mu_home_page. html; European Muon Working Groups, http://muonstoragerings.cern.ch/ Welcome.html. G. A. Blair, W. Porod and P. M. Zerwas, Phys. Rev. D 6 3 (2001) 017703 [hepph/0007107]. M. Battaglia and K. Desch, arXiv:hepph/0101165. J. Ellis, J. L. Feng, A. Ferstl, K. T. Matchev and K. A. Olive, arXiv:astro-ph/0110225. DAMA Collaboration, R. Bernabei et al, Phys. Lett. B 436, 379 (1998). J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi, Phys. Rev. D 53 (1996) 2442; J. Hisano, D. Nomura and T. Yanagida, Phys. Lett. B 437 (1998) 351; J. Hisano and D. Nomura, Phys. Rev. D 59 (1999) 116005; W. Buchmuller, D. Delepine and F. Vissani, Phys. Lett. B 459 (1999) 171; M. E. Gomez, G. K. Leontaris, S. Lola and J. D. Vergados, Phys. Rev. D 59 (1999) 116009; J. R. Ellis, M. E. Gomez, G. K. Leontaris, S. Lola and D. V. Nanopoulos, Eur. Phys. J. C 14 (2000) 319; W. Buchmuller, D. Delepine and L. T. Handoko, Nucl. Phys. B 576 (2000) 445; J. L. Feng, Y. Nir and Y. Shadmi, Phys. Rev. D 61 (2000) 113005; J. Sato and K. Tobe, Phys. Rev. D 63 (2001) 116010; J. Hisano and K. Tobe, Phys. Lett. B 510 (2001) 197; S. Baek, T. Goto, Y. Okada and K. Okumura, hep-ph/0104146; S. Lavignac, I. Masina and C.A. Savoy, hep-ph/0106245.
57. D. F. Carvalho, J. R. Ellis, M. E. Gomez and S. Lola, Phys. Lett. B 515 (2001) 323 [arXiv:hep-ph/0103256].
388
Decline and Fall of the Standard Model?
John Ellis 58. J. R. Ellis, J. Hisano, S. Lola and M. Raidal, arXiv:hep-ph/0109125; and references therein. 59. H. Murayama and A. Pierce, arXiv:hepph/0108104. 60. J. R. Ellis, J. S. Hagelin, S. Kelley and D. V. Nanopoulos, Nucl. Phys. B 311 (1988) 1. 61. C. K. Jung, arXiv:hep-ex/0005046; Y. Suzuki et al. [TITAND Working Group Collaboration], arXiv:hepex/0110005. 62. I. Antoniadis and K. Benakli, Int. J. Mod. Phys. A 15 (2000) 4237 [arXiv:hep-ph/0007226]. 63. J. R. Ellis, N. E. Mavromatos and D. V. Nanopoulos, arXiv:gr-qc/9909085.
389
T H E HIGGS PUZZLE: E X P E R I M E N T A N D THEORY FABIO ZWIRNER Dipartimento di Fisica, Universitd di Roma 'La Sapienza', and INFN, Sezione di Roma, Piazzale Aldo Mow 2, 1-00185 Roma, ITALY E-mail: [email protected] T h e present experimental and theoretical knowledge of the physics of electroweak symmetry breaking is reviewed. Data still favor a light Higgs boson, of a kind that can be comfortably accommodated in the Standard Model or in its Minimal Supersymmetric extension, but exhibit a non-trivial structure that leaves some open questions. The available experimental information may still be reconciled with the absence of a light Higgs boson, but the price to pay looks excessive. Recent theoretical ideas, linking the weak scale with the size of possible extra spatial dimensions, are briefly mentioned. It is stressed once more that experiments at high-energy colliders, such as the Tevatron and the LHC, are the crucial tool for eventually solving the Higgs puzzle.
Rome is a city so full of religious symbols that it provides some inspiration on how to organize a talk on the physics of electroweak symmetry breaking, where firm experimental and theoretical results are mixed, so far, with a certain amount of beliefs. 1
The Standard Model (The Orthodoxy)
The obvious starting point for any discussion of the Higgs puzzle (= 'what is the physics of electroweak symmetry breaking?') is the Standard Model (SM), by now firmly established as the renormalizable quantum field theory of strong and electroweak interactions at presently accessible energies: in the spirit of the preface, it can be called 'The Orthodoxy'. The only SM ingredient still escaping experimental detection, in a theoretical construction that works incredibly well, is the Higgs 1 boson, H. Its properties are controlled by some well-known parameters of the fermion and gauge sectors (including the Fermi constant Gp, which sets the value of the weak scale) plus an independent one, the Higgs mass mn • The elementary complex spin-0 field (ft, an SU(2)L doublet of weak hypercharge Y = +1/2 (in the normalization where Q = T^L + Y), is by now considered to be an essential
part of what we call the SM. Indeed, it plays a fundamental role in the description of two symmetry-breaking phenomena. The first is the spontaneous breaking of the SU(2)L X U(l)y gauge symmetry down to the U{1)Q of QED, described by the following part of the SM Lagrangian:
CS = {D^)\D^)
-fi24>U- K4>U? • (1)
The second is the explicit breaking of the global flavor symmetry that is present if only gauge interactions are switched on. This is realized by the Yukawa part of the SM Lagrangian, CY = huq[EuR(j) + hD~qEdR(t>
+hET[eR = io'2(f>*, hU'D'E
(2)
are 3 x 3 complex
matrices and generation indices have been omitted. Over the years, our confidence in this description has been progressively reinforced by increasingly precise tests of both these symmetry-breaking phenomena (here the focus will be on gauge symmetry breaking, since the theoretical aspects of flavor symmetry breaking are discussed in another talk at this Conference 2 ). However, the ultimate, crucial test of the SM remains the direct search for the Higgs particle, by far the most important experimental enterprise in today's particle physics.
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Fabio Zwirner 1.1
The Higgs Puzzle: Experiment and Theory
Direct searches for the SM Higgs
The experimental status of the searches for the SM Higgs particle is reviewed in detail in another talk at this Conference 3 . Here I will just summarize the present situation from the preliminary LEP-combined results 4 released for the conferences of Summer 2001: CM
• The data still show an excess, at the level of 2.1a, over the expected SM background, mainly due to ALEPH data and to the four-jet final state (to be compared with the 2.9cr excess in the preliminary data of November 2000). • The maximum likelihood occurs at rrifj = 115.6 GeV, with 3.5% probability of a fluctuation of the SM background. • The lower bound on the Higgs mass is mH > 114.1 GeV at 95% c.L, to be compared with an expected bound of 115.4 GeV. • Three out of the four LEP experiments have not yet released their final results at the time of this Conference: the final combination of the LEP results is expected for the end of 2001. 1.2
SM fits to the Higgs mass
Besides direct searches, additional information on the SM Higgs boson come from the fits to m,H based on electroweak precision data, whose experimental aspects are discussed in another talk at this Conference 5 . A popular summary of the available information 6 is the famous 'blueband' plot of the LEP Electroweak Working Group, displayed / 2 of t h e in Fig. 1: it gives the A\2 = X2 •X^4„ global SM fit to electroweak precision data as a function of m # . As evident from Fig. 1, the fit clearly favours a light Higgs. The default fit, represented by the solid curve in Fig. 1, gives mH = 88^35 GeV and mH < 196 GeV at 95% c.L. An alternative fit (see below for an explanation), represented by the dashed
391
<
Excluded
'(/
Preliminary
10 m H [GeV]
Figure 1. A x 2 as a function of m g from the global fit to the SM. The region excluded by the direct searches at LEP is also shown.
line, gives ran < 222 GeV at 95% c.L and a slightly higher central value. The band represents a (debatable) estimate of the theoretical uncertainty. Notice that the fit does not include the information coming from direct searches. Notice also that, in both fits, more than half of the x 2 curve falls in the shaded region, excluded at 95% c.L by direct searches. Given the importance of the issue, it is worth examining in more detail how the preference for a light SM Higgs arises. For given values of the remaining SM input parameters, precise electroweak data combined with updated theoretical calculations give logarithmic sensitivity to mH, mostly via two pseudo-observables: the leptonic effective electroweak mixing angle, sin 2 6*?. = (1 — vi/ai)/<±, and the mass of the W boson, mw- There are still small theoretical uncertainties in the evaluation of radiative corrections, in principle reducible by more refined calculations. A recent progress along these lines is the calculation 7 of the com-
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner plete fermionic two-loop contribution to mw, but other calculations of the same order are still missing. Larger uncertainties come from non-negligible errors in other parameters entering the fit. An important one is the hadronic contribution to the running of the electromagnetic coupling constant, Aa^d, as extracted from a dispersion integral over a parametrization of the measured crosssection for e+e~ —> hadrons, including the recent data 8 from BES and CMD-2. A conservative, 'data-driven' fit 9 gives A ^ K )
= 0.02761 ± 0.00036,
Preliminary 0.23099 ± 0.00053 A,(Pt)
0.23159 ±0.00041
AiSLC
0.23098 ± 0.00026
c
T— *
A,b
0.23152 1 0 . 0 0 0 1 7 XZ/d.o.f.: 1 2 . 8 / 5
3
10 -
(3)
> O I..
£V,y
J
X i Aa,\;'a= 0.02761 ± 0.00036 sm,= 91.1875 ±0.0021 GeV am'= 174.3 ± 5 . 1 GeV
(4)
There are many other determinations, as reviewed for example in Ref. n , all consistent with the previous ones, but with a tendency to be closer to Eq. (3) than to Eq. (4). The second important uncertainty in the input parameters is the one associated with the experimental determination of the top quark mass from the CDF and DO experiments at Fermilab 12 :
0.2324 ± 0.0012
Average
0.23
= 0.02738 ± 0.00020.
0.23272 ± 0.00079
-*
corresponding to the 'default' input of the blueband plot, whereas a more aggressive, 'theory-driven' fit 10 , corresponding to the 'alternative' input of the blueband plot, gives Aa{^d(mz)
0.23226 + 0.00031
0.232
0.234
• 2jePt
sin 6 eff Figure 2. Determination of sin 2 0"Ff from the asymmetry measurements. The SM prediction is also shown, as a function of m / j , with t h e uncertainties from A a i d(mz) and mt added linearly.
quark charge asymmetry) to give larger values of sin2 #eT? (and of mjj) than the leptonic asymmetries (forward-backward asymmetry, mtop = 174.3 ± 5.1 GeV. (5) r polarization asymmetry, SLD left-right The individual experimental determina- asymmetry). The average of the hadronic l tions of sin 2 0*J*j and mw, with the corre- determinations alone gives sin e eff{had) = sponding theoretical predictions and uncer- 0.23230 ±0.00029, the average of the leptonic ones sin 2 9lef}(lep) = 0.23113 ± 0.00021, cortainties, as taken from Ref. 6 , are displayed responding to a discrepancy at the level of in Figs. 2 and 3. A careful inspection of Figs. 1-3 reveals 3.3cr. This effect was larger in Winter 2001: that the SM fit is not entirely a bed of roses, the change is mostly due to a — 0.5cr shift of the bb forward-backward asymmetry, AF'B, as stressed, for example, in Ref. 13 (on the basis of the data available in Winter 2001). after a new DELPHI analysis based on a First, the quality of the overall fit turns neural network to tag the b-charge, and an out to be acceptable but not exceptional, improvement in the jet-charge measurement of the ALEPH analysis. The most precise X2/dof = 22.9/15, corresponding to a 'probability' of 8.6%. The main reason for this hadronic determination comes indeed from can be seen from Fig. 2: there is a system- ApB, and has now a pull of 2.9<7 with reatic tendency of the hadronic asymmetries spect to the central value of the global SM fit. (bb and cc forward-backward asymmetry plus Keeping in mind the possibility of a statisti-
392
Fabio Zwirner
The Higgs Puzzle: Experiment and Theory Mass of the W Boson
Experiment
Mw
ALEPH
[GeV]
80.471 ±0.049
80.398 ±0.069 80.490 ± 0 . 0 6 5 2
X /dof = 32.5/39 80.450 ± 0.039
-mm
Aa ( 5 ) fla
had_
0.02761 ±0.00036 linearly added to
m 80.2
80.4 M w [GeV]
Mt = 174.3±5.1 GeV
80.6
Figure 3. The measurements of my/ at LEP. T h e lower plot shows the SM prediction, as a function o f m H , with the uncertainties from A a ^ ( m z ) and mt added linearly.
cal fluctuation, this can be viewed as a small problem either for the SM or for the experimental analyses. Radical modifications of the Zbb vertex appear unlikely, given the fact that Aj, from SLD and Rb are well-behaved. Also, measuring Ap^ is a very delicate experimental task, since flavor and charge of the b-quarks need to be tagged simultaneously, with more complicated systematics than in the measurement of Rb- On the other hand, all the experimental determinations of mw are in good agreement and point to a light Higgs boson: those of Fig. 3 can be combined with the ones from the UA2, CDF and DO experiments at pp colliders, giving mw = 80.454 ± 0.060, to produce a global
393
world average mw = 80.451 ± 0.033. Notice that, with the present errors, the main parametric uncertainty affecting the theoretical determination of mw is the one coming from mt, whereas mt and Aa h^d(mz) give comparable uncertainties in the theoretical determination of sin d^ff • Given the small discrepancy between hadronic and leptonic asymmetries, the exercise of looking at what happens, when dropping the hadronic asymmetries from the fit, may not be entirely academical. The result is the following: the quality of the SM fit improves, but the central value of m # is pushed down, so that the consistency of the SM fit to ran with the limits from direct searches becomes marginal [with a significant residual dependence, which should not be forgotten, on Aahld(mz) and mt]. Is there a SM crisis lurking around the corner? A prudent attitude before answering this question may be appropriate, taking into account that the final heavy-flavor analyses from LEP and improved determinations of mw and mt from the new Tevatron run will be available soon. It may well be, however, that we must wait until the discovery (or the exclusion) of a light Higgs boson to definitively settle the issue.
1.3
The SM as an effective theory
If we believed that the SM is the whole story, the talk could end here. However, we all know that the SM cannot be the ultimate theory of elementary particles, valid at arbitrarily high energy scales, since it does not contain a quantum theory of gravitational interactions and some of its couplings are not asymptotically free. Thus, the SM must be seen as an effective field theory, valid up to some physical cut-off scale A, where new physics must be introduced into the theory. On general grounds, A could be anywhere between the TeV scale and the Planck scale, MP = G~1/2/VS^ - 2.4 x 10 18 GeV, where
Fabio Zwirner
The Higgs Puzzle: Experiment and Theory tests, neutrino masses, proton decay, . . . . In this framework, an old question 14 can be addressed in the light of present experimental data: given our knowledge of the top quark mass and of the bounds on the Higgs mass, can we put some firm bounds on the cut-off scale A? The qualitative aspects of the answer can be appreciated by remembering that, in the SM, the top and Higgs masses are associated with the largest Yukawa coupling ht and with the quartic Higgs selfcoupling A, respectively, via tree-level relations of the form mt oc htv and m2H oc Au2, where v is the vacuum expectation value of the Higgs field. Also, the scale-dependence of A is controlled by the renormalization group equation
GN is Newton's constant, characterizing the observed gravitational interactions. Assuming that the SM correctly identifies the degrees of freedom at the weak scale (this may not be true, as will be discussed later, in the case of the Higgs field), we can write down the most general local Lagrangian compatible with the SM symmetries, classifying the possible operators according to their physical dimension, and scaling all dimensionful couplings by appropriate powers of A. The resulting dimensionless coefficients are then to be interpreted as parameters, which can be either fitted to experimental data or (if we are able to do so) theoretically determined from the fundamental theory replacing the SM at the scale A. Very schematically (and omitting all coefficients and indices, as well as many theoretical subtleties):
4
t-eff
2
2
2
[A + A $ ] + [(D$) + * #tf +F»VF^
+ ¥ * $ + $4
+ F^F^
*CT^*FMV
A $2F^FM + - "A2"
A
* * * *
A2 (6)
where * stands for the generic quark or lepton field, <E> for the SM Higgs field, F for the field strength of the SM gauge fields, and D for the gauge-covariant derivative. The first bracket in Eq. (6) contains two terms, a cosmological constant term and a Higgs mass term, that are proportional to positive powers of A, and are at the origin of two infamous hierarchy problems. The second bracket in Eq. (6) contains operators with no powerlike dependence on A, but only a milder, logarithmic dependence, due to infrared renormalization effects between the cut-off scale A and the weak scale. The last bracket in Eq. (6) is the starting point of an expansion in inverse powers of A, and contains operators associated with rare processes, precision
-T^TT
dlogQ
= - ^
16TT2
(A2 + A/i? - hAt;) + ... , (7) w
v
*
*
'
where Q is the renormalization scale and the dots stand for smaller one-loop contributions, controlled by the electroweak gauge couplings, and higher-order contributions. For any given values of mt and A, we can extract a 'triviality' upper bound on win observing that, if rriH is too large, A(Q) blows up at a scale Qo < A, developing a Landau pole. This leads to some well-known constraints, supported by more rigorous arguments and by lattice calculations: m # < 200 GeV if A ~ MP, mH < 600 GeV if A ~ 1 TeV. Similarly, we can extract a 'stability' lower bound on rrifj by observing that, if m,H is too small, then X(Q) becomes negative at Qo < A, and another minimum of the SM potential develops at () ~ QoSince the results of the previous subsection point to rather small values of mjj, the presently hot issue is the stability bound, recently revisited in 15 . When implementing the stability bound, three options are possible: 1) we can require absolute stability, i.e. the correct electroweak vacuum must have lower energy than the 'wrong' vacuum; 2) we can require stability with respect to high-temperature fluctuations in the cosmo-
394
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner logical evolution of the early Universe; 3) we can require stability with respect to quantum fluctuations at approximately zero temperature. The latter is the most conservative option, and amounts to requiring that the lifetime of the correct electroweak vacuum should be larger than the present age of the Universe, Tu ~ 1010 yrs. The present results are illustrated 15 in Fig. 4, where
sensible value) and van = 115 GeV (close to its minimum allowed value and to the location of the slight experimental effect discussed in subsection 1.1), then option (1) leads to mt < (166 ± 2) GeV. After a new complete one-loop calculation of the tunneling probability at zero temperature, option (3) leads to mt < (175 ± 2) GeV, still in full agreement with the data. Therefore, it may be premature to claim evidence of new physics below Mp from SM vacuum stability, even if we are at the border of the allowed region, a situation for which possible theoretical reasons have been suggested 16 . 2
Figure 4. Instability, meta-stability and stability regions of the SM vacuum in the (mjf,mt) plane, for &s{mz) = 0.118 (solid curves) ±0.002 (dashed and dash-dotted curves). The shaded area indicates the experimental range fro mt, Eq. (5), at la (darker) and 2a (lighter).
as{mz) = 0.118 ± 0.002 and A = MP have been assumed, and in Fig. 5, where ran = i
" • ' i '
M S S M (The Dogma?)
In the SM effective Lagrangian of Eq. 6, the mass term for the Higgs field has a quadratic dependence on the cut-off scale A. When we try to extrapolate the SM to scales much higher than the weak scale, this gives rise to the infamous gauge hierarchy problem. The natural solution to this problem is to introduce new physics close to the weak scale. The present best candidate for such new physics is the Minimal Supersymmetric extension of the Standard Model (MSSM), extensively discussed in another talk at this Conference 17 . 2.1
Some virtues of the MSSM
Figure 5. Running of the quartic Higgs coupling A(/t) for mH = 115 GeV, mt = 165,170,175, 180, 185 GeV and as(mz) ~ 0.118. Absolute stability [X(Mweak) > 0] is still possible if mt < 166 GeV. The hatched region is excluded by the meta-stability bound.
The main virtue of the MSSM is that, if the mass splittings Amsusy that break supersymmetry (SUSY) are of the order of the weak scale Mweak ~ 1 TeV, then its cut-off scale can be naturally taken to be AMSSM = A2susy/Amsusy, where Asusy is the scale of spontaneous SUSY breaking. In hiddensector supergravity models, where Asusy ~ ^MweakMp, such cut-off scale can then be pushed very close to Mp (this is not true if SUSY breaking occurs at lower scales, as in 'gauge-mediated' models).
115 GeV and as(mz) = 0.118 have been assumed. If we set A ~ Mp (its maximum
Another virtue of the MSSM is that, in contrast with other possible solutions of the hierarchy problem, it is generically as good as
^ in GeV
395
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner the SM in complying with electroweak precision data. This is due to the fact that the soft SUSY-breaking mass terms do not break the SU(2)L x U{l)y gauge symmetry. Indeed, it was recently observed 18 that, if sneutrinos and charged sleptons (and, to a lesser extent, charginos and neutralinos) have masses close to their present experimental bounds, then the MSSM may lead to an improved consistency between direct and indirect bounds on the Higgs mass, when the hadronic asymmetries are left out of the global fit. This result is illustrated in Figs. 6 and 7, drawn in planes -7
-8
o x « ID
-10
-11
1
' ' I ' ' ' ' I ' ' ' ' I + : m e a s u r e d values blue: l c r V r e d : MSSM
: SM, m H = 1 1 3 G e V - > 1 3 5 GeV I
, ,
, , I • ,
—i—i—i—I—i—i—i—i—I—i—i—i—i—I—i—i—r-
,
1 I ,
1 ,
,
6
+ : measured values blue: 1 a red: MSSM
e x x 10
Figure 7. T h e same as in Fig. 6 b u t for e\ and £3.
tonic asymmetries and the ratio Rf, have been included in the fit. The elliptic contours represent the region allowed by the data at the lcr level. The irregular contours enclose the typical MSSM predictions for a light spectrum. The fat dot with an arrow shows the : SM, m H =113 GeV-»135 GeV SM prediction for a Higgs mass varying beI , • , , I • • , , I • , , , tween 113 GeV and 135 GeV. We can see 6 that, for a light MSSM spectrum, the agreex 10 J ment between data and theoretical predictions can improve.
Figure 6. Measured values (cross) of £3 and £2, with their lcr region (solid ellipse), obtained from mw, T;, sin 2 d^fUlep) and i?(,. The area inside the irregular curve represents the MSSM prediction for m e - t between 96 and 300 GeV, m ± between 105 and 300 GeV, |/i| < 1 TeV, tan/3 = 10, miR = 1 TeV and rrij\ = 1 TeV.
characterized by two of the three flavourindependent parameters (ei,e2,£3) that are often used in non-SM fits to precision data. We remind the reader that t\, related to Veltman's parameter 5p, is mainly controlled by mt, £2 is particularly sensitive to mw and £3 is mainly controlled by sin 2 9*?Ulep). Only the W mass, the leptonic Z width, the lep-
Another important piece of indirect evidence in favour of the MSSM is the fact that, when combined with a condition on the grand unification of all gauge couplings and with the hypothesis of a 'desert' between the weak scale and the grand unification scale, it leads 19 to one successful prediction for the gauge couplings at the weak scale. To gauge the significance of this success, we can perform a simple-minded but illuminating exercise. We can consider the one-loop renormalization group equation for the running gauge coupling constants da A bA = — oc\ + . . dlogQ 2TT 396
(A = 1,2,3), (8)
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner where 6.4 are the one-loop beta-function coefficients, determined by the gauge quantum numbers of the particle spectrum at the weak scale. If we are agnostic about the precise value of the unified gauge coupling and of the grand unification scale, but we assume the normalization of the U(l)y gauge coupling suggested by the simplest grand-unified models, we can perform a unification test by considering the only variable controlling the prediction for the gauge couplings at the weak scale, the ratio B = (63 — 62)/(&2 — b{). The SM value of this ratio is BSM ^ 0.53, its experimental value is Bexp ~ 0.71, and the MSSM value is BMSSM ^ 0.72. A reasonable error estimate is A B ~ 0.03, completely dominated by the the fact that we do not know the details of the MSSM spectrum and of the spectrum of the underlying theory around the grand unification scale. This is an impressive success, and it is difficult to believe that it is accidental and that we are being fooled by a malicious Nature and by theorists. Any other extension of the SM claiming to be better than the MSSM must face this important phenomenological hint.
2.2
The MSSM Higgs sector
If we take seriously the MSSM, then it is important to extract its predictions for the Higgs sector. As is well known, the MSSM Higgs sector contains two complex doublets, which after gauge symmetry breaking give rise to five physical degrees of freedom, three neutral (h, H, A) and two charged (H±). The prediction of SUSY is that the MSSM Higgs sector depends, at the tree level, only on known SM parameters and two more parameters, for example TUA and tan/3 = v^/vi. After including quantum corrections, the predictions of SUSY are not lost, but the dependences become more complicated and involve all the rest of the MSSM spectrum, in particular the parameters of the top-stop sector 20 . An intense theoretical effort has been devoted 397
over the last years to the precise computation of the MSSM Higgs properties, and we are now at the stage where the calculation of the most important two-loop corrections is being completed. When the top quark mass will be known more precisely, these calculations will be important for reliably comparing models of SUSY breaking with the available bounds on the spectrum. Of course, the relevance of all this could increase further if and when SUSY particles and SUSY Higgs bosons will be found. So far, two-loop corrections to the neutral Higgs boson masses have been computed mostly in the limit of vanishing momentum on the external lines of the Higgs and gauge boson propagators. In this limit, analytical formulae at 0(atas) a r e available, for arbitrary values of the relevant MSSM parameters 21 , and have been implemented in computer codes. As for the C ( a 2 ) corrections, which can be of comparable numerical importance, at the time of this Conference there are only partially analytic formulae 22 for m/,, valid in the limit TUA ^> mzThe general calculation of the 0 ( a 2 ) corrections (in the zero-momentum limit) has been recently completed 23 and agrees with Ref. 22 in the appropriate limit. The effects of the 0 ( Q 2 ) corrections is illustrated in Fig. 8, taken from Ref. 22 . We can see that these corrections can be sizeable, increasing rrih by several GeV in the case of large mixing in the stop mass matrix. Armed with the relevant radiative corrections [the C ( a 2 ) ones have not yet been adequately implemented in the codes, but will presumably be included in the final LEP analyses], experimentalists have searched for direct signals of the MSSM Higgs bosons, as reviewed in another talk at this Conference 3 and described in more detail in Ref. 24 . The small Higgs signal in the SM analysis has its counterpart in the MSSM analysis: some excesses at the ~ la level are reported both in the e + e~ —• hA channel, at (mh, mA) ~ (83,83), (93,93) GeV, and in the
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner
140
' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' M s = l TeV
yU.= - 5 0 0 GeV
Figure 8. The mass mj, vs. the stop mixing parameter X^r , for some representative values of t h e remaining MSSM parameters. T h e two-loop corrections are included either at O(atces) (lower lines) or at 0(atas + a1) (upper lines). The fine structure corresponds to two different methods of implementing the corrections.
e+e~ —• hZ channel, for rrih ~ 97,115 GeV. The lower bounds on the MSSM Higgs masses are notoriously difficult to illustrate, due to their dependence on many parameters. Examples of exclusion plots are presented in Figs. 9 and 10, for a representative choice of MSSM parameters. In a 'benchmark' case characterized by a large mixing in the stop mass matrix, which should lead to conservative bounds on (771^,777,1) and on tan/?, the data have been interpreted 24 in terms of the following exclusion regions at 95% c.l.: (mh,mA) < (91.0,91.9) GeV and tan/? < 2.4. For small stop mixing, the limits are typically stronger. There are other recent interesting studies of the MSSM Higgs sector that would deserve to be discussed. There is just the time to briefly mention them, referring the reader to the corresponding papers. There is a new experimental analysis of the Tevatron data 25 , on the search for pp —> bb(p —• bbbb (
value, tan /3 > 40-50. Some recent theoretical studies 26 have considered the possibility of radiatively induced CP-violating effects in the Higgs sector, coming from explicit CP-violating phases in the squark-gluino sector, and have analyzed the resulting complications in the discussion of the MSSM Higgs searches. Other theoretical studies 27 have examined the implications of the experimental bounds on the MSSM Higgses for different models of SUSY-breaking 'mediation'. 2.3
Some weak points of the MSSM
It would be misleading to end this section without mentioning that, besides its virtues, the MSSM has also, in our present view, a number of weak points. To begin with, the MSSM with its soft SUSY breaking provides only an incomplete, technical solution of the hierarchy problem, since the overall mass scale of the soft terms is set 'by hand'. These soft terms also introduce a very large number of free parameters into the model: this problem is going to stay with us until when a standard model for spontaneous supersymmetry breaking will
398
Fabio Zwirner
0
20
The Higgs Puzzle: Experiment and Theory
40
60
80
100 120 140 mh0 (GeV/c2)
Figure 9. The MSSM exclusion region in t h e (mh,niA) plane, for the 'rre^-max' benchmark scenario. T h e central region is excluded by L E P searches, the lateral ones are theoretically inaccessible in such a scenario.
emerge and/or SUSY particles will be found. ' More seriously, after many years of experimental searches at increasing energy scales, which explored a large part of the theoretically most appealing region from the point of view of the hierarchy problem, no direct experimental hint for the existence of the MSSM Higgs or SUSY particles has been 3n found. Taking all this into account, we should not take the MSSM as a dogma for the new physics at the weak scale, but keep an open mind for the possible alternatives. 3
Can we do without a light Higgs? (The Heresy?)
This part of the talk will touch an issue that it often triggers heated discussions: can we do lo without a light Higgs? Some people view this is as a heresy, some others almost take it for or granted, so it is worth reviewing it, even if the le state of affairs has not changed in an imporr-
399
Figure 10. The MSSM region of the (771,4,tan/3) plane excluded by LEP searches, for the ' m / , - m a x ' benchmark scenario.
tant way during the last year. Since, to the taste of most theorists, there is no satisfactory model without a light elementary Higgs, we may take an agnostic point of view and work at the level of an effective field theory. The most drastic departure from the SM consists in getting rid of the elementary Higgs field, and having the electroweak gauge symmetry SU{2)L x U(l)y non-linearly realized (so doing, of course, we define a nonrenormalizable effective theory whose cut-off scale cannot be much above the TeV scale). This approach has a long history, from the pioneering papers of Ref. 28 to some recent phenomenological discussions 29 after the LEP and Tevatron data. In this approach, the effective Lagrangian is constructed from the Goldstone bosons wa associated with electroweak symmetry breaking, assembled into the group element £ = exp(2iwara/v), where v ~ 256 GeV. Concentrating on the terms that can affect the W and Z propagators, thus playing a major role in the discussion
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner of electroweak precision tests, we can write
renormalization, must be combined with finite contributions Kg (for sin 2 O^ff) an<^ Kw £eff = jTr (D^D'tf) (for mw)- A similar phenomenon occurs in the effective theory with the Higgs field, with + X > d ; ( E , A , . . . ) , (9) the only difference that the logarithmic dei pendence is on run /rnz- At the level of both where effective theories, Kgtw depend on the cutoff and on the unknown dimensionless coefD^ = 9ME + igW^Y, - ig'ZBy (10) ficients of the higher-dimensional operators, is the covariant derivative. The first term in on which we can get reliable information only (9) describes the W and Z masses, as can be if we know about the underlying fundamental seen immediately in the unitary gauge T, — 1. theory. With the present data, it is still posThe higher-order operators Oi are scaled by sible to have A(m.tf) ^> mz without excessive appropriate powers of the cut-off A of this fine-tuning of the quantities KgtwHiggsless theory, and are characterized by diA more careful analysis, however, reveals mensionless coefficients £j. the present advantage of the light Higgs hyA less drastic approach consists in keep- pothesis. First, it must be said that, despite ing the elementary Higgs field , so that a lot of effort, so far there are no good candiSU{2)i x U(l)y can be linearly realized, dates for the underlying theory that realizes but in allowing the most general set of non- the desired situation, i.e. the phenomenorenormalizable operators compatible with logically correct magnitudes and signs of Kg the electroweak gauge symmetry and with and K\y, without disrupting the predictions Poincare invariance. Also this approach has for other observables, and avoiding 'ad hoc' a long history, from the early paper of Ref. 30 theoretical constructions. Also, it can be to other recent phenomenological discussions immediately seen, in the linear realization, 31 after the LEP and Tevatron data. In this that there is an obvious correlation: if we incase, the appropriate effective Lagrangian is crease rnu we must correspondingly decrease Ceff=CsM()
+ YlciOi(,A,...),
(11)
i
where A is the cut-off and Cj are the dimensionless coefficients of the various operators In both approaches, the theoretical expressions for the two key pseudo-observables in the fits, sin 9^?* and mw, differ from the SM ones. For given values of all the other parameters, in the SM they are just functions of TTIH, with their leading dependences proportional to log(mjj/mz)In these new frameworks, the dependences become more complicated:
^ — - { ! ° g i + ^ (*'*)• mz
l
l o
S^
\Ci,AJ
(12) In the Higgsless effective theory, the logarithmic dependence on A/mz, generated by
A, and tune the coefficients Cj, to keep agreement with the data: then mn ~ mz and A > mz looks as the most natural solution! There was a recent survey 3 2 of models that may evade the constraint of having a light Higgs with ran ~ mz- Three classes of models were identified, making reference to the (S,T) parameters, analogous to the (£3,61) parameters of Fig. 7: (i) those in which new physics can produce negative contributions to the S parameter; (ii) those with a new vector bosons Z' close to the weak scale; (iii) those in which new physics can produce positive contributions to the T parameter. Without going to the details, the important point is that all these models exhibit a rich phenomenology around the TeV scale, accessible to accelerators such as the Tevatron 3 3 , the LHC 3 4 and a possible high-energy lin-
400
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner ear e+e 4
collider
.
N e w theoretical ideas (Crackpot religions?)
Electroweak symmetry breaking is a testing ground for new ideas that are restlessly explored by adventurous theorists, despite the fact that some of their most conservative colleagues may view them (in the words of Monty Python) as 'crackpot religions'. It is appropriate to comment here on some ideas that have been very actively explored in the last years, focusing on the aspects that are most strictly related with Higgs physics. The two big hierarchy problems of our present theories are the cosmological constant problem and the gauge hierarchy problem, related with the two operators of dimension d < 4 in the SM effective Lagrangian, conveniently rewritten as: ^•eff
=
h-cosm + Aweak4>
+ ... .
(13)
We must explain why the scales of the vacuum energy and of the Higgs mass satisfy the phenomenological bounds A 0(1O~ 3 eV) (as discussed in another talk at this Conference 36 ) and Aweak ~ 0 ( 1 TeV), with the intriguing numerical coincidence A cosra ~ A2weak/MP. Are the two hierarchy problems related? It turns out that they are in supergravity and superstring theories, where supersymmetry becomes a local symmetry and gravity is automatically included. In these theories, formulating an acceptable model for SUSY breaking is difficult, precisely because the problem of the weak scale (most probably linked to the scale of SUSY-breaking masses) and the problem of the cosmological constant scale must be addressed at once. Many theorists feel that models formulated in more than four space-time dimensions may offer unconventional solutions to these problems and, perhaps, some exotic phenomenology to be explored experimen-
401
tally. Since these models are the subject of another talk at this Conference 3 7 , some comments related with electroweak symmetry breaking and the gauge hierarchy problem will be sufficient here (for other recent reviews and references on extra dimensions, see e.g. Ref. 3 8 ). One of the most interesting features of models with extra dimensions is the fact that the hierarchy Mweak/Mp can be linked with some geometrical object, in the simplest case a compactification radius R characterizing the size of one or more compactified dimensions. Such a relation is strongly model-dependent. In toroidal compactifications, we can get power-like relations such as (M^eak/Mp) oc R~n, where n is an integer and the dimensionful proportionality coefficient is model-dependent. In 'warped' compactifications, we can get exponential relations of the form (Mweak/Mp) ~ exp(—MpR). The gauge hierarchy problem is then reformulated in a very interesting way: it amounts to understanding the stability and the dynamical origin of the value of the radius R that fits the phenomenological value of Mweak. There is no compelling idea so far in this direction, but some intriguing features are emerging and are at the center of an intense theoretical activity. Before describing some of the possibilities, it is worth mentioning that the problem of determining R is analogous to the problem of understanding the stability and the dynamical origin of Amsusy, the scale of SUSY-breaking mass splittings, in conventional, four-dimensional models of spontaneous SUSY breaking. The analogy becomes evident in those (higher-dimensional) superstring 39,40 and supergravity 41 models where the radius R does indeed control Amsusy. If there are symmetries of the higherdimensional theory whose breaking is nonlocal in the extra dimensions, symmetrybreaking quantities may be shielded from UV effects, and determined by the infrared dy-
Fabio Zwirner
The Higgs Puzzle: Experiment and Theory
namics. As an example, the field-dependent one-loop effective potential of some superstring 40 (and field-theory 42 ) compactifications does not contain positive powers of the string scale (cutoff scale A)
that had initially a classical scale invariance, it may be regarded as the analogous of soft breaking in the MSSM. This mechanism may be stable and related to a dimensional transmutation via the 'holographic' picture 47 . Coming back to the main subject of V1(R,4>) = R-4 + R~202 + (p4 + ... , (14) the present talk, what features may emerge for Higgs phenomenology? It may be too where all coefficients have been omitted and early to tell. One possibility is the mixthe dots stand for logarithmic corrections asing between the Higgs boson(s), charged unsociated with the infrared running of the couder the electroweak gauge symmetry, and plings. Starting from a higher-dimensional the spin-0 fields, neutral under the electheory whose symmetries forbid a Higgs mass troweak gauge symmetry, that are associated term (and ignoring the radius dynamics), ran with the compactification radius ('radion') and v = (
402
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner CDF PRELIMINARY Run 1 X)
eorrbired CDF/DO thresholds
95% C.L. upper limits; II bb
X
t
•* —
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80
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_J O X UJ
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04
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.
.
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160
180
200
(GeV/c 2 )
Figure 12. T h e integrated luminosity required per experiment, to either exclude a SM Higgs boson at 95% c.l. or discover it at the 3cr or 5
Standard ModeT~—^^ .
120
;
UI
.
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,
.
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,
,
,
!
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,
,
,
,
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Higgs Mass (GeV/c2) Figure 11. Preliminary upper limits (at 95% c.l.) on production cross-sections times branching ratios, as functions of mjj, from Run I of the C D F experiment.
from CDF 49 (DO had a slightly smaller sensitivity). With the luminosity and detectors of Run I, Tevatron is still more than one order of magnitude away from the sensitivity required by the SM Higgs properties. However, as described in detail in a dedicated study 50 , and summarized in Fig. 12, things will be different, and very challenging, in the near future. For run < 135 GeV, the focus of the present attention, CDF and DO will search for the SM Higgs boson considering its associated production with a weak gauge boson, pp -> V + {H -> bb) (V = W±,Z), and looking at a number of different final states: (Zi/)(6&), {l+r)(bb), {W){bb). Serious backgrounds are Vbb, VV, it, single top, and others. For run > 135 GeV, the channel gg —> H —> W i y W becomes accessible, and the useful final states are (^l^jj) and (l+l~uV). (In this Section I will always stand for e or fi.) The results of Fig. 12 are obtained by combining the statistical power of both experiments and all the channels mentioned
above. The lower edge of the bands is the calculated threshold; the bands extend upward from these nominal thresholds by 30% as an indication of the uncertainties in btagging efficiencies, background rate, mass resolution, and other effects. The Higgs hunt will continue at the LHC (whose status is summarized by another talk at this Conference 3 4 ) . In the mass region run > 130 GeV, the job of the ATLAS and CMS experiments will be relatively easy, thanks to the gold-plated channel H -> ZZ^ -> 4 ^ , with other channels as a backup for the mass regions with less statistics: H -+ W W W —• Ivlv for mH ~ 2mw ± 30 GeV, H -> ZZ -> l+l~i>v (and possibly H —>• WW -> li/jj or H -+ ZZ -> l+l~jj) for mH > 600 GeV. In the case of a light Higgs, m # < 130 GeV, various different signals are available. Earlier studies have defined the strategies for signals such as inclusive H —> 77, it + (H —> bb, 77) and V + (H —• bb, 77). The combined discovery potential of the ATLAS and CMS experiments, for different integrated luminosities, is summarized 51 in Fig. 13. During the last year, there was progress 52 in the study of the channel qq —> (WW -> H)+jj: exploiting the two tagged forward jets, the
403
Fabio Zwirner
The Higgs Puzzle: Experiment and Theory gated
56
. The NLO QCD corrections to ~> tiH + X were computed by two different groups 57 .
PP{PP) L = 10tV' l- = 30fb'' L-lOOfb'1
ATLAS + CMS (noK-factors)
6
10
(GeV)
Figure 13. Sensitivity for the discovery of a SM Higgs boson at the LHC, as a function of mu • The overall statistical significance, integrated over different channels, is plotted for three different integrated luminosities (10, 30 and 100 f b - 1 ) , and assumes the combined statistical power of the ATLAS and CMS experiments.
background can be consistently reduced, allowing the study of decay channels such as H -^ W^W* -> lul'v, which may be a discovery mode for TO# ~ 115 GeV. There are many other recent phenomenological studies on Higgs physics at highenergy colliders that would deserve a detailed discussion. Time limitations just permit a brief mention of some SM studies, with reference to the corresponding papers, leaving aside analogous studies for the MSSM and for more exotic possibilities. Soft and virtual NNLO QCD corrections to gg —> H + X have been computed 5 3 . 'Strong' weak effects at high-energies (Bloch-Nordsieck violations) were studied 54 : in particular, (ayy/7r)log (s/m^y) corrections to a(e + chadrons) and an enhanced mu dependence in WLWL —> hadrons. The crosssection for Higgs + 2 jets via gluon-gluon fusion was computed 55 . High-px Higgs signals from WW —> H —> bb were investi-
404
Conclusions
In the presence of an experimental and theoretical puzzle, as recalled by the title assigned to this talk by the Organizers, conclusions can only be tentative. It is clear that the search for the 'Higgs boson' (or, more generally, for the dynamics underlying the spontaneous breaking of the electroweak gauge symmetry) is the main goal of high-energy physics in the present decade. Direct searches and electroweak precision tests strongly constrain the possibilities: with the presently available information, the existence of at least one light Higgs boson with SM-like (or MSSM-like) properties looks like the best bet, but there is still room for the unexpected. It is important to stress that, in all 'natural' models, the Higgs boson is not alone: the accompanying physics may be even richer in implications (as, for example, in the case of supersymmetry), and we must be prepared to fully explore the TeV scale. While not very successful so far, the theoretical search for plausible alternatives to the SM and the MSSM is worth pursuing, as confirmed by the many ongoing activities along different directions, in particular extra dimensions. The final (scientific) judgement is coming, and experiment will express it with the help of run II of the Tevatron, of the LHC, and hopefully more facilities to come . . . In our quest for the fundamental laws of Nature, there is no substitute for the highenergy frontier!
Fabio Zwirner
The Higgs Puzzle: Experiment and Theory
Questions
Pietro Slavich for useful comments. This work was supported in part by the European Union under the contracts HPRN-CT2000-00149 (Collider Physics) and HPRNCT-2000-00148 (Across the Energy Frontier).
Q. Bennie Ward, MPI and Univ. of Tennessee: There is the ultra-conservative view that we have a light Higgs, they will find it and there is nothing else. It is that way because God made it like that, unnatural or not. The theories in extra dimensions you mention are non-renormalizable so, if you would find them, you are still left with their non-renormalizable artifacts. Why would you say one of these scenarios is better than the other? A. In view of naturalness arguments, the possibility of finding a light Higgs and nothing else at the weak scale seems unlikely. Rigorously, we cannot exclude that the gauge hierarchy problem is solved by mysterious infrared-ultraviolet connections that we are unable to understand with the tools of conventional quantum field theory. However, not even the cosmological constant violates so far the naturalness criterion, since gravitational interactions have been tested only up to energy scales of the order of 10~ 3 eV, not far from the phenomenological value of Acosm in the normalization of Eq. (13). Coming to the second part of your question, extra dimensions are just one out of many possibilities for the new physics at the Fermi scale. Their phenomenology may be described by an effective field theory, but the latter must eventually find an ultraviolet completion: this may be provided, for example, by an underlying superstring theory. Acknowledgments The author would like to thank Riccardo Paramatti and Paolo Valente for precious technical help in the preparation of the talk, Giuseppe Degrassi for discussions on the content of section 1.2, Juliet Lee-Franzini and
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References 1. P.W. Higgs, Phys. Lett. 12, 132 (1964); Phys. Rev. Lett. 13, 508 (1964); Phys. Rev. 145, 1156 (1966); F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964). 2. R. Barbieri, these Proceedings. 3. G.G. Hanson, these Proceedings. 4. The LEP Higgs Working Group, LHWG Note/2001-03, hep-ex/0107029. 5. J. Drees, these Proceedings. 6. A summary of the preliminary results of the LEP Electroweak Working Group is available at the LEPEWWG home page, http://lepewwg.web.cern.ch/LEPEWWG 7. A. Freitas, W. Hollik, W. Walter and G. Weiglein, Phys. Lett. B 495, 338 (2000) [hep-ph/0007091]. 8. J. Z. Bai et al. [BES Collaboration], hep-ex/0102003; R. R. Akhmetshin et al. [CMD-2 Collaboration], hepex/9904027. 9. H. Burkhardt and B. Pietrzyk, Phys. Lett. B 513, 46 (2001). 10. A.D. Martin, J. Outhwaite and M.G. Ryskin, Eur. Phys. J. C 19, 681 (2001) [hep-ph/0012231]. 11. F. Jegerlehner, hep-ph/0104304. 12. L. Demortier, R. Hall, R. Hughes, B. Klima, R. Roser and M. Strovink [The Top Averaging Group for the CDF and DO Collaborations], FERMILABTM-2084. 13. M.S. Chanowitz, hep-ph/0104024. 14. N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Nucl. Phys. B 158, 295 (1979). 15. G. Isidori, G. Ridolfi and A. Strumia, Nucl. Phys. B 609, 387 (2001) [hep-
Fabio Zwirner ph/0104016]. 16. C D . Froggatt, H.B. Nielsen and Y. Takanishi, hep-ph/0104161. 17. J. Ellis, these Proceedings. 18. G. Altarelli, F. Caravaglios, G.F. Giudice, P. Gambino and G. Ridolfi, JHEP 0106, 018 (2001) [hep-ph/0106029]. 19. H. Georgi, H. R. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974); S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D 24, 1681 (1981); L. E. Ibanez and G. G. Ross, Phys. Lett. B 105, 439 (1981). 20. J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B 257, 83 (1991) and Phys. Lett. B 262, 477 (1991); Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85, 1 (1991) and Phys. Lett. B 262, 54 (1991); H. E. Haber and R. Hempfling, Phys. Rev. Lett. 66, 1815 (1991). 21. R. Hempfling and A.H. Hoang, Phys. Lett. B 331, 99 (1994) [hepph/9401219]; S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Rev. D 58, 091701 (1998) [hep-ph/9803277]; Phys. Lett. B 440, 296 (1998) [hepph/9807423]; Eur. Phys. J. C 9, 343 (1999) [hep-ph/9812472]; Phys. Lett. B 455, 179 (1999) [hep-ph/9903404]; R. Zhang, Phys. Lett. B 447, 89 (1999) [hep-ph/9808299]; J.R. Espinosa and R. Zhang, JHEP 0003, 026 (2000) [hepph/9912236]; G. Degrassi, P. Slavich and F. Zwirner, Nucl. Phys. B 611, 403 (2001) [hep-ph/0105096]. 22. J.R. Espinosa and R. Zhang, Nucl. Phys. B 586, 3 (2000) [hepph/0003246]. 23. A. Brignole, G. Degrassi, P. Slavich and F. Zwirner, preprint DFPD-01/TH/40, RM3-TH/01-14, ROME1-1327/01, to appear. 24. The LEP Higgs Working Group, LHWG Note/2001-04 [hep-ex/0107030], LHWG Note/2001-05 [hep-ex/0107031], LHWG
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25.
26.
27.
28.
29.
30. 31.
32. 33. 34. 35. 36. 37. 38.
39.
40.
406
Note/2001-06 [hep-ex/0107032] and LHWG Note/2001-08 [hep-ex/0107035]. T. AfFolder et al. [CDF Collaboration], Phys. Rev. Lett. 86, 4472 (2001) [hepex/0010052]. M. Carena, J.R. Ellis, A. Pilaftsis and C.E. Wagner, Phys. Lett. B 495, 155 (2000) [hep-ph/0009212]. S. Ambrosanio, A. Dedes, S. Heinemeyer, S. Su and G. Weiglein, hepph/0106255. T. Appelquist and C.W. Bernard, Phys. Rev. D 22, 200 (1980); A.C. Longhitano, Phys. Rev. D 22, 1166 (1980) and Nucl. Phys. B 188, 118 (1981). B.A. Kniehl and A. Sirlin, Eur. Phys. J. C 16, 635 (2000) [hep-ph/9907293]; J.A. Bagger, A.F. Falk and M. Swartz, Phys. Rev. Lett. 84, 1385 (2000) [hepph/9908327]. W. Buchmuller and D. Wyler, Nucl. Phys. B 268, 621 (1986). L.J. Hall and C. Kolda, Phys. Lett. B 459, 213 (1999) [hep-ph/9904236]; R. Barbieri and A. Strumia, Phys. Lett. B 462, 144 (1999) [hep-ph/9905281]; C. Kolda and H. Murayama, JHEP 0007, 035 (2000) [hep-ph/0003170]. M.E. Peskin and J.D. Wells, Phys. Rev. D 64, 093003 (2001) [hep-ph/0101342]. Y.Y. Kim, these Proceedings. L. Maiani, these Proceedings. R. Heuer, these Proceedings. M. Turner, these Proceedings. L. Randall, these Proceedings. I. Antoniadis and K. Benakli, Int. J. Mod. Phys. A 15, 4237 (2000) [hep-ph/0007226]; V. A. Rubakov, hepph/0104152. R. Rohm, Nucl. Phys. B 237, 553 (1984); C. Kounnas and M. Porrati, Nucl. Phys. B 310, 355 (1988); S. Ferrara, C. Kounnas, M. Porrati and F. Zwirner, Nucl. Phys. B 318, 75 (1989). I. Antoniadis, Phys. Lett. B 246, 377
The Higgs Puzzle: Experiment and Theory
Fabio Zwirner (1990). 41. J. Scherk and J. H. Schwarz, Phys. Lett. B 82, 60 (1979) and Nucl. Phys. B 153, 61 (1979); P. Fayet, Phys. Lett. B 159, 121 (1985) and Nucl. Phys. B 263, 649 (1986). 42. I. Antoniadis, S. Dimopoulos and G. R. Dvali, Nucl. Phys. B 516, 70 (1998) [hep-ph/9710204]. 43. A. Delgado, A. Pomarol and M. Quiros, Phys. Rev. D 60, 095008 (1999) [hep-ph/9812489]; I. Antoniadis, K. Benakli and M. Quiros, hep-th/0108005; R. Barbieri, L.J. Hall and Y. Nomura, Phys. Rev. D 63, 105007 (2001) [hep-ph/0011311]; N. Arkani-Hamed, L.J. Hall, Y. Nomura, D.R. Smith and N. Weiner, Nucl. Phys. B 605, 81 (2001) [hep-ph/0102090]; G.R. Dvali, S. Randjbar-Daemi and R. Tabbash, hep-ph/0102307. 44. H. Georgi, A. K. Grant and G. Hailu, Phys. Lett. B 506, 207 (2001) [hep-ph/0012379]; R. Contino, L. Pilo, R. Rattazzi and A. Strumia, JEEP 0106, 005 (2001) [hep-ph/0103104]; N. Arkani-Hamed, A. G. Cohen and H. Georgi, Phys. Lett. B 516, 395 (2001) [hep-th/0103135]. For some works appeared after the Conference, see also: D. M. Ghilencea, S. Groot Nibbelink and H. P. Nilles, hep-th/0108184; C. A. Scrucca, M. Serone, L. Silvestrini and F. Zwirner, hep-th/0110073. 45. C. Kounnas, F. Zwirner and I. Pavel, Phys. Lett. B 335, 403 (1994) [hepph/9406256]. 46. W.D. Goldberger and M.B. Wise, Phys. Rev. Lett. 83, 4922 (1999) [hepph/9907447]. 47. N. Arkani-Hamed, M. Porrati and L. Randall, JEEP 0108, 017 (2001) [hep-th/0012148]; R. Rattazzi and A. Zaffaroni, JHEP 0104, 021 (2001) [hep-th/0012248]. 48. G.F. Giudice, R. Rat-
407
49. 50. 51.
52.
53.
54.
55.
56.
57.
tazzi and J.D. Wells, Nucl. Phys. B 595, 250 (2001) [hep-ph/0002178]; E. Perazzi, G. Ridolfi and F. Zwirner, Nucl. Phys. B 574, 3 (2000) [hep-ph/0001025] and B 590, 287 (2000) [hep-ph/0005076]. L. Moneta [CDF collaboration], hepex/0106050. M. Carena et al, hep-ph/0010338. F. Gianotti, based on the ATLAS Technical Design Report, CERN/LHCC/9914. For a recent review, appeared after this Conference, see also: J. G. Branson, D. Denegri, I. Hinchliffe, F. Gianotti, F. E. Paige and P. Sphicas (for the ATLAS and CMS Collaborations), hepph/0110021. N. Kauer, T. Plehn, D. Rainwater and D. Zeppenfeld, Phys. Lett. B 503, 113 (2001) [hep-ph/0012351]. S. Catani, D. de Florian and M. Grazzini, JHEP 0105, 025 (2001) [hep-ph/0102227]; R.V. Harlander and W.B. Kilgore, Phys. Rev. D 64, 013015 (2001) [hep-ph/0102241]. M. Ciafaloni, P. Ciafaloni and D. Comelli, Phys. Rev. Lett. 87, 211802 (2001) [hep-ph/0103315] and Nucl. Phys. B 613, 382 (2001) [hepph/0103316]. V. Del Duca, W. Kilgore, C. Oleari, C. Schmidt and D. Zeppenfeld, Phys. Rev. Lett. 87, 122001 (2001) [hepph/0105129]. V.A. Khoze, A.D. Martin and M.G. Ryskin, Eur. Phys. J. C 21, 99 (2001) [hep-ph/0104230]. W. Beenakker, S. Dittmaier, M. Kramer, B. Plumper, M. Spira and P.M. Zerwas, Phys. Rev. Lett. 87, 201805 (2001) [hep-ph/0107081]; L. Reina and S. Dawson, Phys. Rev. Lett. 87, 201804 (2001) [hep-ph/0107101].
T H E M U O N ANOMALY: E X P E R I M E N T A N D T H E O R Y J. P. MILLER for the Muon (g-2) Collaboration1 Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215 USA E-mail: [email protected] A summary is given of the present status of the theory and experiment of the anomalous magnetic moment of the muon. A difference between predicted and measured values is an indication of physics beyond the Standard Model. A new experimental measurement has produced a value which differs from a recent Standard Model prediction by about 1.6 standard deviations. When first announced, the discrepancy was about 2.6 standard deviations, but theorists have recently found an error in the sign of the largest term in the standard model hadronic light-by-light contribution which reduces the difference. Additional d a t a are being analyzed and elements of the theory are being scrutinized to provide, in the future, a sharper test of theory.
1
Introduction
The magnetic moment of a particle is given in terms of its spin by
U=
9&
2mc
3
and the anomaly is defined as a = \(g — 2). Historically, the measurement of particle magnetic moments has been a valuable test of existing theories. For example, magnetic moment measurements on the hyperons have provided essential information on their substructure, and the electron anomaly has been the most stringent test of QED. The Dirac theory predicts that g = 2 (a — 0) for point particles with spin \. While the hyperons have g factors very different from 2 because of their complex substructure, the leptons have j w 2 and anomalies which are nearly zero, consistent with the current evidence that they are point particles. The Standard Model predicts lepton anomalies on the order of one part in 800 due to their field interactions. In the cases of the electron and the muon, both the Standard Model predictions and the measurements are extremely precise, a relatively rare situation resulting in valuable tests of the theory. As we shall
see, however, the muon typically has a much stronger sensitivity than the electron to any physics which has not been included in the Standard Model. By far the largest contribution to the lepton anomalies comes from the lowest order electromagnetic diagram, the Schwinger term (left diagram in Fig. 1), which gives a{QED;\) = ^ , e.g. the same for muons and electrons. The next order electromagnetic diagrams, which involve virtual lepton (Fig. 1) or hadron (Fig. 2) loops, are small compared to the Schwinger term, however, they are much larger for the muon than the electron as a result of the additional available rest mass energy. The difference in the contribution between the electron and muon in diagrams involving massive virtual particles typically scales as (2^-) 2 « 40000, and it is this large factor which makes aM far more sensitive than ae to any unknown massive particles. It is instructive to compare the values of the electron and muon anomalies. From Penning trap 2 experiments, we have for the electron aeex_p = (1159652.1884 ± .0043) x 10" 9 (4 ppb) and positron aeef = (1159652.1879 ± .0043) x 10~ 9 (4 ppb), agreeing within errors as required by CPT invariance. These val-
408
J. P. Miller
The Muon Anomaly: Experiment and Theory
QED
(9.4 ppm)
H+
CERN
(10 ppm) E821 (97) n+
-•
(13 ppm)
-
(5 ppm)
E821 (98)
n+
1 o o
| o o
O O
O i—
a>
LO CD
CT> LO CO
592 ooo
Figure 1. QED contributions to the anomaly. The first diagram is the lowest-order Schwinger term. The other diagrams are representative of higher-order QED contributions.
-
(1.3 ppm) E821 (99) H+ I I 1 I II II II1M I M M I | IMI | M M | M M
CD
o o o CO
CJ> LO CO
o
o o - *
LO CD
o
o _ o ^Z LO
a)
LO CD
'
o
i— X
Figure 3. Experimental measurements of a M .
yh Figure 2. The first-order hadronic diagram.
ues are are in good agreement with the theoretical prediction of QED to fourth order in f, af = (1159652.1535 ± .0240) x 10~ 9 (21 ppb) 3 . The theoretical error is dominated by the error in the value of a taken from Quantum Hall Effect experiments. If one assumes the correctness of QED, then the best determination of a comes from the electron anomaly measurements. T h e hadronic and electroweak contributions, 1.63(3) x 1 0 - 1 2 and 0.030 x 10~ 12 , respectively, are small and the errors are negligible compared to the experimental errors. The theoretical and experimental values for the aM are not known nearly as well as for ae. In 1999, prior to t h e new published result, the world average of measured values was ae*p = (1165920.5 ± 4.6) x 10" 9 (4 ppm). This included 9.4 and 10 ppm results for the positive and negative muon, respectively, in a series of famous experiments at CERN ending in the 1970's, 6 as well as the results from the new Brookhaven muon (g-2)
409
experiment (E821) using positive muon data taken in 1997 (13 ppm) 7 and 1998 (5 ppm) 8 . All of these measurements are in agreement within their errors, as shown in Fig. 3; the negative muon data were incorporated under the assumption of CPT invariance. Using the recent published compilation of the theoretical ingredients to a^ by Czarnecki and Marciano, 3 af = (1165915.96 ±0.67) x 10" 9 (0.6 ppm), which used the hadronic evaluation by Davier and Hocker,4 we find that agreement between experiment and data was -,th good: (4.5 ± 4.7) x 10" 9 . Recently, an error in the hadronic light-by-light contribution was found, 30 which changes the theoretical prediction to off = (1165917.68 ± 0.67) x 10" 9 (0.6 ppm). This improves the agreement between theory and experiment: ,th =_ (2.8 ±4.7) x 10 - 9 ..exp The new experimental result for aM+, based on a sample of 1 billion positrons collected in 1999 by E821, 9 is ajf p (£821) = (1165920.2±1.4±0.6) x 10" 9 (1.3 ppm). The new world value changes very little, ae*p = (1165920.3 ± 1.5) x 10" 9 (1.3 ppm). Comparing with the uncorrected theoretical number gives a, 2.6 a difference between measurement and theory: Aa^ = a^p < = (4.3± 1.6) x 10" 9 (3.7 ± 1.4 ppm). Including the
The Muon Anomaly: Experiment and Theory
J. P. Miller light-by-light correction, Aa M = a^p — aft = (2.6 ± 1.6) x 10" 9 (2.2 ± 1.4 ppm), a 1.6a difference. Two additional data sets, from 2000 and 2001 runs, are currently being analyzed. The 2000 data set consists of about 4 billion events for the /x+ and 2001 consists of about 3 billion events for the /J,~ . The original stated goal of E821 was to reduce the anomaly measurement error to 0.35 ppm. Ideally, one would also equalize the errors on the /x+ and yT in order to optimally test CPT invariance and to study systematic issues in the experiment. We expect to come close to this goal, but this will require a future data run with 6 billion events. 2
Theory Status
The Standard Model contributions to a^ can be conveniently separated into QED, electroweak, and hadronic portions. Although the anomaly is dominated by the QED contribution, there are significant hadronic and EW contributions at the level of « 58.3 ppm and « 1.3 ppm, respectively. We discuss each of these contributions below, with emphasis on the hadronic contribution, whose error dominates the overall error in af/1. The QED contribution, using a from aexp a n c j c a i c u i a t e d to fifth order in — (some of the highest order diagrams were estimated), contributes 3 an error of 21 ppb to aft, a^ED = 116584705.7(2.9) x 1 0 ~ n . Kinoshita 10 reports that some of the fourth order terms are being re-calculated with 128 bit precision, which may result in a small shift in the QED contribution; this is expected to have minimal impact on the comparison between experimental and theoretical values of The lowest order electroweak diagrams, involving the exchange of a W, Z or Higgs, are shown in Fig. 4. The electroweak contribution, including the 25% reduction from higher order terms, is 3 a^w — 151(4) x
+389
-194
<1 -ll
X 10 Figure 4. Lowest-order electroweak contributions.
10 _11 (1.30 ± 0.03)ppm. The theoretical uncertainty is very small. The central value is right on the edge of the current experimental error, and it will be a significant contribution at the experimental error goal of 0.35 ppm. The lowest order hadronic diagram is shown in Fig. 2, where a hadron loop has been inserted into the Schwinger diagram. Since these contributions involve the strong interaction at low energies, they cannot be calculated from first principles. Their contribution can, however, be determined from measured e+e~ scattering cross sections over all energies through the use of the dispersion relation, Eq. 1, (also see Fig. 5(a))
a,(had;l)
= ( ^ )
2
f°° ^K(s)R(s)
(1)
K(s) is a slowly varying function and the e+e~ data enter through the ratio of cross sections, R(s) = ' ' f f . ^ ' . The low energy data are the most important as a result of their large amplitude and the \ term in the integrand, where y/s is the center-ofmass energy. High quality hadronic T decay data from LEP and Cornell can be used to augment the isovector part of the e+e~ data at energies below mTc2 (second diagram in Fig. 5) using isospin invariance (to relate for example 7r-7r° channels in r decays to ir+ir~ channels in e+e~ collisions) and the CVC hypothesis (to connect the W~ and photon intermediate states). 11 There have been a number of evaluations of a M (had;l) over the past two decades. We
410
J. P. Miller
The Muon Anomaly: Experiment and Theory
V/vwi^r (a) Figure 5. The electron scattering and tau decay diagrams relevant to the determination of the lowest order contribution to a^.
Table 1. As of 1995, contributions to a^(had;l) as a function of e+e~ energy, illustrating the (soon-to-be obsolete) sources of error. 1 2 . W i t h the incorporation of new e + e ~ and T data, the errors below 5 GeV decrease significantly from the values shown in the table.
V^GeV
a^had; 1)
Error, ppm
<1.4
87. %
1.29
1.4-• 2.0
4.6%
0.21
2 . 0 - • 3.1
4.0%
0.30
2.0 -> 2.6
2.9%
0.27
2.6-> 3.1
1.1%
0.12
J / * (6 states)
1.3%
0.08
QCD 3.1 - • oo
3.0%
0.03
Total
800
1000
900
Eon,
MeV
Figure 6. Preliminary pion form factor d a t a from Novosibirsk in the vicinity of the p resonance. 1 3 Inset: data the u> interference region.
1.37
will look in some detail at those performed since 1995. The contributions of e+e~ data to a^had; 1) in different energy ranges, from the evaluation by Brown and Worstell, 12 are indicated in Table 1. (We note that the new data which are becoming available will render this table obsolete.) The largest contribution to the value and error are for y/s < 1.4 GeV, a region dominated by the effects of the p resonance (see Figs. 6-8). The other energy ranges give a considerably smaller contribution to the error, however for an 0.35 ppm measurement they cannot be neglected, particularly in the range 1.4 —» 2.6 GeV. Since 1995, there has been a substantial improvement in the data quality, but major
411
portions of the data are either preliminary or are still in the process of being incorporated into evaluations of a^(had;l). Data on the pion form factor (which can be directly related to the e+e~ cross section) from the CMD2 and SND experiments at the VEPP-2M accelerator in Novosibirsk are nearing publication. They cover the important energy range \/s < 1.4 GeV. Preliminary data in the p resonance range (600 to 930 MeV) from CMD2 are shown in Fig. 6. 13 Their anticipated systematic error of 0.6% in this range would reduce the error contribution from the e+e~~ data in this energy region by better than a factor of two. The VEPP2000 project is an upgrade under construction at Novosibirsk which will extend quality e+e~ measurements up to 2 GeV, with an order of magnitude or more improvement in luminosity. Data relevant to the low energy region are also being taken by the KLOE 14 experiment at DA^NE. They operate at the mass, and then derive e+e~ cross sections at lower energies using the so-called radiative
The Muon Anomaly: Experiment and Theory
J. P. Miller
•
BESII 1999(Prellmlnary)
•
BESII 1998, P B L 84(2000)594
O
Gamma2
D
Mark)
•
pluto
o 60°<6r<120' • 5°<0I<21°
Figure 8. Preliminary and published e + e ~ data, 2-5 GeV, from BESII, along with older d a t a from other experiments 1 5 . 400
500
700
800 900 2 K invariant mass, MeV
been produced over the last few years as described by P. Roudeau at this conference, have significantly reduced the contribution to Figure 7. Preliminary pion form factor d a t a from rathe error of a M (had;l) for energies below the diative return measurements (KLOE). 1 4 r mass. 11 In addition, new analysis results should be available soon from ALEPH. 16 17,18 have questioned, however, return method. In this approach, the initial Some authors whether there are sufficient controls over rastate electron or positron radiates away some diative corrections and corrections to the apof its energy via a photon, providing access to scattering at energies below the <j> mass. proximations of CVC and isospin invariances. Preliminary data are shown in Fig. 7. Cur- In addition, there appears to be an overrently their systematic errors are on the or- all normalization disagreement between the 19 der of a few percent, however, they expect to T data from ALEPH and Cornell. The r improve this in the near future to the point data represent, nevertheless, valuable addi+ that they are competitive with the Novosi- tions and checks on the e e~ data at low enbirsk data. This measurement, along with ergies, and various groups plan to study these possible plans at other e+e~ machines such issues in the future. as the B-factories and Cornell which have acA list of a M (had;l) evaluations is given cess to higher energies, will contribute signif- in Table 2. Various combinations of ingrediicantly to the next wave of precision e + e~ ents were used: e+e~ data from a wide range data. of experiments, r decay data from LEP and There are new, preliminary and published data from BESII 15 in the important energy range 2 - 5 GeV (Fig. 8). Note especially that in the range 2 — 3 GeV, which has the largest contribution to ^ ( h a d j l ) , BESII data have much smaller errors and the central values are 15% lower compared to the old MARK I and Gamma2 data. High quality r decay data, which have
CESR, or theoretical input from perturbative QCD (pQCD) in the higher energy regions where it can be relied upon but where the data quality is poor. Eidelman and Jegerlehner 20 , EJ95, relied primarily on e+e~ data, using pQCD only at the highest energies (> 20 GeV). Brown and Worstell 12 , BW96, used essentially the same data set as EJ95, but took into account the
412
J. P. Miller
The Muon Anomaly: Experiment and Theory
correlation of errors among data points coming from the same experiment. BW96 and EJ95 values and errors are in excellent agreement, suggesting that the correlation issue was not so important. Adel and Yndurain 21 , AY95, used pQCD in regions where the e+e~ data were poor, and obtained a value somewhat higher than, but still in agreement with, EJ95 and BW96. The theoretical input enabled hem to quote a smaller error. In 1998, Adelman, Davier and Hocker, 11 ADH98, did a full re-evaluation using updated values of the data sets used by EJ95 and BW96, obtaining the same error and a central value which was lower but still consistent within errors. ADH98 then incorporated the high quality r data from ALEPH, producing a dramatic improvement in the error of the contribution below the T mass, and reducing the overall error in a^ by 40%; inclusion of T data increased the central value somewhat. Subsequently, Davier and Hocker 22 , DH98a, refined the e + e - and r evaluation of ADH98 by applying pQCD above 1.8 GeV in regions where the data were poor, resulting in another 20% decrease in the error and a decrease in the central value. Most of the changes can be attributed to the effect of using pQCD from 1.8 to 3 GeV, where the old data are rather poor, as seen in Fig. 8. The DH98a evaluation was done before the new BESII data (Fig. 8) were available in this energy range; their pQCD calculations are in very good agreement with the BESII data, and about 15% below the old data, pointing to the reliability of pQCD at these energies. In a subsequent work (DH98b) the same authors applied QCD sum rules at low energies, resulting in slight further reductions in error and central value. The value from DH98b was used in the Czarnecki and Marciano 3 theoretical compilation and also by E821 9 to compare with their new experimental number. Some preliminary and published theoretical evaluations of a M (had;l) have appeared since the E821 publication of Brown, et al. 9
413
Table 2. A list of a number of recent evaluations of a,n(had; 1). T h e last entry is the E821 experimental 'measurement' of a M (had;l), obtained by subtracting the QED, E W and higher order hadronic contributions from the experimental number. This is an updated version of a similar table found in Ref. 26 .
Ref.
a^,(had; 1) (xlO 1 1 )
Comment
EJ95 2 0
7024(153)
e+e-
BW96 12
7026(160)
e+e~
AY95 21
7113(103)
e+e",QCD
6950(150)
e+e-
ADH98 11
7011(94)
e+e~,T
22
6951(75)
e+e_,r pQCD
DH98b 4
6924(62)
e+e~,T pQCD, sum rules
N01 2 3
7021(76)
e+e~,T
TY01 2 4
6966(73)
e+e_,r space-like Fv
E01 2 5
6932(65)
e+e-
E821 9
7350(153)
Expt -[ QED +EW+(Had>l)]
ADH98
DH98a
11
J. P. Miller
The Muon Anomaly: Experiment and Theory
Narison 23 , N01, has used essentially, the same r and e+e~ data sets at low energies and for the resonances as ADH98, with QCD applied to the continuum at the higher energies (> 1.7 GeV), arriving at nearly the same value as ADH98, but with a slightly smaller error. Troconiz and Yndurain 24 , TY01, have applied the maximum available data (including some preliminary data) and theory, following the earlier approach of AY95, and also incorporated pion form factor data from pion scattering at low energies, to arrive at a value which compares closely to DH98b, with a slightly larger central value and error.
Fig. 10 (LOL), presents special problems because, unlike other hadronic terms, it cannot be estimated based on experimental data. The value used in Czarnecki and Marciano 3 is an average of the values and the errors of two separate determinations 28, 29 (which are in agreement within errors), a^(had;LOL)= —85(25) x 1 0 ~ n . Both calculations use models motivated by chiral perturbation theory to calculate the contributions at low energies. The largest contribution comes from the 7T° pole term, with lesser contributions from the r? and rf poles. Other contributions can be w 20 — 30% in size relative to the pole terms, but when added together they largely cancel. After the publication of the new E821 experimental result 9 and after this talk was given at LP01, Knecht and Nyffeler 30 calculated the pion pole contribution using Large-Arc and short-distance properties of QCD. They obtained virtually the same magnitude as in references 28 and 29 but with the opposite sign: a^had; LOL, 7r°) = +5.8(1.0) x 10" 1 0 . The signs of the 77 and 77' poles also change, however, Knecht and Nyffeler only estimated their magnitude using a VMD model; their total pseudo-scalar contribution is aM(had; LOL, PS) = +8.3(1.2) x 10~ 10 . The sign error has since been acknowledged by the authors of 28 and 29 (see references 3 1 and 3 2 ) . Changing the signs of the pole and axial vector terms, but keeping the other terms as calculated in 28 and 29 the same, increases the theoretical value of aM by 17.2 x 10~~10, very close to just reversing the sign on the entire LOL contribution. Knecht and Nyffeler plan in the future to calculate all of the other terms in the hadronic LOL contribution. Several other groups are also considering new ways to tackle this difficult calculation. Ultimately, the hadronic LOL term may prove to be the limiting factor in the theoretical error of a p .
Finally, Eidelman 13 , E01, has produced a preliminary number based entirely on e+e~ data (except for pQCD at the very highest energies), including the new preliminary results from Novosibirsk and BESII. He obtains a value and error which are almost the same as DH98b. What can we conclude from this series oia^had; 1) determinations? The first thing we note is that within their stated errors, all of the evaluations are in agreement. In particular, the most recent evaluations are in excellent agreement even with their smaller errors, although we note that the DH98b evaluation has the smallest value leading to the largest discrepancy between theory and experiment. Secondly, an analysis which incorporates all of the new r and e+e~ data would be helpful. Eidelman, Davier and Hocker are presently collaborating on such an evaluation. When the final analyses, which include the latest excellent data are completed, we can expect a more reliable value for a^{had; 1) with a smaller error. The higher order hadronic contributions, a^(had;> 1), can be separated into two parts. One part, involving higher order diagrams such as those in Fig. 9, have a relatively small contribution to aM and the error is negligible:27 a^{had;> 1) = -101(6) x lCT 11 . The other part, involving the hadronic light-on-light diagram in
The theoretical error on a^(had;l) has gone down dramatically over the years, and with new, more accurate calculations of the
414
J. P. Miller
The Muon Anomaly: Experiment and Theory
-101 (6) X i d " Figure 9. Some diagrams hadronic contributions.
of
the
higher-order
(Fig 4). If supersymmetry is to explain all of Aa™ew: then its contribution is large: almost two times bigger than the electroweak contribution. Of course, the presently observed AoM may also be due to a statistical variation in the experimental number or to errors in the experiment or theory. When the additional data are analyzed, and with the continued extensive studies of the theory, one can anticipate that major progress will be made in understanding any non-zero AaM.
3
Figure 10. Diagram for the hadronic light-on-light contribution.
light-by-light contribution, the error and reliability of a1^ should continue to improve significantly. New physics will be reflected by a nonzero value of Aa";ew = afj°p — a*!1. Some fj,
\L
IX
examples are muon substructure, anomalous gauge couplings, leptoquarks, or supersymmetry. In a minimal supersymmetric model with degenerate sparticle masses (see Fig. 11), the contribution to Ao™£"' would be substantial in the case where tan/3 is large: AafSY « 140 x 1 0 - 1 1 ( l ° < f ^ ) 2 t a n / 3 , where rh is the sparticle mass. For 4 < tan/3 < 40, rh « 150 - 500 GeV. Note that the supersymmetric diagrams (Fig 11) are analogous to the electroweak diagrams
Figure 11. Lowest order diagrams for SUSY contributions.
415
Experiment
The ongoing muon (g-2) experiment at Brookhaven National Laboratory, E821, had its beginnings in the early 1980's. Its original goal was to measure aM to 0.35 ppm, or about 20 times better than the CERN 33 experiment. It received Laboratory approval in 1987, and major construction on the storage ring magnet began in the early 1990's. The first data were taken in 1997, with one major run in each year 1998-2001. The experimental technique follows the general one used in the CERN experiment with a number of important improvements and innovations. The Brookhaven AGS delivers up to 7 x 10 12 protons per bunch, with energies of 24 GeV, onto a water-cooled, rotating nickel target. There are 6-12 bunches per « 2.5 second AGS cycle, each about 50 ns wide FWHM and spaced 33 milliseconds apart. Secondary pions emitted from the target with momenta of 3.1 GeV/c are sent down a 72 m straight section of alternating magnetic quadrupoles, where highly polarized muons from forward pion decays are collected. The beam is then momentum-selected for either pions or the slightly lower-momentum muons, and then is injected through a field-free inflector36 region into a circular storage ring possessing a very homogeneous magnetic field. For the case of pion injection, with the pion momentum slightly higher than that of the central storage ring momentum, a small
The Muon Anomaly: Experiment and Theory
J. P. Miller fraction (RJ 25 ppm) of the muons from pion decays will have the correct momenta and directions to be stored. The efficiency of this process is low, and the very high intensity of pions and secondary particles associated with pion interactions with surrounding materials creates severe background problems for the detector system near the injection time ('flash'). An essential improvement over prior experiments was the incorporation of direct muon injection. With muon injection, the number of stored muons is increased by a factor of 10, while the 'flash' is reduced by a factor of 50 because most of the higher-momentum pions are blocked by beam-line collimators. In the homogeneous B field of the storage ring, charged particles follow a circular path (slightly modified by the electric quadrupole field) which would cause them to strike the inflector after one revolution. Muon injection therefore requires an in-aperture magnetic pulse at 90° around the ring from the injection point (provided by the pulsed 'kicker') in order to center the muon orbits in the storage region. With either muon or pion injection, positive (negative) muons are stored in the ring with spins initially polarized anti-parallel (parallel) to their momenta. In a magnetic field (no E-field) the spins precess relative to the muon momenta according to (2a = us — ujc = — a M ^ | . Here toa and coc are the angular frequencies of spin rotation and momentum rotation (or cyclotron angular frequency), respectively. Note that all of the muons precess at the same rate in a given field, regardless of their momenta. Two quantities must be measured with precision to determine aM: (ja and B, each being time averaged over the ensemble of muons. Actually, instead of measuring B, we determine the frequency of precession of the free proton, Up, in the same average magnetic field as the muons via NMR measurements. The anomaly is given by Eq. 2,
where R = $ ^ . A = ^ = 3.183 345 39(10) is the ratio of the muon and proton magnetic moments determined from other experiments 34,5 . The analyses of < toa > and < Up > were independent, and furthermore concealed offsets were maintained in each value so that no one could calculate aM prior to the completion of the analyses. The average trajectories of muons in the storage ring can only be known moderately well. Therefore the B field needs to be as uniform as possible to minimize the dependence of a given muon's precession rate on its exact trajectory in the storage ring. This prohibits the use of a gradient magnetic field to store (focus) the beam. E821 follows the CERN approach of using a quadrupole electrostatic field to provide the focusing. In the presence of the electric field, the precession is described by Eq. 3,
wa = - — [ a „ B - (a„ - -=—-)/? x E] (3) mc 7^ — 1 The "magic" 7 « 29.3, or pM w 3.094 GeV/c, is chosen so that a^ — TTZT[ ~ 0, minimizing the effect of E on Qa. Because not all stored muons have the exact magic momentum, a small correction ( « 0.6 ppm) must be applied to the final value for wa. Equation 3 is strictly valid only for muon motion perpendicular to B; the up-down motion associated with vertical betatron oscillations leads to another small correction of « 0.2 ppm, the so-called "pitch correction". The practical limit to the strength of a ferric field with the required homogeneity is w 1.5T; E821 chose B = 1.45T, leading to a ring radius of 7.112m. The storage ring aperture radius is 4.5 cm, giving a « ±0.6% ( « ±0.4%) base-to-base range in stored momenta for pion (muon) injection. The cyclotron period is r c = 4- = — « 149.2ns, the
416
J. P. Miller
The Muon Anomaly: Experiment and Theory
1,025 miHione*(E- 2 GeV. 1999 data)
Figure 12. Spectrum of number of positrons versus time, from the 1999 d a t a sample. There are a total of 1 billion e+ above 2 GeV.
precession period is Ta « 4.365 /is and the dilated muon lifetime is r = 7-ro ~ 64.38 jus. Decays are typically measured for at least ten muon lifetimes, or about 4000 cyclotron and 150 precession periods. A log plot of the 1999 data set, folded into 100/xs periods, is shown in Fig. 12. The error on aM from the combined / i + and /i~ data sets from the CERN 6 g-2 experiment is 7 ppm with a 1.5 ppm systematic error. By comparison, E821 must keep the systematic errors in B(wp) and ua to less than a few tenths of a ppm to approach its experimental precision goal of 0.35 ppm. 3.1
The Magnet and the of u>p
Determination
The storage ring, 35 Fig. 13, is a continuous C-magnet open to the inside. A cross-section view, Fig. 14, shows its essential features. It contains more than 600 tons of magnet steel. Three superconducting coils, which provide exceptional B-field stability with time, are used to power the magnet. The entire magnet is wrapped in thermal insulation to reduce
417
Figure 13. Overhead schematic view of the storage ring magnet. T h e detectors are distributed in uniform intervals around the inside of the ring. The beam is brought in through a hole in the back of the magnet yoke, indicated by the solid line at 10 o'clock.
gap changes due to temperature change. The storage region of 4.5 cm radius is defined by a series of circular collimators inside an evacuated chamber. The pole gap is 18 cm high and 53 cm wide. Many shimming options were incorporated in order to achieve the desired field uniformity. The very high-quality steel of the pole tips is decoupled from the lower quality steel and the imperfections (including holes for cryogenic leads, etc.) of the yoke, by« means of an air gap. Iron wedges in the gap can be moved radially to locally adjust the dipole field. The thickness and position of iron pole bumps can be adjusted to minimize quadrupole and sextupole fields. Thin sheets of iron were affixed to the pole tips to improve local uniformity. Current-carrying wires attached to circuit boards and mounted on the pole faces, with one set forming a closed loop covering 12° in azimuth and another set going entirely around the ring, provide a final fine-tune of the dipole field. A continuous monitor of the B-field was
J. P. Miller
The Muon Anomaly: Experiment and Theory
ilipn!-. •MiiirciiiMi m i l
Jl'ili' 1W-|'P
l».|l-ii...
DlllCI
Ariiiy »l NMK pilllil'S I111IVI-S
Miron^li lii'.-im luhi' nil r.ililr <MI
g 2 Magnet in Cross Suction
Figure 14. Cross section view of t h e storage ring magnet. The means of shimming t h e magnet and measuring its field are indicated.
Magnetic Field Uniformity (Azimuthal Average, 1 ppm c o n t o u r s , e x c e p t '97)
/^<
-JS~~\ 11 J j
'
\
•
•
•
'
'
/
(
/
/
///l
w
V^'^
/
/"'
provided by 360 NMR probes placed in fixed positions around the ring, above and below the storage region. A subset of probes, those most highly correlated to the average B-field, provided feedback to the magnet power supply to compensate for the slight field drifting which are mainly the result of ambient temperature changes. Two separate off-line analyses of the B-field used somewhat different combinations of probes to determine the average field as a function of time, with comparable results. The B-field in the storage region was mapped in 1 cm intervals every three to four days with 17 NMR probes mounted transversely on a movable cable-driven trolley. This was accomplished inside the vacuum, with essentially no geometrical changes to the magnet or vacuum chamber configuration. The NMR probes on the trolley were calibrated against a standard spherical water NMR probe, which was normalized to the precession frequency of a free proton. The fixed probes, in the off-line analysis, tracked the trolley probes to better than 0.15 ppm over time. The steady improvement in the B-field provided by shimming is illustrated in Fig. 15. The marked improvement from 1999 to 2000 is attributable to the replacement of the inflector, which had a damaged superconducting fringe-field shield.
xlcm
1 9 9 7 run
-S^^\
1 9 9 8 run
- // \
--—"""^---''^i
' f—"^i 1 9 9 9 run
2 0 0 0 run
Figure 15. B-field contours across the storage region in E821, averaged in azimuth, for succeeding run cycles. The 1997 contours are 2 ppm, the rest 1 ppm.
418
The distribution of muons inside the storage region was determined from an analysis of the debunching of the beam as a function of time. At the time of injection, muons are localized in the ring with a full width at half maximum of about 120 degrees. As a result, the time spectrum from a given detector at early times will contain oscillations with a period equal to the cyclotron period (the so-called "fast rotation" structure). Muons with high momenta have smaller cyclotron frequencies than those with low momenta, causing the bunches to spread out around the ring and the amplitude of the oscillations to diminish with time ("debunching" lifetime w 20/xs). The analysis of the debunching ver-
J. P. Miller
The Muon Anomaly: Experiment and Theory
Table 3. Systematic errors in wp for the 1999 data set.
Source of errors
Error (ppm)
Inflector fringe field
0.20
Fixed probe calibration
0.20
Fixed probe interpolation
0.15
Trolley Bo measurements
0.10
H distribution
0.12
Absolute calibration
0.05
Others 1
0.15
Total Syst error on UJP
0.4
' higher multipoles, trolley temperature stability, kicker eddy currents.
3.2
Determination ofu>a
The decay positrons from //+ —> e+uePfl have energies in the range 0 —• 3.1 GeV. In the muon rest frame, the higher energy positrons are preferentially emitted parallel to sM+. When the muon spin is parallel to the muon momentum, there will be more high energy muons in the lab frame than when the directions are anti-parallel. The number of positrons in the lab frame above a given energy threshold Et versus time therefore oscillates at the precession frequency according to Eq. 4,
N{t) = N0e-i
x
(l + Acos(w a i + (/>a),
sus time gave the radius of curvature distribution of the muons, which in combination with simulations of the betatron motion of the muons produces the radial and vertical distribution of muons in the storage aperture. The distributions thus deduced were folded geometrically with the map of NMR frequencies to obtain < UJP >. Corroborating information on the horizontal and vertical distributions of muons, as well as information on the betatron motion, at early times, was provided by scintillating fiber hodoscopes which could be inserted into the storage region. The hodoscopes were sufficiently thin that useful beam profile data could be taken for many tens of microseconds before the beam was degraded. The final value for the average field is ^ ^ = 61 791 256 ± 25 Hz (0.4 ppm). The sources of systematic errors are given in Table 3. The improvements in the 2000 data set are the installation of a new inflector with far less fringe field, greatly reducing the first item in the Table, and better trolley calibrations.
419
(4)
where each of N0 and A depend strongly on Et, while <pa depends slightly on Et. The positrons, generally having lower momenta than the muons, are swept by the B field to the inside of the storage ring, where they are intercepted by 24 scintillating fiber/lead electromagnetic calorimeters 37 uniformly spaced around the ring. The typical energy resolution of the calorimeters is i? = E(GeV) • Since a low energy positron arrives at the detectors more quickly after muon decay than a high energy positron (the average distance traveled is less), the actual measured times at the detectors relative to the muon decay time will depend slightly on energy, therefore
J. P. Miller
The Muon Anomaly: Experiment and Theory
tomultiplier tubes, whose sum is sent to a waveform digitizer (WFD) 3 8 which samples the photomultiplier pulse height every 2.5 ns. Both the time of arrival and the energy of the positron are determined from the WFD information. For 1999, the analysis occurred in two steps. First, in the production step, WFD data were converted to positron energies and times. There were two separate productions of the data. They each developed independent algorithms to handle the WFD data, which eventually evolved to become similar. The second step involved performing \ 2 minimization fits to the data in Fig. 12 to obtain u>a. The parent distribution in Eq. 4 provided a good x2 fit to the 1998 data sample, with five variable parameters: No, r, A, uia and 4>a. It did not however provide a good fit to the 1999 data, which has 15 times more positrons. It was necessary to account for small but noticeable effects from pulses overlapping in time at high rates (pile-up), betatron motion of the stored muons, and muon losses.
At times close to injection, the bunching of the muons leads, in addition to the previously mentioned oscillations, to an enhancement of the pileup. The oscillations are eliminated from the time spectra by using a bin width = TC, adding to each arrival time a time uniformly randomized over ±-if, and summing all detectors around the ring. The pile-up enhancement is accounted for by the last term in Eq. 6; the constants are held fixed to values determined in separate pile-up studies.
There were four independent analyses of the positron time spectra for the 1999 data set, two for each production. They used different methods to handle these additional effects. The time spectrum, with these additional effects, can be described by a 14 parameter function, Eq. 5 (not all parameters are necessarily variable in a fit):
f(t) = {N0e~i [1 + A cos toat + cf>a} + p{t)} x b(t) x l(t)
(5)
The pile-up term, p(t), with parameters np, Ap, Acfip, is given by Eq. 6
p(t) =
N0e~2i
The amplitude np of pile-up was generally less than 1% even at the earliest decay times, with an asymmetry Ap small compared to the (g-2) asymmetry, A. The artificial pileup spectrum gave the expected | lifetime, and when subtracted from the main spectrum, did a very good job of eliminating events above the maximum electron energy of 3.1 GeV, which apart from energy resolution effects could only be due to pileup. The properties of the artificial pile-up spectrum matched very well with the results of multiparameter pile-up fitting. The coherent betatron oscillation (CBO) term, b(t), with parameters As, UJB, 4>B, and TB, is described by Eq. 7, b(t) = l + ABCos{ujBt + 4>B)-e~(^)'2
x (np + Ap cos (ujat + a + A0 P )) x (l + a p e " ^ ( ^ ) 2 )
Two of the analyses constructed a simulated pileup time spectrum by combining single positron pulses, from data, into pileup pulses. The pileup spectrum was then subtracted from the primary spectrum, thus eliminating the p(t) term from their fits. A third analysis varied np and Ap, with Aa and a.
(6) 420
(7)
The need for b(t) is due to the effects of betatron motion of the muons combined
The Muon Anomaly: Experiment and Theory
J. P. Miller with the restricted aperture of the inflector. Muons are injected into the ring through the inflector, whose aperture was considerably smaller than the storage ring aperture because of mechanical and geometrical limitations. This creates a muon beam with narrow horizontal (1.8 cm) and vertical (5.6 cm) waists at the inflector exit at injection time. The more important horizontal waist case will be discussed here. In a perfectly uniform B field with no electric field, the muon trajectories, projected into the plane of the magnet, are circles. After the muons are kicked, the position of the horizontal waist would ideally be in the center of the storage region. The kick, however, was generally less than 100% of its optimum value. Therefore the average radius of muons at the narrow waist, at injection time, was larger than the central storage region radius. At 180 degrees around the ring from the narrow waist, the muons are spread out to fill the ring aperture, and have an average radius more nearly equal to the central ring radius. The acceptance of the electron calorimeters depends to a slight extent on the horizontal width and especially on the average radial position of the muon beam. Thus the detector positron acceptance will be different at the narrow waist compared to the opposite side of the ring. When we add electrostatic focusing, the position of the narrow waist (or focus) will move around the ring at the so-called CBO frequency, which is the cyclotron frequency minus the horizontal betatron frequency, JCBO = /c(l - v 7 ! - n). For the field index n = -jSr^rh = 0.137, pBo or
'
ICBO ~ 475 kHz. As a result, we get a small oscillation at « 475 kHz superimposed on the time spectrum. The amplitude of the CBO is typically a few tenths of a percent of the total number of counts, and T\, is long, about 100 fj,s.
One analysis allowed all four CBO parameters to vary. Two kept UJB fixed to the value obtained from a Fourier transform of the residuals from a five-parameter fit. The
421
frequencies from the Fourier transform and the fit were in good agreement. The muon loss term, Eq. 8, has two parameters, a^L and T^L,
l{t) = 1 + a^L • e'(^]
(8)
Muon losses are thought to be caused by the slight drift of the orbits of muons whose trajectories bring them close to collimators. The drift could be caused by the small non-uniformities in the E and B- fields, although the exact mechanism is not known. Indeed, when the beam is 'scraped' for about 15 /is right after injection, by temporarily displacing the stored muon beam several millimeters vertically and horizontally in order to force the loss of muons with trajectories close to the collimators. The rate of muon loss is markedly reduced after the scraping is turned off, compared to the no scraping case. After scraping, losses are generally less than i=sl% at early decay times, with the rate of losses decreasing with a short lifetime of T nL ~ 20/j.s. In addition there was a roughly constant loss rate of « 0.1% per muon lifetime at all decay times, as determined by comparing the measured decay rate with that expected from special relativity. The two analyses which allowed both parameters to vary obtained the same loss lifetime as was observed in a third analysis which held T^L fixed to the value determined using separate muon loss detectors. It is important to realize that only two of the 14 parameters in Eq. 5 have a large correlation to uja: (j)a and A
The Muon Anomaly: Experiment and Theory
J. P. Miller
=
N++Nz-N°-N2 N+ + JV2- + ^
Table 4. Results of the four analyses for ioa. R is defined by ioa = 27r/o(l — Rx 1 0 - 6 ) . /o is the nominal precession frequency.
#Par.
2
/DOF
R(ppm)
13
1.012 ±0.023
143.24 ±1.24
10
1.005 ±0.023
143.08 ±1.24
9
1.016 ±0.015
143.30 ±1.23
3
0.986 ±0.025
143.37 ±1.28
X
Avg.
143.17 ±1.24
Table 5. Systematic errors in uia for the 1999 d a t a set.
Source of errors
Error (ppm)
Pile-up
0.13
AGS background
0.10
Lost muons
0.10
Timing shifts
0.10
E field, pitch
0.08
Binning, fit procedure
0.07
Debunching
0.04
Gain changes
0.02
Total Syst error on ua
0.3
+ N%
= Acos(cjat + <pa) + (-^)2
(9)
where N+ = N^t + ?f), JV2" = N2(t - *f), N$ = N3(t), and N% = N4(t). The muon lifetime cancels, and r(t) is sufficiently insensitive to the CBO and the muon losses that these effects can be neglected in the fit. The insensitivity to the CBO is a consequence of — being not so different from ^f. We arrive LOB
I
at a three parameter fit which has different responses to systematic errors compared to the conventional multi-parameter fits. The results of the four analyses are given in Table 4. All of the results are well within the bounds expected for correlated data sets. The final value for toa is the average of these results, f£ = 229072.8 ± 0.3 Hz(1.3 ppm), after a correction of ±0.81 ± 0.08ppm for the effects of the electric field in Eq. 3 and for vertical betatron oscillations ("pitch" correction). 8 Note that the data are not sensitive to the sign of uja; this however is welldetermined from many other experimental measurements, and is implicit in the value of A which we use to extract the value of aM. The sources of systematic error in u>a are given in Table 5. The AGS background is the result of unwanted particle injection into the ring after the initial injection. The improvements for the 2000 data run were the addition of a sweeper magnet in the beam-line to eliminate errors due to the AGS background, and an increase in the number of lost muon detectors in order to reduce the muon loss error. 4
Conclusions and Outlook
The muon anomalous magnetic moment can be both measured and calculated (within the Standard Model) to a high precision, and given its high sensitivity to new physics, its measurement affords an exceptional oppor-
422
J. P. Miller
The Muon Anomaly: Experiment and Theory
tunity to probe for new physics beyond the Standard Model. The new world average value of a+ shows a 2.2 ±1.4 ppm difference from the Czarnecki and Marciano 3 theory compilation, after the sign of the LOL pole term is corrected. Many theoretical ideas have been put forward to explain any difference, including supersymmetry, leptoquarks, muon substructure, etc. It could of course also be explained by a statistical fluctuation, an error in the experiment, or an error in the Standard Model calculation. All aspects of the theoretical calculation of aM are being heavily scrutinized. New high quality e+e" data from VEPP-2M and Beijing as well as r decay data from LEP, are being analyzed now, and should have an impact on aft in the next few months. Longer term, Novosibirsk and Beijing have upgrade plans, and DA$NE (and perhaps the B-factories and Cornell) have plans to use the radiative return process to measure e+e~ cross sections. Further calculations of the lightby-light term are being considered by several groups. One can reasonably expect a continued steady improvement in the error and reliability of aft. In E821, analysis is under way on the ss 4 billion positrons (/x+) from the 2000 run (about four times larger than the 1999 data set) and on the « 3 billion electrons (/i _ ) from the 2001 run. Systematic errors are expected to be reduced for both data sets. Once these data are analyzed, it should be possible to make a more definitive statement concerning whether the measured anomaly agrees with theory. Comparison of the [i+ and fi~ anomalies is a test of both the systematic errors in E821 and also CPT imparlance. With another data run, E821 expects to achieve 0.3 ppm statistical error on ae*p and an estimated 0.3 ppm systematic error, not far from the original goal of 0.35 ppm overall error. It is interesting to note that any new physics affecting aM may also lead to a non-
423
zero permanent electric dipole moment for the muon, through its CP violating part. Assuming that the CP violating phase for new physics 4>cp ~ 1, then dimensional arguments, along with the observed value for Aa M , give 39 dM « 10~ 22 . Even if aM experiment and theory were to agree, the muon EDM is interesting in its own right: it is the only currently accessible EDM from a second generation particle. Comparing with the electron, the current limit on the electron dipole moment is « 4 x 10"~27e — cm. If the EDM scales by the first power of the mass, then a 10~ 24 e — cm muon measurement is competitive with that of the electron. There are speculations, however, that the electron EDM could be small due to an accidental cancellation which may not apply to the muon. Or, if the scaling is with the square of the mass or higher, the muon then becomes more sensitive than the electron to new physics. 40 There are a number of models which predict dp in the range 10~22e~cm to 10 _ 2 4 e —cm.39 The presence of an EDM adds the term
~&*S
+
®
(10)
to Eq. 3, where the EDM is given by d^ = i ( ^ n c ) - ^ n t n e (§"2) experiment, the effect of the dominant (3 x B term is to tip the precession vector radially by an angle 3 = t a n - 1 TP-. This causes an increase in the precession frequency to w « uia \fl + rf. It also causes an oscillation about zero of the average vertical component of the positron momenta, which can be observed as an oscillation, with frequency u>, in the average vertical position of positrons on the face of the calorimeters. In the unlikely event that all of AaM can be attributed to a muon EDM, then d,, = (2.3 ± 0.7) x 10" 1 9 . The CERN (g2) 6 experiment has set the best limit on the muon EDM so far, d^ < 1 x 10 _ 1 8 e - cm, deduced from limits on the vertical oscillations. While this value for d^ is larger than any the-
The Muon Anomaly: Experiment and Theory
J. P. Miller ory predicts, it is nevertheless not ruled out by CERN limit. E821 expects to reduce the limit by about a factor of five from an improved measurement of the vertical oscillations. A dedicated experiment to measure the muon EDM to the 10 _ 2 4 e — cm level is currently being developed at Brookhaven National Laboratory. 41 It would use a new technique where a muon momentum and an applied electric field would be selected so that the second term cancels the first term in Eq. 3. One is only left with the motion in a vertical plane described by Eq. 10. In this technique, there is a very large enhancement of the EDM signal relative to the "noise" over the technique used in the g-2 experiments. It is planned to mount this experiment over the next few years.
5
Grosse-Perdekamp 11 , A. Grossmann 6 , M.F. Hare 1 , D.W. Hertzog 7 , V.W. Hughes 11 , M. Iwasaki 10 , K. Jungmann 6 , D. Kawall 11 , M. Kawamura 10 , B.I. Khazin 3 , J. Kindem 9 , F. Krienen 1 , I. Kronkvist 9 , R. Larsen 2 , Y.Y. Lee 2 , I. Logashenko 1 , R. McNabb 9 , W. Meng 2 , J. Mi 2 , J.P. Miller1, W.M. Morse 2 , D. Nikas 2 , C. Onderwater 7 , Y. Orlov 4 , C.S. Ozben 2 , J. Paley 1 , C. Polly 7 , J. Pretz 1 1 , R. Prigl 2 , G.zu Putlitz 6 , S.I. Redin 11 , O. Rind 1 , B.L. Roberts 1 , N.M. Ryskulov 3 , S. Sedykh 7 , Y.K. Semertzidis 2 , 3 Yu.M. Shatunov , E. Sichtermann 11 , E. Solodov3, M. Sossong7, A. Steinmetz 11 , L.R. Sulak 1 , C. Timmermans 9 , A. Trofimov1, D. Urner 7 , P. von Walter 6 , D. Warburton 2 D. Winn 5 , A. Yamamoto 8 , D. Zimmerman 9 1
Acknowledgments
The author would like to thank R. Carey, D. Hertzog, K. Jungmann and Y. Semertzidis for helpful comments on this manuscript. The author's work is supported by the U.S. National Science Foundation. Opinions regarding the theoretical content of a^ are solely those of the author and do not necessarily reflect the opinions of the E821 experiment. E821 is supported by the U.S. Department of Energy, the U.S. National Science Foundation, the German Bundesminister fiir Bildung und Forschung, the Russian Ministry of Science, and the U.S.-Japan Agreement in High Energy Physics. References 1. H.N. Brown 2 , G. Bunce 2 , R.M. Carey 1 , P. Cushman 9 , G.T. Danby 2 , P.T. Debevec7, M. Deile 11 , H. Deng 11 , W. Deninger7, S.K. Dhawan 11 , V.P. Druzhinin 3 , L. Duong 9 , E. Efstathiadis 1 , F.J.M. Farley 11 , G.V. Fedotovich3, S. Giron 9 , F. Gray 7 , D. Grigoriev3, M.
Boston University, Boston, 2 Massachusetts 02215, USA Brookhaven National Laboratory, Physics Dept., Upton, NY 11973, USA 3Budker Institute of Nuclear Physics, Novosibirsk, Russia 4 Newman Laboratory, Cornell University, Ithaca, NY 14853, USA 5 Fairfield University, Fairfield, Connecticut 06430, USA 6 University of Heidelberg, Heidelberg 69120, Germany 7 University of Illinois, Physics Dept., Urbana-Champaign, IL 61801, USA 8 KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan 9 University of Minnesota, Physics Dept., Minneapolis, MN 55455, USA w Tokyo Institute of Technology, Tokyo, Japan n Yale University, Physics Dept., New Haven, CT 06511,US A 2. Van Dyck, Schwinberg, Dehmelt, Phys. Rev. D34, 722(1986). 3. A. Czarnecki and W.J. Marciano, Nucl. Phys. (Proc. Suppl.J B76, 245 (1999). 4. M. Davier and A. Hocker, Phys. Lett. B435, 427 (1998).
424
The Muon Anomaly: Experiment and Theory
J. P. Miller 5. D.E. Groom, et al, the Particle Data Group, Eur. Phys. J C 1 5 , 1 (2000). 6. J. Bailey, et al, Nucl. Phys. B150, 1 (1979). 7. R.M. Carey, et a l , Phys. Rev. Lett. 82. 1632-1635(1999). 8. H.N. Brown, et al., Phys. Rev. D62, 091101 (2000). 9. H.N. Brown, et a l , Phys. Rev. Lett. 86, 2227 (2001). 10. T. Kinoshita, private communication. 11. R. Alemany, M. Davier, A. Hocker, Eur. Phys. J. C2, 123 (1998). 12. D.H. Brown and W. Worstell, Phys. Rev. D54, 3237 (1996). 13. S. Eidelman, I. Logashenko, CMD2 collaboration, private communication. 14. Data and plot from A. Denig, private communication, also see the contributed paper in this conference by the KLOE collaboration, hep-ex/0107023. 15. BESII collaboration, Phys. Rev. Lett. 84, 594 (2000); Preliminary data and plot from Z. Zhao, private communication. 16. M. Davier, private communication. 17. S.I. Eidelman and V.N. Ivanchenko, Nucl. Phys. Proc. Suppl. 40, 131 (1995). 18. K. Melnikov, SLAC-PUB-8844, hepph/0105267, May 2001. 19. Data from Cornell, Jon Urheim, private communication. 20. S. Eidelman and F. Jegerlehner, Z. Phys. C67, 585( 1995). 21. K. Adel and F.J. Yndurain, hepph/9509378,1995 and Rev. Acad. Ciencas (Esp.), 92, 736 (1985). 22. M. Davier and A. Hocker, Phys. Lett. B419, 419 (1998). 23. S. Narison, hep-ph/0103199, March 2001; Phys. Lett. B513, 53( 2001). 24. J.F. Troconiz and F.J. Yndurain, hepph/0106025, 2001. 25. S. Eidelman, preliminary result from Novosibirsk, private communication.
425
26. W. Marciano and B. Roberts, hepph/0105056, May 2001. 27. B. Krause, Phys. Lett. B390, 392 (1997). 28. M. Hayakawa and T. Kinoshita, Phys. Rev. D57, 465 (1998). 29. J. Bijnens, E. Palanta, J. Prades, Nucl. Phys. B474, 379 (1996). 30. M. Knecht and A. Nyffeler, hepph/0111058, 6 Nov 2001. Also see M. Knecht, A. Nyffeler, M. Perrottet, and E. de Rafael, hep-ph/0111059, 6 Nov 2001. 31. M. Hayakawa and T. Kinoshita, hepph/0112102, 16 Dec 2001. 32. J. Bijnens, E. Palanta, J. Prades, hepph/0112255, 19 Dec 2001. 33. J. Bailey et al., Nucl. Phys. B150, 1 (1979). 34. W. Liu, et al., Phys. Rev. Lett. 82, 711 (1999). 35. G.T. Danby, et al., Nucl. Instrum. Methods A457, 51 (2001). 36. F. Krienen, D. Loomba and W. Meng, Nucl. Instrum. Methods A283, 5 (1989). A. Yamamoto, et al., Proc. of 15th Int. Con}, on Magnetic Technology, Science Press Beijing, 246 (1998). 37. S. Sedykh, et al., Nucl. Instrum. Methods A455, 346 (2000). 38. R. Carey, et al., to be published, Nucl. Instrum. and Methods. 39. J.L.Feng, K.T. Matchev and Y. Shadmi, "Theoretical expectations for the muon's electric dipole moment," hep-ph/0107182. 40. K.S. Babu, S.M. Barr and I. Dorsner, "The scaling of lepton dipole moments with lepton mass," hep-ph/0012303. 41. R.Carey, et al., "Request for R&D Funds Toward a Proposal for the Muon Electric Dipole Moment Experiment", submitted to the Brookhaven National Laboratory Program Advisory Committee, Fall, 2001, http://www.bnl.gov/edm/.
S E A R C H E S FOR N E W PARTICLES GAIL G. HANSON Indiana University, Department of Physics, Bloomington, Indiana 4^405, USA E-mail: [email protected], [email protected] The status of searches for new particles and new physics during the past year at the Fermilab Tevatron, at HERA and at L E P is summarized. A discussion of the hints for the Standard Model Higgs boson from LEP2 data is presented. Searches for non-Standard Model Higgs bosons are also described. Many searches have been carried out for the particles predicted by supersymmetry theories, and a sampling of these is given. There have also been searches for flavor changing neutral currents in the interactions of the top quark. In addition, searches for excited leptons, leptoquarks and technicolor are summarized.
1
Introduction
much longer!
One of the most tantalizing physics topics of the past year has been the possible evidence for Standard Model Higgs boson production from the LEP experiments. Both the November 2000 combination, which led to a request for an extension of LEP running, and the combination just prepared for the summer conferences are presented here. Searches for Minimal Supersymmetric Standard Model (MSSM) Higgs bosons and searches in other extensions of the Standard Model have been performed and are summarized. A light Higgs boson with mass near 115 GeV could be the lightest SUSY Higgs h° with nearly Standard Model couplings. There have been extensive searches for the supersymmetric partners of the ordinary particles in pp, e+e~, and e^p collisions, as well as searches for excited fermions, leptoquarks, and technicolor. In the interests of fitting into the time allowed, I was able to cover only a few of the possible search topics. For example, there were many contributions in various supersymmetry scenarios which I would have liked to discuss in more detail, and I did not discuss the area of large extra dimensions. I have given references only to the experimental papers, and I refer the reader to them for the theoretical references - otherwise my list of references would have been
2
Searches for Higgs Bosons
2.1
Standard Model Higgs Search
*S
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in ~ \. , , i , , , j , , , i , . , i , , . i , , , I , , i i , , 100 102 104 106 108 110 112 114 116 118 120 mf/GeV/c2) Figure 1. The background probability (1 — CLi) as a function of mjj f ° r the four LEP experiments combined for year 2000 data as shown at the November 3, 2000, L E P C meeting.
Preliminary results of searches for the Standard Model Higgs boson at LEP2 were presented 1 at the November 3, 2000, meeting of the LEP Experiments Committee (LEPC) using most of the data collected in 2000. The background probability as a function of the test mass mn for the combination of all four LEP experiments is shown in Fig. 1. For background only, (1 — CLb) will be 0.50 on the average. The combination of the four LEP experiments presented at the November 3 LEPC meeting showed an excess of 2.9a
426
Searches for New Particles
Gail G. Hanson significance, or (1 — CL\,) = 0.0042, at TBH ~ 115 GeV. The negative log-likelihood ratio —21nQ for the LEP combination is shown in Fig. 2. The value of m H = 115.0Jlg;| GeV is given by the point at which the observed —21nQ versus mn has its minimum value. The lower limit was raH > 113.5 GeV at 95% confidence level (C.L.) with a median limit of 115.3 GeV expected for background only.
—25
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100 102 104 106 108 110 112 114 116 118 120
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m^GeV/c2) Figure 2. Negative log-likelihood ratio —21nQ as a function of mjj for the four L E P experiments combined for year 2000 d a t a as shown at the November 3, 2000, LEPC meeting.
H° Figure 3. Higgsstrahlung process for production of the Standard Model Higgs boson in e+e~ collisions at LEP.
At LEP the SM Higgs boson is expected to be produced mainly through the Higgsstrahlung process e + e~ —> HQZ°, shown in Fig. 3, with small additional contributions from i-channel W and Z boson fusion processes. Searches are performed in the channels HZ —• bbqq (four jet), HZ —> bbvv (missing energy), HZ —> bbr+T~ or T+T~qq (tau), and HZ —> bbe+e~ or bbjj,+ yT (leptonic).
427
Figure 4. Observed and expected behavior of t h e likelihood ratio - 2 1 n Q as a function of t h e test mass mH, obtained by combining t h e d a t a of all four LEP experiments. T h e solid line represents the observation; the dashed/dash-dotted lines show the median background/signal + background expectations. The dark/light shaded bands around t h e background expectation represent the ± l / ± 2 standard deviation spread of the background expectation obtained from a large number of background experiments. T h e dotted line is the result of a test where the signal from a 115 GeV Higgs boson has been added to the background and propagated through t h e likelihood ratio calculation.
Each event is assigned a probability s, of being a signal event and a probability bi of being a background event at a test Higgs mass ma. The event weight to* is given by Wi = (si + bi)/bi. The sample likelihood £ is the product of the weights. The logarithm is taken, and then the method is log-likelihood ratio:
L i k e l i h o o d r a t i o <5(TOH)
£(S + b) c(b) •
(1)
Two hypotheses are tested: background only, with compatibility measured by 1 — CLb, and signal plus background, with compatibility measured by CLs+b (CLS = CLs+b/CLb). The event weights in terms of s/b for mn = 115 GeV are given in Table 1 for the current combination 2 and for the November 3 LEPC combination 3 for the events with the ten largest weights in the current combination. Apart from the L3 missing energy event (and the OPAL event marked "*", which was
Searches for New Particles
Gail G. Hanson recorded after the deadline for the November 3 combination and was reprocessed with calibrations for that data set, giving it a higher weight), the event weights show only small changes. The L3 event weight changed because the event was unlikely either for signal or background, and higher statistics Monte Carlo simulations resulted in a lower weight. All four LEP experiments have published preliminary results for the 2000 data, 4 and L3 has published their final analysis. 5
d
10 10~ W~ 10~ 10~ io'
100 102 104 106 108 110 112 114 116 118 120 m^GeV/c2)
Figure 7. Confidence level CLS for the signal + background hypothesis. Solid line: observation; dashed line: median background expectation. T h e dark/light shaded bands around t h e median expected line correspond to the ± l / ± 2 standard deviation spreads from a large number of background experiments.
d 2a 3a Observed ; \ ,' iixjxvieti Ib£ signat+baciigrouiiii' IKxpecied foil background \>
4a -5
100 102 104 106 108 110 112 114 116 118 120 ntf/GeV/c2) Figure 5. The probability (1 — CLb) as a function of the test mass mn. Solid line: observation; dashed/dash-dotted lines: expected probability for the background/signal + background hypotheses.
£> SO. 14
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Observed Expected for background Fspecled for Msinai (iti.,-115.6 GeV
LEP
% 0.1 a 1| 0.08 Q,
0.06 0.04 0.02 0 -15
-10
10 15 -2 ln(Q)
Figure 6. Probability density functions corresponding to a test mass mjr = 115.6 GeV, for the background and signal + background hypotheses. The observed value of —2 In Q which corresponds to the data is indicated by the vertical line. T h e light shaded region is a measure of the compatibility with the background hypothesis, 1 — CLf, (3.4%), and the dark shaded region is a measure of compatibility with the signal + background hypothesis, CL3+\, (44%).
Figure 4 shows the negative loglikelihood ratio — 21nQ versus mn for the current LEP combination of the preliminary results of three LEP experiments and the final result of one experiment. The minimum is observed at WH = 115.6 GeV. The probability (1 — CLb) versusTOHis shown in Fig. 5. AtTOH= H5.6 GeV, 1 - CLb = 0.034, corresponding to a probability of background fluctuation of 2.1 standard deviations. The probability density functions corresponding to a test mass ma = 115.6 GeV, for the background and signal plus background hypotheses, are shown in Fig. 6. The area under the background curve below the observed value of — 2lnQ corresponds to 3.4% probability of compatibility with background, and the area under the signal curve above the observed value of — 21nQ corresponds to 44% probability of compatibility with signal plus background. Figure 7 shows the the distributions of CLS versusTOH,which give the lower limit of m H > 114.1 GeV at 95% C.L. with a median limit of 115.4 GeV expected for background only. Figure 8 shows the reconstructed Higgs mass distributions for special non-biasing selections with low (Fig. 8a), medium (Fig. 8b),
428
Gail G. Hanson
Searches for New Particles
Table 1. Comparison of event weights between November 3, 2000, L E P C and current combination.
mtfc (GeV)
Nov. 3 s/b
Current s/b
4-jet
114
4.7
4.7
ALEPH
4-jet
113
2.3
2.3
3
ALEPH
4-jet
110
0.9
0.9
4
L3
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2.1
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5
OPAL*
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111
0.4
0.7
6
DELPHI
4-jet
114
0.5
0.6
7
ALEPH
Lept
118
0.6
0.6
8
ALEPH
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115
0.5
0.5
9
ALEPH
4-jet
114
0.4
0.5
10
OPAL
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113
0.5
0.5
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. _jJ£~-#vttii' Reconstructed Mass mM [GeV/c ]
Reconstructed Mass mH [GeV/c2]
Reconstructed Mass m„ [GeV/c ]
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Figure 8. Distributions of the reconstructed Higgs mass, m ^ , from three special, non-biasing, selections with increasing purity of a signal from a 115 GeV Higgs boson.
and high (Fig. 8c) purity. 2.2
MSSM Higgs Search
In the Minimal Supersymmetric Standard Model (MSSM) there are two scalar field doublets resulting in five physical Higgs bosons: two neutral CP-even scalars, h° and H° (with m-ho < TOHO), one CP-odd scalar, A0, and two charged scalars, H^. At tree level, rriYfi < rr»z, m^o < TOH°, rnz < rn-^o, and m.}j± < mw- Loop corrections, predominantly from t and i, modify these mass relations, unfortunately for LEP2. However, in the MSSM, there must be a lowest mass neu-
429
tral Higgs boson h° with m^o < 135 GeV. At the current e+e~ center-of-mass energies accessible to LEP, the h° and H° bosons are expected to be produced predominantly via two processes: the Higgsstrahlung process e+e~ —» h°Z° (as for H$M) and the pair production process e+e~ —> h°A°. The cross sections for these two processes, <7hz and a^A, are related at tree level to the SM cross sections by the following relations:
e+e
h°Z° : a h z = sin2(/3 - Q) O%£ (2)
Searches for New Particles
Gail G. Hanson LEP8° ™n '--'" "--liminarv CQ.
c 10
0
20
40 60
80 100 120 140 mho (GeV/c2)
0
20
40
60
80
100 120 140
mho (GeV/c2)
Figure 9. The MSSM exclusion for the m h o - m a x benchmark scenario. T h e excluded (hatched) and theoretically disallowed (dark grey) regions are shown as functions of the MSSM parameters in two projections: (left) the (m h o, mAo) plane and (right) the (m h o, tan/3) plane. The dashed lines indicate the boundaries of the regions expected to be excluded at t h e 95% C.L. if only SM background processes are present.
constrained MSSM (CMSSM) the sfermion and gaugino masses are unified. In addie+e" -> h°A° : ahA = cos2(/3 - a) A a^ tion, in minimal supergravity-broken MSSM (3) (MSUGRA) the trilinear couplings are equal where a^ ls the Higgsstrahlung cross section (AQ), the scalar masses (including Higgs) are for the SM process e+e~~ —> H^MZ°, and A is unified, and the electroweak symmetry scale a factor accounting for the suppression of the determines /x. P-wave cross section near production threshThe results of the Standard Model Higgs old. searches are used for the e + e~ —> h°Z° chanThe angle /? is defined in terms of the nel, with the cross sections modified as in vacuum expectation values v\ and i>2 of the Eq. (2), and the decay branching ratios detwo Higgs field doublets: tan/3 = 1*2/^1 • The termined by the supersymmetry parameters. angle a is the mixing angle that relates the Dedicated analyses are done for the assophysical mass eigenstate h° with the field ciated production of a scalar h° and pseudoublets. doscalar (A0) Higgs. The search channels are In addition, the following parameters are hA -> bibb (Ah-4b) and hA -> T+T~bb or needed to specify the MSSM: MSUSY', /•*, the bbr+T- (Ah-tau). Higgs boson mass parameter; M\, M2, M3, The presence of an MSSM Higgs boson the gaugino masses at the electroweak scale signal is tested in a constrained MSSM in (gaugino unification gives a common gaug- which the parameter A is the common trilinino mass rrii/2 a t the GUT scale and Mi = ear Higgs-squark coupling parameter. Three (5/3) tan 2 0WM2); AT, Ab, At, the third fam- benchmark scenarios are considered: the "noily trilinear Higgs-sfermion coupling parame- mixing" scenario, in which there is no mixing ters; m,f, the scalar fermion masses (sfermion between the scalar partners of the left-handed mass unification gives a common sfermion and right-handed top quarks, MSUSY — mass mo at the GUT scale); and m^o, the 1 TeV, M 2 = 200 GeV, fi = -200 GeV, running mass of the CP-odd scalar A0. In
430
Gail G. Hanson Xt(= A - ncotp) = 0, 0.4 < tan/3 < 50, 4 GeV < m\o < 1 TeV, and the gluino mass nig = 800 GeV; the "m^o —max" scenario, which is designed to yield the maximal value of ni|,o in the model, corresponds to the most conservative range of excluded tan/3 values for fixed values of MSUSY and the top quark mass, and has the same values of the parameters as in the no-mixing scenario except for the stop mixing parameter Xt = 2MsusV, and the "large fx" scenario, which is designed to illustrate choices of MSSM parameters for which h° does not decay into pairs of b quarks and uses parameters MSUSY = 400 GeV, M2 = 400 GeV, fi = 1 TeV, m-& = 200 GeV, 4 < mAo < 400 GeV, and Xt = -300 GeV. Figure 9 shows the MSSM exclusion regions for the Who—max benchmark scenario for the combination of the preliminary results of the four LEP experiments. 6 In the m^o—max scenario, the limits obtained are mho > 91.0 GeV and mAo > 91.9 GeV at 95% C.L., and the range 0.5 < tan/? < 2.4 is excluded for a top quark mass less than or equal to 174.3 GeV.
2.3
Searches for New Particles
20
40
60
100
80
120
M„» (GeV)
Figure 10. Combined LEP experimental limits on Higgs bosons produced with Standard Model cross sections and decaying into di-photons. T h e 9 5 % C.L. upper limit on the di-photon branching fraction is shown as a function of the Higgs mass. Also shown (dotted line) is the branching fraction obtained for the benchmark fermiophobic model. The median expected limits and the ± 2 standard deviation confidence level region are denoted by the dashed curves.
LEP PRELIMINARY
Non-Standard Model Higgs Searches
Searches for Higgs bosons decaying into photons have been carried out by the four LEP collaborations, and the combination 7 of preliminary results is shown in Fig. 10. A lower bound of 108.2 GeV is set at 95% C.L. for Higgs bosons produced with the Standard Model cross section af^ and not decaying into fermion pairs. Searches for Higgs bosons produced with the Standard Model hZ cross section and decaying hadronically but not necessarily into b quarks have been combined for the four LEP experiments for the first time. 8 The combination of preliminary results in shown in Fig. 11. A lower limit of 112.9 GeV at 95% C.L was obtained for h decaying 100% hadronically. Two Higgs Doublet Models (2HDMs) are
- expected foi bjckgrouml
10
60
70
80
90
100
110
m„ (GeV)
Figure 11. Combined LEP flavor independent 95% C.L. upper limits on the production cross section as a function of Higgs mass, normalized to the expected Standard Model values and assuming BR(/i —• hadrons) = 1.0. The observed limit is shown as the solid curve and the expected median limit by the dashed curve. The bands correspond to 68.3% and 95% confidence intervals from the background-only experiments.
extensions of the Standard Model in which two scalar doublets and five physical Higgs
Searches for New Particles
Gail G. Hanson
OPAL
-Vs = 183-208 GeV
PRELIMINARY
ADLO Preliminary
^140 O 5*120 100 80
...
60 '•'•K'?,
40 >;,<,-
\' ;\ 20:^
i
°(I
2u m„ [GeV]
Figure 12. Excluded (mAo, mho) region independent of a, together with the expected exclusion limit. A particular (m A o, m h o ) point is excluded at 95% C.L. if it is excluded for 0.4 < tan/3 < 58.0 (darker grey region), 0.4 < tan/3 < 1.0 (lighter grey region) and 1.0 < tan/3 < 58.0 (hatched region) for —7r/2 < a < 7r/2. T h e cross-hatched region is excluded using constraints from Tz only. Expected exclusion limits are shown as a dashed line.
bosons occur but without the constraints of the parameters of supersymmetry. In Type II 2HDMs the first Higgs doublet couples only to down-type fermions and the second Higgs doublet couples only to up-type fermions. The Higgs sector in the MSSM is a Type II 2HDM. In Type II 2HDMs h° and A 0 are produced as in Eqs. (2) and (3), and the branching ratios are determined by a and /?, which are the only free parameters besides the Higgs masses. Limits have been obtained 9 on Type II 2HDMs with no CP violation in the Higgs sector and no additional particles besides the five Higgs bosons by interpreting the results of searches for h° and ^4°. An example is shown in Fig. 12 for which 1 < m^o < 58 GeV and 10 < mAo < 65 GeV are excluded at 95% C.L. for all values of a and tan/3 in the ranges scanned (—7r/2 < a < -n/2 and 0.4 < tan/3 < 58.0).
Figure 13. 95% C.L. lower limits for combined d a t a from the LEP experiments for the masses of righthanded scalar leptons versus the mass of the lightest neutralino. Observed limits: solid lines; expected limits: dotted lines.
3
Searches for Supersymmetry
In supersymmetric (SUSY) models each of the "normal" particles (leptons, quarks, and gauge bosons) has a supersymmetric partner (scalar leptons, scalar quarks, and gauginos) with spin differing by half a unit. Most of the searches for these supersymmetric particles are performed within the MSSM assuming .R-parity conservation. i?-parity is a multiplicative quantum number defined as Rp
= (_I)3B+L+2SJ
w h e r e
B )
Z )
a n d
g
a r e
the baryon number, lepton number, and spin of the particle, respectively. .R-parity discriminates between ordinary and supersymmetric particles: Rp = + 1 for the ordinary SM particles and —1 for their supersymmetric partners. If .R-parity is conserved, supersymmetric particles are always produced in pairs and always decay through cascade decays to ordinary particles and the lightest supersymmetric particle (LSP), which must be stable. In gravity mediated SUSY breaking, the LSP is the lightest neutralino x?> a n d the gravitino G is heavy. In gauge mediated
432
Searches for New Particles
Gail G. Hanson ALO Preliminary
ADLO Preliminary
ADLO Preliminary ,100-
"^ 100-
o
T->'bi v'
0=0°
b->bX?
6=0°
- i 9080 7060-
1
50
>
90 100 m w + „ Ms.o/GeV/c')
40J
40
9=56"/. mi l^i&T
fusion 50
60
70
80 90 1C M s,oP(GeV/c2)
mtmi
20 0
MUM
fe*^#M 50 60 70
8b 90 100 Msb«om(GeV/c2)
Figure 14. 95% C.L. lower limits for combined data from the LEP experiments for the masses of scalar top and scalar bottom quarks versus the mass of the supersymmetric decay product. Limits are shown for zero mixing angle and for the mixing angle at which the t\ (bi) decouples from the Z°.
SUSY breaking, the G is very light (LSP) and X? G7, for example. 3.1
Searches for Scalar Leptons
Scalar leptons (sleptons, £±) can be produced in pairs in e+e~~ collisions: e+e~ —> £+£~. They decay, for example, to the LSP x? and a lepton of the same flavor: £~ —> yQtr. The topology is acoplanar leptons £+£~, and observation depends on A M Mi- — M^a since the x? is undetectable. Preliminary searches for sleptons from the four LEP experiments have been combined, 10 and the excluded regions are shown in Fig. 13. The combined LEP 95% C.L. lower limits for AM > 10 GeV are: M gR > 99 GeV, M A R > 95 GeV, and M^ > 80 GeV. [Note: £^, £^ are the scalar partners of the right-handed, left-handed £~~, and + ^ R / R ) is smaller than a(e e
ilk)] 3.2
Searches for Squarks and Gluinos
The SUSY partners of top and bottom quarks (stop, t, and sbottom, b) have been searched
433
for in the LEP experiments. Stop and sbottom are mixtures of the SUSY partners of the left- and right-handed quarks, with the lowest mass squarks denoted by t\ = £L COS Of + iR,sin#j and h\ = 6 L C O S ^ + &Rsin^, where Ol and 9^ are the mixing angles. Searches are carried out for t\ —> cx°, t\ -—> b£v, and &i —> bxl- A M is the mass difference between the stop or sbottom and the SUSY decay product, Xi o r v. Exclusion regions for combinations 11 of preliminary data from the four LEP experiments are shown in Fig. 14 for no mixing and for the mixing angles for which the t\ and 61 decouple from the Z°. The 95% C.L. lower limits are shown in Table 2. Experiments at hadron colliders are sensitive to searches for scalar quarks (q) and gluinos (5). An example is shown in Fig. 15 of a recent search 12 by CDF based on the signature of large missing energy from the two LSPs and three or more hadronic jets resulting from the decays of the q and/or g. They obtain 95% C.L. limits of mg > 195 GeV independent of rriq and rrig > 300 GeV for the case rrig « mg.
Searches for New Particles
Gail G. Hanson Table 2. The excluded Mi C.L. for AM > 10 GeV.
Lower limit for t\
and M^
regions at 95%
,tanp=2 . , . , u=, -200 . , ,GeV .,, , •"-
Lower limit for b\
ADLO
Vs > 206.5 GeV
' '_ _ ~
m „ > 103.5 GeV for i t > 300 GeV
(GeV)
(GeV) *l
cx\
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97
56
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(°)
o
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97
0
100
95
68
92
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100-
Excluded at 95 1 C.L. 99-
Mv (GeV) £p+ ^ T jets search for gluinos and squarks
ft
Figure 16. 95% C.L. lower limits for combined d a t a from the LEP experiments for the mass of the lightest chargino versus the mass of the scalar neutrino.
CDF PRELIMINARY j JLdt=84 pb ' Vs=] 8 TeV 1mSUGRA
ISAJET 7 37 + PROSPINO |
lanp=3 95% CL
L J
> o
at the kinematical limit. The exclusion region from the combination 13 of preliminary searches from the four LEP experiments is shown in Fig. 16. The 95% C.L. lower limit is M-+ > 103.5 GeV for Mv > 300 GeV. Limits on the x.i LSP mass are obtained from combined searches for charginos, sleptons, and MSSM Higgs bosons. The exclusion regions for MSUGRA constraints and for CMSSM constraints for the combined preliminary LEP searches 14 are shown in Fig. 17. The 95% C.L. lower limits are M^o > 60 GeV for MSUGRA and M*o > 45.6 GeV for CMSSM, both for 175 GeV top quark mass.
mg(GeV/c )
Figure 15. T h e 95% C.L. region in the rriq—mg plane newly excluded by CDF. Results from some previous searches by CDF, DO, LEP, UA1 and UA2 are also shown.
3.3
Searches for Charginos and Neutralinos
Charginos (x^1 can be produced in pairs in e + e~ collisions: e+e~ —> xtxi • They can then typically decay as xt ~~* XiW* —> Xi^ + i/ or XiQQ'- The signature is large missing energy and large missing transverse momentum, and detection depends on A M = M-+ — M^o. There are several topologies:
3.4
Searches for R-parity SUSY
Violating
In .R-parity violating SUSY decays, theMightest supersymmetric particle is expected to be unstable. Many searches have been performed for .R-parity violating SUSY. One example 15 from HI is shown in Fig. 18. In Xi Xj this case the squarks are assumed to be prohadronic with large multiplicity, large mulduced through an .R-parity violating Aj -fe tiplicity with isolated lepton, and low mulcoupling. They decay either through the tiplicity (acoplanar leptons). At large TOO same coupling or through an R-parity con(heavy scalar leptons) the cross section is the serving gauge decay into a x * , a x ° , or a j . largest. The lower limit for M~+ is nearly
434
Searches for New Particles
Gail G. Hanson X° Neutralino LSP Constraints in MSUGRA
X° Neutralino LSP Constraints in MSSM Unification at GUT Scale (CMSSM)
lfl
A D L O preliminary
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With L E P Combined results
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30
40
Figure 17. 95% C.L. lower limit for t h e combined L E P d a t a for t h e LSP mass versus tan/3 for MSUGRA (left) and CMSSM (right).
Minima? bupergravity + R Violation >. " °
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-
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Figure 18. Region excluded by H I in t h e (mo, m j / a ) plane for (j, < 0, A® = 0 and tan 0 = 2 (left) or t a n j3 = 6 (right) for an .R-parity violating coupling A'131 = 0.3. The regions excluded by DO and L3 are also shown.
4
Single Top Quark Production
Searches for flavor-changing neutral currents (FCNC) have been performed at the Fermilab Tevatron in rare decays of the top quark and at LEP and HERA in single top quark
435
production. FCNC are suppressed at tree level in the Standard Model (GIM mechanism) . Small contributions occur at the oneloop levd I n e + e - t h e S M c r o g s s e c tion ^ 9 ^ Extensions to the Standard is 10 M o d e l ) s u c h a s S U S Y a n c j multiple Higgs
Gail G. Hanson
Searches for New Particles
doublet models, can allow FCNC at the tree level.
K
T
,K
7
exclusion regions in the AC7 — K% plane are shown in Fig. 20 for CDF, ZEUS, 17 HI, 1 8 and the combination 19 of preliminary LEP data. QCD and ISR corrections to the Born-level cross sections are used for the LEP combination.
. q(u,c)
LEP e+e-^tq^bWq
e"bWX
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Figure 19. Single top quark production at LEP and HERA.
80
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-
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Figure 21. A comparison of the HI events with isolated leptons and large missing PT with the predictions of Standard Model single W production. P* is the transverse momentum of the hadronic system and Mj," is the transverse mass of the hadronic system.
r
%
0.2
• .X^>. \
0.2
U.4
XX
0.6
" x x X :\.:x \ ' 0.8 1
Figure 20. The light grey region shows the combined LEP exclusion region at 95% C.L. in the KZ — ft-y plane for mt = 174 GeV with QCD and ISR corrections. The exclusion curves for different values of mt are also shown. The hatched area shows the CDF exclusion region, and the two vertical lines with arrows show the ZEUS and HI Ktu-y exclusion regions.
5
Events with Isolated Leptons and Large Missing pr
The HI experiment 20 at HERA observes an excess of events with isolated leptons and large missing transverse momentum (PT)The primary Standard Model process is sinCDF performed a search 16 in the top de- gle W production. The presence of these excays t —> 7c(w) and t —+ Z°c(u) in pp col- cess events increases the lower limit on K 7 in lisions at i / i = 1 . 8 TeV. Searches for single the single top quark search. Figure 21 shows a comparison of the events with the predictop production at LEP and HERA can be described by the processes shown in Fig. 19. tions for single W production for electrons and muons separately. The excess above the The FCNC transition can be described usSM expectation is mainly due to events with ing the anomalous coupling parameters K 7 transverse momentum of the hadronic sysand Kz, which represent the tree-level 7 and Z° exchange contributions. The 95% C.L. tem (P*) greater than 25 GeV where 10
436
Searches for New Particles
Gail G. Hanson events are found compared to 2.8 ± 0.7 expected. The numbers of events in the electron and muon channels for P* < 25 GeV and P* > 25 GeV are shown in Table 3. The ZEUS experiment 17 does not observe an excess; the numbers of events for P* > 25 GeV for ZEUS are also shown in Table 3. Table 3. Comparison of numbers of events with isolated leptons and large missing p x with the predictions of Standard Model single W production for HI and ZEUS. P£ is the transverse momentum of the hadronic system.
HI
electron
muon
obs.
exp.
obs.
exp.
P£ < 25 GeV
6
6.6
2
1.0
Pfi > 25 GeV
4
1.3
6
1.5
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electron
Pfi > 25 GeV
6
Searches for Leptoquarks
Leptoquarks are resonant states carrying both baryon number and lepton number. Searches for them have been performed at the Tevatron and at LEP 2 1 and especially at HERA, 22 where they may be produced directly through e ± -quark fusion, and decay into e ± -quark or i^(i/)-quark. Leptoquarks can be scalar or vector states. F = L + 31? is preserved. Figure 22 shows ZEUS and HI limits on the Yukawa coupling constant A versus the leptoquark mass for first generation leptoquarks. 7
Searches for Excited Fermions
muon
obs.
exp.
obs.
exp.
1
1.1
1
1.3 Z.W.g
Figure 23. Excited fermion production at HERA.
Constraints on Scalar Leptoquarks Excited fermions arise naturally in models that predict a substructure in the fermion sector. Searches for pair production of excited leptons and singly produced excited leptons have been carried out at LEP. The effective electroweak Lagrangian describing chiral magnetic transitions from excited to ordinary leptons can be written -11 limit e" p. Preiun,} -II limit
C-w
f
e p, 9 4 - 97)
1 .- fAV 9f\w» t*a 2A
325 350 375 400
+9'f'^Bi
M LQ (GeV) Figure 22. Limits on the Yukawa coupling constant A versus the leptoquark mass M L Q for first generation scalar leptoquarks. Limits from L E P and Tevatron are also shown.
437
eL + h.c.
(4)
where A corresponds to the compositeness scale, the subscript L stands for left-handed, g and g' are the SM gauge coupling constants, and the factors / and / ' are weight factors associated with the two gauge groups SU(2)
Gail G. Hanson
Searches for New Particles
l
DELPHI&OPAL preliminary
f=r
f'/f e [ - 5 ; + 5 ] H1 Preliminary
Excited Electron Limits (Summer 2001)
s t
i*
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ep
/•
..-•'•'
/i
1
1
Vx/V\A^V—-^^^ 10 110
125
140
150
175 200 225 v* mass (GeV)
Figure 24. 95% C.L. upper limits on the ratio of the coupling to the compositeness scale for combined L E P search for excited leptons at yfs = 189 — 209 GeV (left), for ZEUS, HI and combined LEP searches for excited electrons (center), and for HI search for excited neutrinos (right).
x U(l). Typical decays of excited leptons are the following: r ± -> ^ 7 , I** -> vW±, l*± _> g±z°, v* -> iAy, v* -> i^W*, and v* -> vZ°. Excited fermion production and decay at HERA can occur through the processes shown in Fig. 23. Figure 24 shows the 95% C.L. upper limits on the ratio of the coupling to the compositeness scale for the combined LEP searches 23 for excited leptons e*, n*, and T* at y/s = 189 - 209 GeV, for ZEUS, 24 HI 2 5 and combined LEP searches for excited electrons, and for the HI search 26 for excited neutrinos. 8
Technicolor Searches
Technicolor represents an alternative to the Higgs mechanism for generating electroweak symmetry breaking. In this model the longitudinal degrees of freedom of the massive SM gauge bosons are the Goldstone bosons associated with the breaking of global chiral symmetry of a new kind of fermions, the technifermions, which besides the SM quantum numbers carry the charge of a new QCD-like interaction called Technicolor. In walking technicolor, the lightest technicolor mesons may be light enough to be observable at LEP2. DELPHI 27 and OPAL 28 have carried out searches for such technimesons: ITT
and px/ior- Figure 25 shows the 95% C.L. excluded regions for these searches. OPAL obtains mPT > 77 (62) GeV for ND = 9 (2), where N^ is the number of technifermion doublets (2 is the minimum number). DELPHI obtains mPT > 89.1 (79.8) GeV for A^D = 9 (2). 9
S u m m a r y a n d Conclusions
There is a "hint" at the two standard deviation level of a signal for a Standard Model Higgs boson from the combined search results of the four LEP experiments. The hint is weaker than it was at the November 3, 2000, LEPC presentation, but the number of events was not enough to establish a signal in any case. An extension of the LEP2 run was requested but unfortunately was not granted. Now we will have to wait until ~ 2007 to find out whether there is a light Higgs boson with TOH ~ 115 GeV. The 95% confidence level lower limit from the LEP searches is 771H > 114.1 GeV with a median limit of 115.4 GeV expected for background only. Many searches for new particles have been performed, but there have been only negative results and new limits established, so we are still left with only questions: Is there another mechanism for electroweak symmetry breaking? Supersymmetry? Tech-
438
Gail G. Hanson
Searches for New Particles DELPHI
>
j'l
01
140
o s
120
1 '
1
r
T ' 1 '
1 ' 1 '
1 '
1 \ OPAL Preliminary I \ \ i7i»y-^bbyMv=200GeV m'-J Dr4y-^bbyMv=100GeV 1 J
~
Hiij Kj —> bqbq'
100 80 60
-excluded I..i.....i i . i V . • ! ... 1 .. .1
1....I..J- 1 -
250 30u 350 400 450 500 550 bOO 2
M(pT) [GeV/c ]
m p/co [GeV]
Figure 25. The 95% C.L. excluded regions in the (MPT/U,T - M^T) plane from DELPHI (left) and OPAL (right). T h e dashed lines show the median expected exclusions for the background only hypothesis.
nicolor? Something we have not even thought of yet? In ten years' time we should have some answers. Acknowledgments I would like to acknowledge all of the contributions to the XX International Symposium on Lepton and Photon Interactions at High Energies which formed the basis for this review. I am extremely grateful to the many people who explained the details of their research to me and sent me figures. I apologize to those whose research I did not have time to cover. I would like to thank the Organizers and the Scientific Secretaries for all their help in preparing the talk. I would also like to acknowledge the support of the U.S. Department of Energy grant number DEFG0291ER40661. References 1. P. Igo-Kemenes, talk given in the LEPC open session (November 3, 2000) on behalf of the LEP Higgs Working Group. See http://lephiggs.web.cern. ch/LEPHIGGS/talks.
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ALEPH, DELPHI, L3 and OPAL Collaborations, The LEP Working Group for Higgs Boson Searches, "Search for the Standard Model Higgs Boson at LEP," CERN-EP/2001-55 (July 11, 2001). The LEP Higgs Working Group, "Standard Model Higgs Boson at LEP: Results with the 2000 Data, Request for Running in 2001," prepared for the LEP Committee and the CERN Research Board (November 3, 2000). See http://lephiggs.web.cern.ch/LEPHIGGS /papers. ALEPH Collaboration, R. Barate et al, Phys. Lett. B495, 1 (2000); L3 Collaboration, M. Acciarri et al, Phys. Lett. B495, 18 (2000); DELPHI Collaboration, P. Abreu et al, Phys. Lett. B499, 23 (2001); OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B499, 38 (2001). L3 Collaboration, P. Achard et al, Phys. Lett. B517, 319 (2001). ALEPH, DELPHI, L3 and OPAL Collaborations, The LEP Higgs Working Group, "Searches for the Neutral Higgs
Searches for New Particles
Gail G. Hanson
7.
8.
9.
10.
11.
12.
Bosons of the MSSM: Preliminary Combined Results Using LEP Data Collected at Energies up to 209 GeV," LHWG Note 2001-04 (July 9, 2001). See http://lephiggs.web.cern.ch/ LEPHIGGS/papers. ALEPH, DELPHI, L3 and OPAL Collaborations, The LEP Higgs Working Group, "Searches for Higgs Bosons Decaying into Photons: Preliminary Combined Results Using LEP Data Collected at Energies up to 209 GeV," LHWG Note 2001-08 (July 2, 2001). See http://lephiggs.web.cern.ch/ LEPHIGGS/papers. ALEPH, DELPHI, L3 and OPAL Collaborations, The LEP Working Group for Higgs Boson Searches, "Flavour Independent Search for Hadronically Decaying Neutral Higgs Bosons at LEP," LHWG Note 2001-07 (July 5, 2001). See http://lephiggs.web.cern.ch/ LEPHIGGS/papers. P. Ferrari and D. Zer-Zion, The OPAL Collaboration, "Two Higgs Doublet Model Interpretation of Neutral Higgs Boson Searches up to the Highest LEP Energies," OPAL Physics Note PN475, July 6, 2001; M. Bluj, M. Boonekamp, J. Hoffman, and P. Zalewski, The DELPHI Collaboration, "Searches for Higgs Bosons in a General Two Higgs Doublet Model," DELPHI 2001-068 CONF 496, July 5, 2001. LEP SUSY Working Group, ALEPH, DELPHI, L3 and OPAL Collaborations, LEPSUSYWG/01-01.1 (June 25, 2001). See http://lepsusy.web.cern.ch/ lepsusy/. LEP SUSY Working Group, ALEPH, DELPHI, L3 and OPAL Collaborations, LEPSUSYWG/01-02.1 (February 16, 2001). See http://lepsusy.web.cern.ch/ lepsusy/. T. Affolder et al., CDF Collaboration,
13.
14.
15. 16. 17.
18.
19.
20.
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"Search for Gluinos and Scalar Quarks in pp Collisions at v's = 1.8 TeV using the Missing Energy plus Multijets Signature," EFI-01-22, FNAL-PUB01/084-E, June 7, 2001, submitted to Phys. Rev. Lett. , hep-ex/0106001. LEP SUSY Working Group, ALEPH, DELPHI, L3 and OPAL Collaborations, LEPSUSYWG/01-03.1 (February 22, 2001). See http://lepsusy.web.cern.ch/ lepsusy/. LEP SUSY Working Group, ALEPH, DELPHI, L3 and OPAL Collaborations, LEPSUSYWG Note. See h t t p : / / lepsusy. web.cern.ch/lepsusy/. C. Adloff et al., HI Collaboration, DESY 01-021, Eur. Phys. J. C20, 639 (2001). F. Abe et al., CDF Collaboration, Phys. Rev. Lett. 80, 2525 (1998). ZEUS Collaboration, "Search for Single Top Production in ep Collisions at HERA," submitted to the International Europhysics Conference on High Energy Physics, Budapest, Hungary, July 12-18, 2001, Abstract 650. HI Collaboration, "Search for Single Top Production in e ± p Collisions at HERA," submitted to the XX International Symposium on Lepton and Photon Interactions, Rome, Italy, July 23-28, 2001, Abstract 512. The ALEPH, DELPHI, L3 and OPAL Collaborations, and the LEP Exotica Working Group, "Search for Single Top Production Via Flavour Changing Neutral Currents: Preliminary Combined Results of the LEP Experiments," LEP Exotica WG 2001-01, Contribution to LP01, July 9, 2001. HI Collaboration, "Observation of Isolated Leptons with Missing PT and Comparison with W Production at HERA," submitted to the XX International Symposium on Lepton and Photon Interactions, Rome, Italy, July 23-28, 2001, Abstract 495.
Gail G. Hanson
Searches for New Particles
21. S. Andringa et al, DELPHI Collaboration, "Search for Single Leptoquark Production in e+e~ Collisions up to v ^ = 208 GeV with the DELPHI Detector," DELPHI 2001-080 CONF 508, June 3, 2001, submitted to the XX International Symposium on Lepton and Photon Interactions, Rome, Italy, July 23-28, 2001, Abstract 222; G. Abbiendi et al, OPAL Collaboration, "Search for Single Leptoquark and Squark Production in Electron-Photon Scattering at ^/s^ = 1 8 9 GeV at LEP," CERN-EP-2001-040, May 17, 2001, submitted to Eur. Phys. J. 22. ZEUS Collaboration, "Search for Leptoquarks in ep Collisions at HERA," submitted to the International Europhysics Conference on High Energy Physics, Budapest, Hungary, July 12-18, 2001, Abstract 600. 23. The ALEPH, DELPHI, L3 and OPAL Collaborations, and the LEP Exotica Working Group, "Search for Excited Leptons: Preliminary Combined Results of the LEP Experiments," LEP Exotica WG 2001-02, Contribution to LP01, July 9, 2001, Abstract 274. 24. ZEUS Collaboration, "Search for Excited Fermions in ep Collisions at HERA," submitted to the International Europhysics Conference on High Energy Physics, Budapest, Hungary, July 12-18, 2001, Abstract 607. 25. C. Adloff et al, HI Collaboration, DESY 00-102, Eur. Phys. J. C17, 567 (2000). 26. Hi Collaboration, "Search for Excited Neutrinos at HERA," submitted to the XX International Symposium on Lepton and Photon Interactions, Rome, Italy, July 23-28, 2001, Abstract 515. 27. W. Adam et al, DELPHI Collaboration, "Search for Technicolor with DELPHI," Contributed paper for EPS HEP 2001 (Budapest) and LP01 (Rome), DELPHI 2001-086 CONF 514, July 1, 2001.
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28. The OPAL Collaboration, "Searches for Technicolor with the OPAL Detector in e + e~ Collisions at the Highest LEP Energies," OPAL Physics Note PN485, July 10, 2001.
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Neutrino Physics
Neutrino Physics Session Chair: Scientific Secretaries:
J. Goodman C.K. Jung J. Klein
H. Sugawara F. Terranova A . oatta
Results from SuperKamiokande Results from K2K Results from SNO
Session Chair: L. Maiani Scientific Secretaries: F. Spada i\. oatta S. Aoki H. Murayama
Experimental review of Neutrino Physics Theory of Neutrino masses and mixings
444
R E C E N T RESULTS F R O M S U P E R - K A M I O K A N D E J. A. GOODMAN FOR THE SUPER-KAMIOKANDE COLLABORATION Department of Physics, University of Maryland College Park, MD, USA 20742-4111 Super-Kamiokande is a 50 Kiloton water-Cherenkov t h a t detects neutrinos in the MeV energy range t h a t are produced in the Sun and neutrinos in t h e GeV energy range produced in t h e atmosphere by cosmic rays. The detector has been operational since April of 1996. In this paper results of our most recent analysis will be presented on both atmospheric and solar neutrinos.
1
Introduction
The existence of neutrinos was postulated in the 1930's. From that time the question of whether or not neutrinos have mass has yet to be conclusively answered. Direct measurements of neutrino mass have proved illusive. If neutrinos have mass then it is possible for them to change flavors as they propagate from their production point. The oscillation probability between two neutrino flavors is given by P = sin2 29 • sin2(1.27 ^ ^ Eu(GeV)
Am 2 (eV 2 ))
where 9 is the mixing angle, L is the flight length of the neutrino, Ev is the neutrino energy, Am 2 = (mf —TO2)is the mass squared difference. Super-Kamiokande is a 50 Kiloton water-Cherenkov detector designed to study neutrino oscillations. It is capable of detecting neutrinos in the MeV energy range that are produced in the Sun and neutrinos in the GeV energy range produced in the atmosphere by cosmic rays.
lected by 11,146 inward facing 50 cm PMTs mounted uniformly on the wall, providing 40% photo-cathode coverage. In the OD, 1885 outward facing 20 cm PMTs monitor the 2.5 m thick veto region. The veto tags incoming particles and is a passive shield for gamma activity from the surrounding rock. The fiducial volume for the analysis of neutrino events starts 2 m inward of the walls of the ID and contains 22.5 kton of pure water. 3
Atmospheric Neutrinos
Primary cosmic rays undergo hadronic interactions in the atmosphere producing copious amounts of pions, many of which decay before further interaction. This decay leads to the production of muons and neutrinos via:
The muons may also decay leading once again to the production of more neutrinos: ^
-> e ± + V^v^)
+ ve(Ve).
This yields an expected ratio of the flux of 2
The Super-Kamiokande Detector
( ^ + ^ ) / ( ^ e +Ve) ~ 2
Super-Kamiokande is a water-Cherenkov detector located in the Kamioka Mine in Gifu, Japan. The cylindrical detector is divided into an inner and outer detector (ID and OD, respectively) by a stainless-steel frame structure that serves as an optical barrier and a mounting point for all photo-multiplier tubes (PMTs). Cherenkov light in the ID is col-
445
In Super-Kamiokande we can observe neutrinos produced in the atmosphere anywhere around the world. Neutrinos produced overhead travel on the average 10-15 km before reaching the detector, while neutrinos produced on the opposite side of the earth travel more than 10,000 km before reaching the detector. Detailed simulations of
Recent Results from Super-Kamiokande
J. A. Goodman the atmospheric neutrino flux is discussed by Honda l.
3.1
Atmospheric neutrino data
In Super-Kamiokande we divide the observed events from atmospheric neutrino interactions into several categories depending on their energy and event topology. Events are divided into energy intervals: events with Evis > 1.33GeV are called multi-GeV events (for historical reasons) while events with E vis < 1.33GeV and P e > lOOMeV/c or P^ > 200MeV/c are called sub-GeV events. Events are characterized as fully-contained (FC) or partially-contained (PC) depending on whether their tracks extend out of the ID. FC events with only one reconstructed ring are subdivided into e-like and /t-like based on likelihood analysis of Cherenkov light pattern. Figure 1 shows a view of the differences between the pattern of light of simulated electrons and muons. Electrons shower and undergo multiple scattering while emitting Cherenkov light while muons travel in approximately straight lines. As a result muon induced rings are much sharper than electron induced rings. This is easily discerned visually and by software. The misidentification fraction is determined to less than 5%. The results of our particle identification are show in Figure 2 along with the expectation from simulation. In Table 1 we show the data from 1289 live-days along with the expectations from the atmospheric Monte Carlo calculations. By computing the double ratio of muon-like events to electron-like events divided by the expectation from Monte Carlo, the dependence on the absolute flux, where there is a ~ 20% uncertainty, is removed. The uncertainty in the Monte Carlo ratio is less than -5%
Figure 1. Shown in the top(bottom) figure is a s i m u lated muon(electron) event in the Super-K d e t e c t o r . Notice the sharpness of the muon ring compared to the electron ring).
(/x-like/e-like) DA TA (/i-like/e-like)MC 446
J. A. Goodman
Recent Results from Super-Kamiokande
Figure 2. Particle id parameter. Datais shown as dots. The lines are Monte Carlo without oscillations.
'«».
i-:^^
^—^rpi^fe^.
\
S 3
The observed values are for sub-GeV: • '
R = 0.644±g;gi? ± 0.051
-1-0.5
• <
'
Gn 0.5
1-1
and for multi-GeV:
3.2
v,M —r vT Oscillation Analysis
In Figure 3 the zenith angle distribution for e-like and mu-like data are shown. In the first of these plots the sub-GeV data with lepton momentum less than 400 MeV/c is shown. This data is insensitive to primary neutrino direction and is useful as a diagnostic. The
0n0.5
Miilti-Getf'^-like''
>
W 5200 o
R = 0.6791^32 ± ° - 0 8 0 These double ratios are consistent with our previous result 2 and shows a deficit of muon neutrinos which can potentially be explained by neutrino oscillations. We have also studied upward going muons which enter the detector from below. These muons come from neutrino interactions in the rock below the detector. Energetic muons traverse the entire detector while lower energy muons may stop in the detector. The zenith angle distribution of these events is also shown in Figure 3. Details of this analysis can be found in Ref. 2.
-0.5
COS0 M|ulti-GeV')i-lik'e'+'PC'
COS0
iZw3
-0.5
0
Q COSO
0.5
1-1
-0.6 -0.4 COS0
-0.2
0 „ 0.5 cos9
upward stopping u
upward through going u
-0.8
-0.5
0
•0.8
-0.6 -0.4 COS9
-0.2
Figure 3. Zenith angle distribution of SuperKamiokande 1289 days FC, P C and UPMU samples. Dots, green line and red line correspond to data, MC with no oscillation and MC with best fit oscillation parameters, respectively.
447
Recent Results from Super-Kamiokande
J. A. Goodman Sub-GeV (Ems < 1.33GeV) Data MC(Honda flux) 2680.4 Iring e-like 2864 4053.2 Iring //-like 2788 multi ring 2159 2680.5 Total 7811 9315.1
> E <
Sin 2 26=1.0, AM 2 =2.4x10- 3 eV 2 X2min=132.4/137 d.o.f.
Multi-GeV FC(Evis > 1.33GeV) Data MC( Honda flux) Iring e-like 626 617.8 Iring /i-like 558 834.0 multi ring 1318 1652.6 2502 Total 3104.5 Partially Contained 754 Total
0.1
1073.8
second and third set of plots shows progressively higher energy and the clear angular dependence of the muon deficit is visible. The bottom plots are for upward going and through going muons. All of this data can be used independently to test the oscillation hypothesis. Doing this yields the allowed oscillation parameters shown in Fig. 4. The minimum x2 is found to be 132.4 with 137 degrees of freedom (d.o.f.) at Am 2 = 2.4 x 10 _ 3 eV 2 , sin226> = 1.00. The deficit of upward going /i-like data is well explained by assuming v i>. —* VT oscillation. \ 2 f° r n o oscillation was found to be 299.3 for 139 d.o.f. Study ofVn Oscillations
and vn
^sterile
Since the number of light (active) neutrinos has been set at three by measurements of the Z° width. The existence of a non-interacting "sterile" neutrino (i/g) has been postulated to explain some experimental results. This neutrino would have neither a charged nor neutral current interaction. If the observed deficit of v^ is due to
02
0.3
DJ
0.3
O.S
0.7
0.8
0.9
v
ii -^ vs oscillation, then the number of interactions observed from up-going neutrinos will be reduced compared to the number that would be expected from the neutral current interactions due to vT. In addition for v^ —> vs oscillations, matter effect will suppress oscillations of high energy {Ev > 15GeV) neutrinos 6 . To observe these effects we: (1) create a neutral current enriched data sample by selecting multiring events with muons, (2) select high energy (Evis > 5GeV) muons and (3) look at upward-going though muons. These data are shown in Figure 5. Using a test of the up(cosO < -0.4)/down(cos 6 > 0.4) ratio for the first two plots and the vertical(cos G < —0.4)/horizontal(cos 0 > —0.4) ratio for the third we are able to exclude the sterile hypothesis at the 99% confidence level. The exclusion regions for these combined results are shown in Figure 6.
3.4
Atmospheric
Summary
The results from our 1289 day atmospheric sample show clear evidence for v^
448
1
sin226
Figure 4. 68,90 and 99% confidence level allowed regions for v^ —> uT oscillation obtained by SuperKamiokande 1289 days result.
Table 1. Event summary for 1289 days
3.3
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Recent Results from Super-Kamiokande
J. A. Goodman
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dilations. Analysis of this data yields a best fit of sin2 29 = 1 and Am2 = 2.3 x 10" 3 eV 2 . In addition our data excludes v^ —> vs oscillations at the 99% confidence level. 4
Figure 5. Zenith angle distributions of: NC enriched sample (top), high-energy PC sample(middle), upthrough-going muon sample (bottom). The solid line is Vfj, —> vT while the dashed line is v^ —• vs
449
Solar N e u t r i n o s
Energy is produced in the Sun through nuclear fusion. For a star such as the Sun, this involves turning 4 protons into a helium nucleus to tap the a particle binding energy. For every a particle made, two neutrinos are produced. The neutrinos, due to their small
J. A. Goodman
Recent Results from Super-Kamiokande
interaction cross section, escape the Sun, essentially undergoing no interactions. Solar neutrinos have been previously detected in chlorine-, gallium-, and water-based detectors 7,8,9,10 . These experiments were each sensitive to different neutrino energy ranges, but all found fluxes significantly lower than those predicted by models of the solar interior, known as Standard Solar Models (SSMs; 11,12 ). This discrepancy between the predicted and measured flux of solar neutrinos is known as "the solar neutrino problem." The solution to the solar neutrino problem is generally believed to involve neutrino oscillations. In the Super-Kamiokande detector neutrinos of sufficient energy (>6 MeV) are detected in real-time by the elastic scatter of electrons. These scattered electrons are used to measure the flux of solar neutrinos, as well as searching for any possible distortions in the neutrino spectrum, and any short or long term time dependence of the flux. An observation of a measurable day/night flux difference, a distortion of the neutrino energy spectrum, or a seasonal dependence to the neutrino flux would provide strong evidence of neutrino oscillations.
4-1
Solar neutrino data
Recoil electrons from solar neutrinos seen in Super-Kamiokande have energies that range from 5 to 18 MeV. At these energies, the electron is limited to a few centimeters in range and the vertex position is found using the relative timing of hit PMTs, assuming that all Cherenkov photons came from a single point. Once a vertex is reconstructed, the direction of the electron is determined using the characteristic shape of the emitted Cherenkov radiation. The energy of the scattered electron is determined from the number of hit PMTs. In order to set the absolute energy scale of the detector, a linear accelerator of electrons (LINAC) has been installed at the
detector 14 . This system allows electrons of a known, fixed energy to be injected into the detector. The energy scale has also been cross checked with the well-known j3 decay of 16 N, which is produced in situ by an (n,p) reaction on l e O . The fast neutrons needed for this reaction are produced by a portable deuteriumtritium neutron generator (DTG; 15 ). The energy scale measured with the DTG agrees with the LINAC to within ±0.3%. The total uncertainty in the absolute energy scale is ±0.6%. We report here solar neutrino data taken between May 31, 1996 and October 6, 2000, representing 1258 live days. The raw data sample consists of 2.0 x 109 triggered events before any background reduction is performed. This sample is reduced through a series of cuts designed to remove known sources of background, including high energy cosmic ray muons and their spallation products, events generated by electrical noise and arcing in the PMTs, and external gamma-ray activity. Additional cuts are performed to remove likely background events with poorly defined vertex positions 16 . After the reduction, a sample of 236,140 events remain, with a signal-to-noise ratio of ~ 1 in the direction of the Sun. The neutrino and scattered electron have a strong angular correlation, and the solar neutrino signal is extracted from the data using the cos9sun distribution. The value of 9sun is the size of the angle between the recoil electron momentum and a vector connecting the Sun to the Earth. The distribution of cos 6sun for the reduced data sample is shown in Figure 7. A strong peak from solar neutrino events is seen. The number of solar neutrino events is extracted from the cos 0sun distribution using a likelihood function that fits the measured background shape and the expected signal shape, based on a detector simulation of solar neutrino events, to the data. This fit is also shown in Figure 7 as a solid line. After 1258 days, a total
450
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Figure 8. Measured solar neutrino flux as a function of zenith angle, relative to the reference SSM flux. The horizontal lin represents the flux measured for all data. The extreme right bin represents d a t a collected after passing through t h e Earth's core (cos0 z > 0.84).
The corresponding 8 B flux at 1 AU is: 2.32±0.03(stat.)+oo7(sys.) x 10 6 cm" 2s-\
of 18,464 ± 204(stat.)i^(sys.) signal events are found. 4-2
Solar Results
The number of signal events is translated into a measured flux using a full detector Monte Carlo simulation taking the input flux and spectrum from the reference SSM, and comparing this to the number of measured signal events. Our detector simulation is based on GEANT 3.21 17 . Neutrinos that produce recoil electrons with energies > 5MeV are produced almost entirely from the (3 decay of 8 B in the solar interior, with a slight admixture of neutrinos from the 3 He-p (hep) fusion reaction. The flux normalization for both fluxes and spectral shape for hep are taken from the BP2000 SSM 11 . For the 8 B neutrino spectral shape, we have taken the recent improved measurement of Ortiz et al. 18 The number of signal events obtained from the cos6sun distribution represents 45.1±0.5(stat.)t^% of the reference flux.
451
(1) The solar neutrino flux as a function of zenith angle is also measured, and the results shown in Figure 8. The zenith angle (8Z) is defined as the angle between the vertical axis at the Super-Kamiokande detector and the vector connecting the Sun to the Earth. The nighttime solar neutrino flux is measured when cos9z > 0, while the day-time flux is measured when cos# z < 0. Additionally, to search for enhancement in the flux for neutrinos passing through the core of the Earth, the night-time period is divided into 6 zenith bins. The flux measured in each of the these zenith bins, relative to the expectations from the reference SSM, are shown in Figure 8. The flux asymmetry between night- and daytime total fluxes is found to be: xf"~t\
= 0.033±0.022(stat.)+°;^ ( s y s .)
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(2) The flux as a function of season is shown in Figure 9, along with the expected variation from the Earth's eccentricity. The measured
J. A. Goodman
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data are consistent (x 2 /d.o.f. = 3.9/7) with the expected annual seasonal variation. A fit to a flat distribution has a x 2 /d.o.f. = 8.1/7. In order to search for distortions in the neutrino energy spectrum, the recoil electron spectrum is examined. This spectrum is obtained by repeating the flux measurement for small slices in recoil electron energy. The measured recoil electron spectra is steeply falling, and is therefore normalized to the expectations from the reference SSM. The normalized recoil electron spectrum is shown in Figure 10. A fit to an undistorted spectrum (flat) gives a x 2 /d.o.f. = 19.1/18. Figure 10 also presents the energy correlated systematic errors that arise from the uncertainties in the energy scale, the energy resolution and the reference 8 B spectral shape. These are the errors that could cause a systematic shift in the measured recoil electron spectral shape, and these errors are considered in the definition19 of the x 2 4-3
0.7
Solar Neutrino Oscillation Analysis
As the measured results show no significant deviation from the expectations of the reference SSM, no solar model independent ev-
j^%^|^ 10
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Figure 10. T h e measured recoil electron spectrum measured at Super-Kamiokande, normalized to the expectations from the reference SSM. Also shown are the energy correlated systematic errors (dotted band) that arise from the uncertainties in the energy scale, the energy resolution and the reference 8 B spectrum.
idence of neutrino oscillations is observed. Therefore, the measured results are used to generate exclusion regions in the neutrino oscillation parameter space where strong deviations are predicted. The measured flux, in combination with the measured recoil electron spectral shape and zenith angle dependence are also used to find allowed regions in this space, areas where the predicted spectral shape, zenith angle dependence and flux are consistent with the observed values. For this analysis, the data were divided into seven zenith angle bins (one day bin, 6 bins in cos# z at night). These zenith angle bins are further divided into eight recoil electron energy bins, to create a "zenith angle energy spectrum" 20 . For each set of neutrino oscillation parameters (sin2 29 and Am 2 ), the expected number of solar neutrinos and the corresponding zenith angle energy spectrum are calculated using a numerical calculation of neutrino survival probabilities, taking into account matter effects as the neutrino propagates from the center of the Sun to the SuperKamiokande detector here on the Earth. The measured and expected zenith angle energy
452
J. A. Goodman
Recent Results from Super-Kamiokande
spectrum are compared using a x2 analysis at each set of neutrino oscillation parameters. This analysis was performed under a two component neutrino oscillation hypothesis, once for active neutrinos (ue —• f^,,-) and once for sterile neutrinos (ve —* ^sterile) • The results of this analysis are shown in Figure 11 for the active case and in Figure 12 for the sterile case. The large, red shaded regions in these figures represent the 95% confidence level (C.L.) exclusion regions based on a flux-independent analysis of the zenith angle energy spectrum. Additionally, the measured zenith angle energy spectrum measured, the measured flux, and the theoretical uncertainty of 8 B neutrino flux are used to generate allowed regions at the 95% C.L. These are regions that are consistent with the observed zenith angle energy spectrum and flux measured at Super-Kamiokande and are shown in the figures as the thin, blue shaded regions near maximal mixing. Finally, the flux measured at Super-Kamiokande is combined with the total fluxes measured in the gallium and chlorine experiments to generate flux-only allowed regions at the 95% C.L. These are regions that predict the correct oscillated fluxes in all three types of solar neutrino experiments under the reference SSM inputs and are shown as green shaded regions in the figures. The flux-only allowed regions must be consistent with the flux-independent zenith angle energy spectrum measured by SuperKamiokande to be considered as a valid solution. The overlap of a particular combined flux-only allowed region (green) with the exclusion regions from the zenith angle energy spectrum analysis (red) would be strong evidence against that allowed region. Because of this, all but a portion of one flux-only allowed region (green) for active neutrinos are excluded at the > 90% C.L. The current SuperKamiokande data favor the so called "Large Mixing Angle" solution (Am 2 cz 1 0 - 4 ~ 10" 5 , sin 2 20 > 0.5) for active neutrinos. The
453
lower portion of this flux-only allowed region is excluded from a lack of a strong day-night flux asymmetry, but the upper half is consistent with the zenith angle energy s p e c t r u m and flux measured at Super-Kamiokande. All flux-only allowed regions for sterile neutrinos are disfavored at the 95% C.L.
sin*(2' ) Figure 11. Neutrino oscillation excluded/allowed regions for the case of active neutrinos. Red s h a d e d regions represent t h e 95% C.L. exclusion r e g i o n s based on a flux-independent zenith angle energy s p e c t r u m analysis. The blue shaded regions represent t h e 9 5 % C.L. allowed regions for an analysis of t h e z e n i t h angle energy spectrum with a flux constraint f o r SuperKamiokande data based on the reference S S M . T h e green shaded regions are t h e allowed r e g i o n s at t h e 95% C.L. based on a flux-only analysis b a s e d o n the results from Super-Kamiokande, in c o m b i n a t i o n with the results from the gallium and c h l o r i n e experiments.
In summary, the Super-Kamiokande detector has precisely measured the flux, recoil electron spectrum, and time variation in the flux of 8 B solar neutrinos over a 1 2 5 8 day period. These data show no strong modelindependent evidence of neutrino oscillation and are therefore used to generate exclusion
J. A. Goodman
Recent Results from Super-Kamiokande this oscillation is to active neutrino flavors (^V> vr)> then Super-Kamiokande should observe these events via their neutral current interactions. Using the SNO result we can predict the Super-Kamiokande electron scattering result ( $ e s ) : Since
~H
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This excellent agreement implies that if one assumes the SSM flux then this would be the first observational confirmation that solar electron neutrinos are oscillating t o other active flavors.
Figure 12. Neutrino oscillation excluded/allowed regions for the case of sterile neutrinos. Region definitions are the same as Figure 12.
5
regions in the neutrino oscillation parameter space. The current data favor the Large Mixing Angle solution for active neutrinos.
We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. This work was partly supported by the Japanese Ministry of Education, Science and Culture, the U.S. Department of Energy and the U.S. National Science Foundation.
4-4
Comparison with the SNO Results
Super-Kamiokande is sensitive to charged current (CC) interactions from electron type solar neutrinos. It is also sensitive to neutral current (NC) interactions from all neutrino flavors, but at a reduced level. The average value of the NC cross section is ~ l / 6 . 5 the CC cross section over the energy interval to which we are sensitive. Recently the SNO collaboration 21 published their measurement of charged current electron neutrinos. They report a value for the flux of
Acknowledgements
References 1. M. Honda et al, Phys. Rev. D52, 4985 (1995); V. Agrawal et al., Phys. Rev. D53, 1313 (1996). 2. Y. Fukuda et al., Phys. Lett. B433, 9 (1998); Phys. Lett. B436, 33 (1998); Phys. Rev. Lett. 8 1 , 1562 (1998); Phys. Rev. Lett. 82, 2644 (1999); Phys. Lett. B467, 185 (1999). 3. M. Ambrosio et al., Phys. Lett. B434, 451 (1998); F. Ronga, for the MACRO Collaboration, in these Proceedings. 4. W.W.M.AUison et al., Phys. Lett. B391, 491 (1997); G. Pearce, for the Soudan 2 Collaboration, in these Proceedings.
- 22 „ - l
This corresponds to ~ 35% ± 3% of the SSM. A simple way to look at this is to say that their result implies that 65% of the electron neutrinos have oscillated to other flavors. If 454
Recent Results from Super-Kamiokande
J. A. Goodman 5. M. Apollonio et al., Phys. Lett. B466, 415 (1999). 6. E. Akhmedov et al, Phys. Lett. B300, 128 (1993); P. Lipari a n d M. Lusignoli, Phys. Rev. D58, 73005 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 505 (1998); Q. Y. Liu et al, Phys. Lett. B440, 319 (1998). 7. B.T. Cleveland et al., Astrophys. J. 496, 505 (1998). 8. J.N. Abdurashitov et al., Phys. Rev. C 60, 055801 (1999). 9. P. Anselmann et al., Phys. Lett. B 327, 377 (1994). 10. Y. Fukuda et al., Phys. Rev. Lett. 77, 1683 (1996). 11. J.N. Bahcall et al., astro-ph/0010346. 12. J.N. Bahcall et al., Phys. Lett. B 433, 1 (1998). 13. Y. Fukuda et al., Phys. Rev. Lett 8 1 , 1562 (1998). 14. M. Nakahata et al., Nucl. Instr. Meth. A 421, 113 (1999). 15. E. Blaufuss et a l , Nucl. Instr. Meth. A 458, 636 (2001). 16. S. Fukuda et a l , hep-ex/0103032 (2001). 17. GEANT Detector Description and Simulation Tool, Cern Programming Library W5013 (1994). 18. C.E. Ortiz et al., Phys. Rev. Lett. 85, 2909 (2000). 19. Y. Fukuda et al., Phys. Rev. Lett. 82, 2430 (1999). 20. S. Fukuda et a l , hep-ex/0103033 (2001). 21. SNO Collaboration, Phys.Rev.Lett. 87 (2001) 071301
455
RECENT RESULTS F R O M K2K C. K. JUNG Dept. of Physics and Astronomy, The State University of New York at Stony Brook, Stony Brook, New York 11794-3800, USA E-mail: [email protected], sunysb. edu for the K2K Collaboration K2K is a long baseline neutrino oscillation experiment using a neutrino beam produced at the KEK 12 GeV PS, a near detector complex at KEK and a far detector (Super-Kamiokande) in Kamioka, Japan. The experiment was constructed and is being operated by an international consortium of institutions from Japan, Korea, and t h e US. The experiment started taking d a t a in 1999 and has successfully taken data for about two years. K2K is the first long baseline neutrino oscillation experiment with a baseline of order hundreds of km and is the first accelerator based neutrino oscillation experiment that is sensitive to the Super-Kamiokande allowed region obtained from the atmospheric neutrino oscillation analysis. A total of 44 events have been observed in the far detector during the period of June 1999 to April 2001 corresponding to 3.85 x 10 19 protons on target. The observation is consistent with the neutrino oscillation expectations based on the oscillation parameters derived from t h e atmospheric neutrinos, and the probability that this is a statistical fluctuation of non-oscillation expectation of 63.9Jig g is less than 3%.
1
Introduction
In the late 1980's, the 1MB and Kamiokande experiments, which were both large underground water Cherenkov detectors, observed smaller atmospheric neutrino flux ratio v^/u,, than the predicted value. 1 ' 2 This was the beginning of so-called "Atmospheric Neutrino Anomaly". These results were not, however, supported by other underground experiments using iron calorimeters: Frejus 3 , NUSEX 4 and Soudan, albeit with limited statistical powers. In Table 1, the measurements of fM/^e flux ratio of these experiments are summarized along with recent measurements in a form of R = (p./e)DATA/(v/e)MC, where p. and e are the number of muon-like (/U-like) and electron-like (e-like) events observed in the detector for both data and Monte Carlo simulation. By making this double ratio one can largely cancel experimental and theoretical uncertainties, especially the uncertainty in the absolute flux. One would expect R to be unity, if the Monte Carlo simulation of an experiment accurately models the data. As can be seen from the table, the measured R
values of 1MB and Kamiokande are substantially lower than unity which could be interpreted as "disappearance" of v^ flux, possibly via neutrino oscillations. By interpreting the anomaly as neutrino oscillation phenomena the Kamiokande experiment obtained allowed region for v^ —* ue and v^ —• Vy_ oscillation scenarios, where x = s or r, utilizing zenith angle dependence of R.b While the interpretation of the anomaly as an indication of neutrino oscillation was exciting and plausible, there were many who believed that the anomaly was due to some unknown systematic errors particular to the water Cherenkov experiments, especially in particle identification. This criticism was answered by a joint (IMB-Kamiokande) beam test experiment at KEK 6 which found that the particle identification methods used by both experiments are valid well within the quoted systematic uncertainties. Furthermore, in 1997 the improved Soudan-2 experiment reported 7 that they measure the ratio closer to the water Cherenkov detector measurements than their previously reported value.
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C. K. Jung
Recent Results from K2K
Table 1. Summary of the measurements of R. T h e first errors are the statistical uncertainties and the second errors are the systematic uncertainties. The exposure is measured in kiloton-years. The measurements of Kamiokande and Super-Kamiokande are presented separately for "sub-GeV" (EViS < 1330 MeV) and "multiGeV" (Evis > 1330 MeV) samples, where Evi3 is defined to be t h e energy of an electron that would produce the observed amount of Cherenkov light.
Experiment Kamiokande (sub-GeV) Kamiokande (multi-GeV) 1MB Soudan-2 Frejus NUSEX Super-Kamiokande (sub-GeV) Super-Kamiokande (multi-GeV)
R 0.62 0.57 0.54 0.67 1.00
± ± ± ± ±
0.06 ± 0.06 0.08 ± 0.07 0.05 ± 0.07 0.15±°$ 0.15 ± 0.08
n QQ+ 0 - 35 u . » y _ 0 25
0.64 ± 0.02 ± 0.05 0.62 ± O.03 ± 0.09
This unsettling situation, however, lasted until 1998 when the Super-Kamiokande (SuperK) experiment reported its analysis of atmospheric neutrinos with its unprecedented high statistics and high quality data resulting in a strong evidence for neutrino oscillations in the atmospheric neutrinos. 8 Figure 1 shows the updated zenith angle distributions of e-like and mu-like data sets of the SuperKamiokande atmospheric neutrino candidate sample. Zenith angle dependent deficit in the mu-like event distributions compared to the non-oscillation expectations is strikingly manifested in the data. On the other hand, the data are fit extremely well with a neutrino oscillation scenario as shown in the figure.9 This finding is a major discovery with far reaching impact in elementary particle physics, cosmology and astrophysics. The phenomenon of neutrino oscillation which requires neutrinos to have non-zero mass alters our view of the world of elementary particles. Namely, the Standard Model (SM), which is the currently prevailing theory of the elementary particles and assumes neutrinos to have zero mass, must be modified. The finding will also make the theories of the Grand Unification more viable and attractive, and thus opening a possibility of long-sought proton decays 10 ' 11 . To confirm the above finding, initially
457
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to investigate' the "atmospheric neutrino anomaly", several long baseline neutrino oscillation experiments using accelerator generated neutrino beams have been proposed. Among them, K2K (KEK to Kamioka) experiment 12 is the first one to be online. The K2K experiment consists of a neutrino beam line, a near detector complex inside the KEK laboratory near the east coast of Japan, and a far detector (the SuperKamiokande detector) 250 km away from KEK. The experiment started taking data in March 1999 and has successfully operated since then. The K2K physics program has three major components: (1) Neutrino oscillations, (2) Neutrino cross-section measurements, and (3) Study of neutrino background to proton decay searches. The neutrino oscillations program has in turn two topics: search for ve appearance signature from possible v^ —> ve oscillations, and analysis of v^ disappearance signatures for v^ —> Vy_ oscillation scenarios. The latter is the main topic of discussion of this paper. The v^ disappearance signatures can come from a comparison of the observed number of z/M events to the non-oscillation expectations at the far detector and/or from a distortion in the observed energy spectrum. If observed, the energy spectrum distortion will
Recent Results from K2K
C. K. Jung r/i
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become the first direct evidence for energy dependent neutrino oscillation, which has not been firmly established so far by other exper-
iments. In Figure 2, the proposed sensitivity (circa 1998) of the K2K experiment for Vy, to vx oscillation using disappearance signatures
458
C. K. Jung
Recent Results from K2K
is shown along with other relevant contours. K2K can measure various neutrino crosssections on water, especially a relative crosssection of the neutral current n° production to the single muon production. This information is useful not only for theoretical modeling but also for a discrimination of fM —• vT oscillation scenario from v^ —> ^ s oscillation scenario in the Super-Kamiokande atmospheric neutrino analysis. A detailed description of this analysis can be found elsewhere. 13 The K2K data also provides valuable information on the proton decay search background studies. Proton decay searches performed at large water Cherenkov detectors rely on the MC simulation of the atmospheric neutrinos to estimate backgrounds to the proton decay candidates. Since the K2K neutrino beam has an energy spectrum similar to the atmospheric neutrinos, K2K can validate these atmospheric neutrino MC simulations using the lkton water Cherenkov detector data in the near detector complex, which collects high statistics neutrino events. Details of this study can be found elsewhere.11 The K2K collaboration is an international consortium of institutions from Japan, Korea, and the United States. There are about 100 collaborating members from 18 institutions.
2
K2K Neutrino Beam Line and Detectors
The K2K experiment is composed of the KEK 12 GeV Proton Synchrotron (PS), a neutrino beamline, near detector complex inside KEK and the Super-Kamiokande detector 250 km away as a far detector. The neutrino beamline is composed of an aluminum target, a pair of horn shaped magnets (so-called neutrino horns), a decay pipe, and a beam dump. The Al target (3 cm diameter, 60 cm long) is embedded inside the first horn as part of the structure and the decay pipe is 200 m long. There are several
459
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sin 2 (29) Figure 2. The K2K sensitivity for neutrino oscillation Vp to vx at 90% C.L. Also shown are the sensitivity of MINOS experiment at Fermilab along with other relevant contours. The MINOS experiment is expected to start data in 2005.
beam monitors for various purposes. A ring imaging gas Cherenkov monitor is located after the second horn to measure pion momentum and angular divergence along with a pair of rotating ionization chambers (segmented pads) which measures azimuthal symmetry and the radial profile of the secondary beam flux. Both of these monitors are remotely movable and they are in the beamline only when they are taking data. An additional ionization strip chamber is located at the entrance of the decay pipe to measure proton beam profile. At the end of the decay pipe, behind the beam dump, an ionization strip chamber and silicon pad detectors are located to measure the muon flux and profile. Since
C.K. Jung
Recent Results from K2K
the neutrino beam is generated from the pion decays in the decay pipe, the K2K neutrino source is not a point source. Thus, predicting the number of neutrino events at the far detector based on the measurements at the near detector requires a good understanding of the beam characteristics. This is the reason why many independent beam monitoring systems are employed. The near detector complex which is located 300 m from the target consists of a one kiloton water Cherenkov detector (a miniature Super-Kamiokande detector), and a finegrained detector system (a system of a scintillating fiber tracker with water targets, a scintillator veto counter, a lead glass calorimeter and a muon ranger detector). Many components of the near detector system are simply straightforward modifications of equipment available from previous projects at KEK. The layout of the experiment is shown in Figure 3. The 1 kton water Cherenkov detector (lkton) is a 10 m in height and 11 m in diameter cylindrical tank viewed by ~800 20" Hamamatsu PMTs. The scintillating fiber tracker 14 (Scifi) also uses water as target material for the neutrino beam, consisting of twenty 2.4mx2.4mx6cm segments totalling seven tons of water. The individual target segments are interleaved with scintillatingfiber tracking layers to provide good transverse vertex definition for neutrino interactions as well as track reconstruction capability. A Pb-glass wall, recycled from the TOPAZ detector at Tristan is located behind the Scifi detector to identify electrons. A Muon Ranger Detector 15 (MRD), consisting of iron plates and drift tubes that were used in VENUS, is used to measure muon energy up to 3.5 GeV with good accuracy. In order to minimize systematic uncertainties, K2K employs a common detector technology, water Cherenkov detectors at both near and far sites, and a common target, water for lkton and Scifi. The two
near-detector components are complementary. The lkton detector has its fiducial volume controlled less precisely due to coarser vertex resolution. Unlike the fine-grained detector, however, the 1-kton detector can reconstruct 7r0s, and due to the large size of the volume one can measure variations of the beam characteristics at larger distances from the beam axis. The Scifi detector has a smaller target volume, but its fiducial volume is much more precisely defined due to accurate vertex measurements. The 1-kton detector measures ve contamination and the fraction of weak neutral current (NC) events v^N —> v^N'+w0, using the same methods as in the Super-Kamiokande detector. The fine-grained detector also measures ve contamination. Quasi-Elastic (QE) reactions {y^N —* /i~N') in the fine-grained detector serve to measure beam uniformity and the neutrino energy spectrum. The far detector for K2K is the SuperKamiokande detector, which has been taking data since April, 1996. Super-Kamiokande is a water Cherenkov detector consisting of 50 kton of ultra-pure water in a 41 m (height) x 39 m (diameter) tank. Its inner volume is viewed by 11,146 20" diameter Hamamatsu photo-multiplier tubes, providing photo-cathode coverage equivalent to 40% of the detector surface area. The inner detector is surrounded by a 2 m thick outer layer of water viewed by 1885 8" diameter Hamamatsu tubes. The outer detector is used to veto particles coming from outside as well as providing shielding against backgrounds emanating from the surrounding rock. A nominal 22.5 kton fiducial volume is used to study neutrino interactions. K2K does not interfere with normal operation of Super-Kamiokande. GPS clocks at both sites are used to define appropriate DAQ time windows for KEK beam pulses arriving at Kamioka. 16 The K2K neutrino beam is generated from the fast extracted 12 GeV KEK PS pro-
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ton beam which has l^ts spill duration with a 9 micro-bunch structure. The design intensity of the protons on target (pot) is 6 x 1012 protons per spill for every 2.2 s. The goal of the experiment is to collect data corresponding to 1020 pot for 5 years of running (4 months of run/year). The energy spectrum of the neutrino beam peaks at around 1 GeV and has a mean energy of 1.3 GeV. The beam is about 97% pure in v^ and contains 2% PM and 1% ue. The K2K near detector construction was completed in January 1999 and the neutrino beam line commissioning was started on January 27, 1999. On March 5, 1999, the K2K physics data taking run was started. By April 2001, the experiment has accumulated data corresponding to 4.6 x 10 19 pot (delivered). The average beam intensity on target was about ^5.5 x 10 12 proton per pulse and the nominal horn current was 250 kA. All detector subsystems worked very well without major problems.
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3
Long Baseline Neutrino Oscillation Analysis
As discussed in the previous section, K2K can look for two neutrino oscillation signatures: ve appearance and v^ disappearance. However, the statistical power of the experiment so far on the ve appearance analysis is too weak to produce a competitive result. Thus, in this paper, we will focus our discussions on the Vp disappearance oscillation analysis.
3.1
Beam Aiming, Stability and Monitoring
In order to obtain an unambiguous result on neutrino oscillations, we must first ensure that the neutrino beam is aimed at the far detector correctly. The K2K neutrino beam line was constructed with an accuracy of ~0.1 mrad and was surveyed using GPS with an accuracy of ~0.01 mrad. Meanwhile the beam aiming accuracy required for the K2K experiment is about 3 ~ 5 mrad which
Recent Results from K2K
C. K. Jung
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is deduced by comparing off-axis neutrino energy spectra with the on-axis energy spectrum at the far detector location. (See Figure 4.) This rather mild requirement stems from the wide-band nature of the K2K neutrino beam. The actual spill-by-spill and day-by-day variations of the neutrino beam direction with respect to the nominal beam direction are also monitored using various beam monitor systems to ensure that there are no wild fluctuations or drifts in the beam direction which would result in a reduction of the neutrino flux at the far detector. The accuracy of the monitored beam direction is found to be less than 1 mrad from all beam monitoring systems for the entire period of K2K operation. The spill-by-spill monitoring of the high energy muon direction which is highly correlated to the neutrino beam direction is done with the muon monitors (Strip ionization chambers and silicon strip pad detectors) located behind the beam dump, 200 m from the target. The measured spill-by-spill direction of high energy muons (E^ > 5 GeV) with respect to the nominal beam direction for the entire data taking time period is found to be well within the ± 1 mrad boundaries.
The day-to-day monitoring of the actual neutrino beam direction and flux stability are done with both lkton {E^ > 0.2 GeV) and MRD (£;„ > 1 GeV). Figure 5 shows the day-to-day measurements of the neutrino beam direction and neutrino flux for the entire data taking time period using MRD. The dashed lines in the left side plots indicate ± 1 mrad off-axis directions from the nominal beam directions denoted by solid lines. As can be seen almost all data points are within the ± 1 mrad boundaries. The top data point on the right side plot are CC interaction rate in unit of interactions/5 x 10 12 ppp (protons-per-pulse) and the bottom data points are the interaction rate measured in a smaller fiducial volume of the detector. Since ultimately the event rate observed at the far detector is normalized by the near detector measurement, changes in the measured event rate in the near detector are not a great concern. However, to minimize any unexpected systematic effects in the experiment, it is desirable to have the rate stable. Indeed the data points guided by the a solid line representing the average event rate show a good stability of the event rate, i.e. the neutrino flux, for the entire operation of the experiment. The apparently low event rate for the June 99 period was partly caused by a sightly different proton target area configuration, especially the neutrino horn current (200 kA instead of 250 kA).
3.2
Near Detector Data Analysis for Neutrino Oscillations
In order to observe the "fM disappearance" signatures at the far detector, we need to measure the neutrino beam flux (in practice event rates) and un-oscillated energy spectrum at the near detector. Since the lkton detector shares similar efficiencies and systematics with the SuperKamiokande detector, it provides the pri-
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mary information on the neutrino event rate and neutrino spectrum measured at the near detector which are extrapolated to the far detector to generate the non-oscillation expectation event rate and energy spectrum. In general, for Charged Current (CC) QE neutrino interaction events (f M +n —> /j,~ +p), one can reconstruct neutrino energy spectrum by measuring muon momentum p^ and production angle cosO^ with respect to the beam direction and using simple two body kinematics: Ev
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where raw and mM are respective neutron and muon masses, and E^ is the muon energy. The recoil protons in the CCQE events are typically not seen in the lkton detector because most of time the protons are created with momenta below Cherenkov threshold, and thus we call these events "single muon" events. In Figure 3.2, reconstructed energy spectrum using lkton single muon event sample is shown along with MC predictions. Also
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shown are the distributions of muon momentum and angle. As can be seen, the data and MC predictions agree fairly well. The left figures also show the background contributions to the distribution from non-QE events. It turns out that the "single muon" event sample contains substantial number of non-CCQE events that have one or more pions generated, but are not seen by the detector. In order to obtain true neutrino energy spectrum one must, then, properly subtract out these background events contributions. This can be accomplished using the data from the the scifi detector where the recoil protons can be observed and its direction can be compared with the predicted direction deduced from the muon observables. This provides us with means to estimate non-QE background contributions to the CCQE event candidate event sample. Figure 3.2 shows a cos# distribution of two track events in the Scifi detector, where cos# is defined as the angle between the reconstructed second (shorter) track and the
C. K. Jung
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expected proton direction calculated using two-body kinematics and assuming that the event is a CCQE event. Since at the large angle region (small cos 9 region) we expect that most of the events are coming from non-QE background events, it is possible to estimate the background contributions by fitting the MC distribution to the data at this region.
the flux are then checked by the information from the gas-Cherenkov pion monitor at the target station. From the light distribution
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Once the event rates and energy spectra are measured at the near detector sub-systems, they are extrapolated to the far detector location to predict the event rate and energy spectrum at the Super-Kamiokande detector. The extrapolation is done by using a detailed beam MC simulation which predicts neutrino flux at the near detector and at the far detector simultaneous. Since the neutrino beam is produced by a line source rather than a single point source, it is necessary to simulate the details of the entire neutrino beam line. The energy dependent far to near ratios of
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Recent Results from K2K
C. K. Jung Table 2. Comparison of lkton and Super-Kamiokande Analysis Characteristics.
Fiducial Vol. E. Threshold ace. x eff. # of Events
lkton 25 tons >1000 p.e. 0.74 63,000
Table 3. Comparison of t h e Predicted Number of Events at Super-Kamiokande. The errors shown are systematic errors and the statistical errors are negligible.
SuperK 22,500 tons >300 p.e. 0.81 63.9
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data of the pion monitor, it is possible to extract information on the pion kinematics, i.e. pion momentum distribution and angular divergence from the proton beam direction. Since neutrinos are produced by simple two body decays of pions, the far to near neutrino flux ratio can be precisely determined by this information. For the neutrino energy regions (Ev > 1 GeV) where the pion monitor is sensitive, we find that the two predictions from the beam MC and the pion monitor match perfectly within the statistical uncertainties. A Super-Kamiokande data analysis procedure similar to that of atmospheric neutrino's is applied to the extrapolated neutrino flux to yield expected number of events and energy spectra for various sets of oscillation parameters. Table 2 shows some characteristics of lkton and Super-Kamiokande analyses as well as the observed number of events at lkton and corresponding nonoscillation predicted number of events at Super-Kamiokande. Similar procedures are applied to extrapolate measured event rates by Scifi and MRD. The resulting non-oscillation predicted number of events at Super-Kamiokande by these systems are shown in Table 3. While the three systems have quite different detector characteristics and consequently different systematic uncertainties, the predicted number of events by these systems are well within the estimated systematic uncertainties of each other. One can notice that the systematic uncertainty in the lkton predicted number of events is the smallest. This is
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because the lkton detector and the SuperKamiokande detector have very similar detector characteristics, and consequently when far to near ratio is taken, some of the systematic uncertainties such as cross-section uncertainties cancel out. The dominant systematic uncertainties in the lkton predicted number come from the uncertainty in the far to near ratio (~7%) and the uncertainty in the lkton fiducial volume determination (~4%). 3.4
Observation of K2K Neutrino Events in Super-Kamiokande
The K2K experiment observed its first neutrino event in the Super-Kamiokande detector in June 19, 1999, which was the first long baseline (of order hundreds of km) neutrino beam event in history. The event vertex was within the 22.5 kton fiducial volume of Super-Kamiokande and it was within ±1.5/[iS time window of the expected time. The expected number of background events is estimated to be about 10~ 4 . By the end of April 2001 the experiment has observed a total of 44 fully contained (FC) events in the 22.5 kton fiducial volume (FV) of the Super-Kamiokande detector compared to the non-oscillation predicted number of 6 3 . 9 I 6 6 events. In addition, the experiment has observed 26 fully contained events in the out of fiducial volume (vertices in between the PMT planes and the surfaces 2m inward from the PMT planes). The event selection criteria for these events are very similar to that used for the atmospheric neutrino analysis. 8 The most
Recent Results from K2K
C. K. Jung powerful discrimination of the K2K events against the random atmospheric neutrino events is a timing cut utilizing the narrow time structure (l.l/us) of the K2K beam in every 2.2 s. Figure 8 shows a summary view of the data reduction for fully contained event analysis. Here AT is defined as the time difference between the SuperK event time and the beam spill time at the KEK PS subtracted by the time of flight of the neutrino from KEK to SuperK (0.83 ms). The absolute times are measured by GPS receivers located in each site and local timing clocks. The one shot timing accuracy of GPS is known to be better than 200 ns and thus the timing cut for final event sample is chosen to be —0.2 < AT < 1.3/us. As can be seen there is only one event that is out of time with the K2K beam. The event is consistent with the expected atmospheric neutrino background rate in the one millisecond time window, and the estimated background to the fully contained fiducial volume events in the signal window is of order 10~ 3 .
Fully Contained Event
Analysis
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In order to perform an oscillation analysis using rate measurements, we must check whether the observed event rate at the far detector remains constant (within the statistical fluctuation) throughout the data taking time period. Irregular event rates beyond the statistically expected fluctuation would indicate some kind of unknown systematic problems either with the neutrino beam or with the far detector. This is checked by plotting the number of observed events (cumulative) as a function of integrated protons on target. Figure 9 shows such plots for all K2K events observed in SuperK including the Outer Detector (OD) events. The OD events are defined as the events that have appreciable OD PMT hits. While the OD events are less well understood because of the poorer resolution of the OD, they are useful in studying the time dependent event rate. The estimated background for the OD event sample is of order one. The diagonal solid lines in the figure show the average event rate slopes. While there are a few noticeable gaps in the distributions, a statistical analysis shows that they are perfectly consistent with fluctuations expected from the Poison statistics. More rigorously, a KS test of the distribution results in KS probability of 20.5%. And if only the FCFV events are used, it results in a KS probability of 32.3%.
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Results of Oscillation Analysis
For the oscillation analysis, we use only the FCFV events since they are the most well understood events from the SuperK atmospheric neutrino analysis. In the future, however, we may be able to use the fully contained out of fiducial volume events as well for the oscillation analysis. Table 4 summarizes a break down of the FCFV events into sub-classes along with non-oscillation expectation and oscillation expectations for various Am 2 values with sin 2 26 = 1.0. While the statistical power is not over-
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Recent Results from K2K
C. K. Jung
Table 4. Observed fully-contained K2K-SK events with vertices in the fiducial volume (FCFV). T h e indentation of entries in the first two columns indicates that some categories are subsets of one above. T h e expectation for "e-like" events changes with oscillation since some are mis-identified v^ events (not ve beam contamination). T h e oscillation expectations assume sin 2 2d = 1.0, a full mixing.
Category FC-22.5kton (all) 1-ring /tx-like e-like multi-ring
Expected for Am 2 in 10~ 3 eV 2 = 3. 5. 7. 41.5 ± 4 . 7 27.4 ± 3 . 1 23.1 ± 2.6 22.3 ± 3 . 4 14.1 ± 2 . 2 13.1 ± 2.0 19.3±3.2 11.6 ± 1 . 9 10.7 ± 1 . 8 2.9 ± 1 . 2 2.5 ± 1 . 0 2.4 ± 1 . 0 19.3 ± 3 . 4 13.3 ± 2 . 3 10.0 ± 1 . 8
Expected (non-osc.) 63.9± b 6 -j 38.4 ± 5 . 5 34.9 ± 5 . 5 3.5 ± 1 . 4 25.5 ± 4 . 3
Observed 44 26 24 2 18
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teractions. A reconstructed neutrino energy spectrum is shown in Figure 10 along with expectations with and without oscillations. The normalizations for the expectations are done using the near detector measurements. Again while the statistics are rather poor to draw any convincing conclusions, the data appear to be consistent with the oscillated expectation given by the SuperK atmospheric neutrino best fit parameters. In order to perform an oscillation analysis using this information one must understand the associated systematic uncertainties, especially the binby-bin correlated errors. At the time of this presentation, the systematic uncertainties of the energy spectrum have not been yet well evaluated. Thus, the figure contains only the statistical error bars of the data points. Rigorous evaluation of the systematic uncertainties is being carried out at this time by the K2K collaboration along with more extensive oscillation analyses that fully utilize the information from the shape of the energy spectrum as well as the overall rate. We expect that these analyses will be completed by the spring of 2002.
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whelming, the data generally indicate a deficit in the observed number of events compared to the non-oscillation expectations. A simple statistical calculation results in a probability that the observed data is a statistical fluctuation of the non-oscillation hypothesis to be less than 3%. A neutrino energy spectrum can be also constructed from these events using the method described earlier. For this purpose only the 24 1-ring /i-like events are used as they are most likely produced by CCQE in-
4
K2K Near Detector Upgrade
The original design of the K2K experiment was optimized to explore the neutrino oscillation parameter space favored by the Kamiokande experiment, i.e., Am2 10"
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eV2 region. The well-established allowed region by the Super-Kamiokande experiment is, however, much lower in Am 2 centered around 3 x 10~ 3 eV 2 . For a fixed neutrino flight distance of 250 km, this Am 2 value corresponds to 600 MeV neutrino energy for the first peak of the oscillation probability, which in turn suggests that the distortion in the energy spectrum (ultimate signature of neutrino oscillation) may occur below 1 GeV energy region in the K2K measured energy spectrum. Thus, in order for us to reduce the systematic uncertainties in the below 1 GeV region and thereby making K2K more sensitive to the low Am 2 neutrino oscillations, it is necessary to upgrade the K2K detector. As the first step towards an upgrade, we plan to remove the lead glass calorimeter wall in the fall of 2001. This will allow us to accumulate more Scifi events below 1 GeV. In the summer of 2003, we plan to install a finely segmented liquid scintillator tracker, which will have high efficiency for short (~5 cm) tracks and will be able to detect a proton down to 400 MeV/c. It will also have a particle identification capability for p/n separation by dE/dx.
Conclusion
K2K is the first accelerator based long baseline neutrino oscillation experiment to test the allowed parameter region obtained by the Super-Kamiokande atmospheric neutrino analysis. The experiment has taken data successfully for about two years since 1999 (June 1999 - April 2001) corresponding to 4.58 (3.85) x 10 19 protons on target delivered (Super-Kamiokande live). Additional data obtained during the period May - July 2001 are being analyzed and the goal of the experiment is to accumulate data corresponding to 10 20 protons on target. With 44 observed events at the far detector compared to the non-oscillation expectation of 63.9l 6 ' 6 , the non-oscillation hypothesis is disfavored more than 2a (97%) level. Both the observed event rates and the energy spectrum are consistent with those expected from neutrino oscillations with the best fit parameters from the Super-Kamiokande atmospheric neutrino analysis. K2K provides a proof of principle for long baseline experimentation with baseline over 100 km. Its success leads us to rich neutrino physics programs of future long baseline experiments: MINOS, CNGS, JHF to Super-Kamiokande, super-beams and ultimately neutrino factories. Neutrino oscillation is the only evidence we have for physics beyond the Standard Model. During the past two decades, we have devoted much of our effort to understand the nature of the quark mixing and associated CP violation. With neutrino oscillation, we have now started a new era of particle physics in which we must dedicate our effort to understand the lepton mixing and possible CP violation in the lepton sector. With some good cooperation of nature, we may ultimately be able to explain the nature of matter-antimatter asymmetry in the Universe through lepto-genesis.
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C. K. Jung Acknowledgments The K2K experiment is co-hosted by KEK, and ICRR, University of Tokyo, and it is supported by the Ministry of Education, Culture, Sports, Science and Technology, Government of Japan, the U.S. Department of Energy, the Korea Research Foundation, and the Korea Science and Engineering Foundation. The collaboration gratefully acknowledges the cooperation of the Kamioka Mining and Smelting Company. The author wishes to acknowledge the support of The Research Foundation of the State University of New York at Stony Brook, and the U.S. Department of Energy under contract^ DEFG0292ER40697.
10. 11.
12.
13.
References 1. K.S. Hirata et al, Phys. Lett. B 205, 416 (1988); K.S. Hirata et al, Phys. Lett. B 280, 146 (1992). 2. D. Casper, et al, Phys. Rev. Lett. 66, 2561 (1991); R. Becker-Szendy et al., Phys. Rev. D 46, 3720 (1992). 3. K. Daum, et al., Z. Phys. C 66, 417 (1995). 4. M. Aglietta, et al, Europhys. Lett. 8, 611 (1989). 5. Y. Fukuda et al, Phys. Lett. B 335, 237 (1994). 6. S. Kasuga et al, Phys. Lett. B 374, 238 (1996). 7. W.W.M. Allison et. al, Phys. Lett. B 391, 491 (1997). 8. Y.Fukuda et al, Phys. Lett. B 433, 9 (1998); Y.Fukuda et al, Phys. Lett. B 436, 33 (1998); Y.Fukuda et al, Phys. Rev. Lett. 81, 1562 (1998). 9. For most recent update of the SuperKamioknde results, see J. Goodman's presentation and paper presented in this conference: XX International Symposium on Lepton and Photon Interac-
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15. 16.
tions at High Energies, Rome, Italy, July 2001, http://www.lp01.infn.it. K.S. Babu, J. C. Pati and F. Wilczek, [arXiv:hep-ph/9812538]. " Physics Potential and Feasibility of UNO," UNO "white paper" edited by D. Casper, C. K. Jung, C. McGrew and C. Yanagisawa, June 2001. Preprint #:SBHEP01-3. The full report is available on the web at: http://nngroup.physics.sunysb.edu/uno/ S. H. Ahn et al [K2K Collaboration], Phys. Lett. B 511, 178 (2001) [arXiv:hep-ex/0103001]. For more details on this subject, see C. Mauger's presentation in NuIntOl workshop: The First International Workshop on Neutrino-Nucleus Interactions in the Few GeV Region, in Tsukuba, Japan, December 2001, http://neutrino.kek.jp/nuint01/. A. Suzuki et al. [K2K Collaboration], Nucl. Instrum. Meth. A 453, 165 (2000), [arXiv:hep-ex/0004024]. T. Ishii et al. [K2K Collaboration], [arXiv:hep-ex/0107041]. H. G. Berns and R. J. Wilkes, IEEE Nucl. Sci. 47, 340 (2000).
SOLAR N E U T R I N O RESULTS FROM T H E S U D B U R Y N E U T R I N O OBSERVATORY JOSHUA R. KLEIN, FOR THE SNO COLLABORATION Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396 We describe here the measurement of the flux of neutrinos created by the decay of solar 8 B by the Sudbury Neutrino Observatory (SNO). The neutrinos were detected via t h e charged current (CC) reaction on deuterium and by the elastic scattering (ES) of electrons. T h e CC reaction is sensitive exclusively to ue's, while t h e ES reaction also has a small sensitivity to i/M's and uT's. T h e flux of ve's from 8 B decay measured by the CC reaction rate is e) = 1.75 ± 0.07 ( s t a t . ) l ° ' J j (sys.) ± 0.05 (theor.) x 10 6 c m ~ 2 s - 1 . Assuming no flavor transformation, the flux inferred from the ES reaction rate is ES(ux) = 2.39 ± 0.34 ( s t a t . ^ o J f (sys.) x 10 6 c m _ 2 s _ 1 . Comparison of <j>cc(ve) t o the Super-Kamiokande Collaboration's precision value of (j>ES{vx) yields a 3.3CT difference, assuming the systematic uncertainties are normally distributed, providing evidence that there is a non-electron flavor active neutrino component in t h e solar flux. The total flux of active 8 B neutrinos is thus determined to be 5.44±0.99 x 10 6 c m _ 2 s _ 1 , in close agreement with the predictions of solar models.
1
Introduction
Over thirty years of solar neutrino experiments i'2'3'4*5'6 have demonstrated that the flux of neutrinos from all sources within the Sun is significantly smaller than predicted by models of the Sun's energy generating mechanisms 7 ' 8 . The deficit is not only universally observed but has an energy dependence which makes it hard to attribute to astrophysical sources: the data are consistent with a negligible flux of neutrinos from solar 7 Be 9 ' 10 , though neutrinos from 8 B (a product of solar 7 Be reactions) are observed. A natural explanation for the observations is that neutrinos born as j/ e 's change flavor on their way to the Earth, thus producing an apparent deficit in experiments detecting primarily j/ e 's. Neutrino oscillations—either in vacuum or matter—provide a mechanism both for the flavor change and the observed energy variations. While these deficit measurements argue strongly for neutrino flavor change through oscillation, a far more compelling demonstration would not resort to model predictions at all but look for non-^e flavors coming from the Sun. The Sudbury Neutrino Observatory
(SNO) was designed to do just that: provide direct evidence of solar neutrino flavor change through the inclusive appearance of non-electron neutrino flavors from the Sun. We present here the first solar neutrino results from SNO, which have also been described in an earlier publication n .
2
SNO D e t e c t o r
SNO is an imaging water Cerenkov detector, which uses heavy water (D2O) as both the interaction and detection medium 12 . Figure 1 shows a diagram of the detector. SNO is located ~ 2 km (6020 k.w.e.) underground in INCO Ltd.'s Creighton Mine, deep enough that the rate of cosmic ray muons passing through the entire active volume is just 3/hour. The 1000 tons of heavy water is contained in a 12 m diameter transparent acrylic vessel, and is surrounded by 2 ktons of light water shielding. The Cerenkov light produced by neutrinos and radioactive backgrounds is detected by an array of 9500 8 inch photomultiplier tubes (PMTs), supported by a stainless steel geodesic sphere. Each PMT is surrounded by a light concen-
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Joshua R. Klein
Solar Neutrino Results from the Sudbury Neutrino Observatory cesses: vx + e~ —> vx + e~ ve+d^p + p + e~ ux+d^p + n + ux
The first reaction, the elastic scattering (ES) of electrons, has been used to detect solar neutrinos in other water Cerenkov experiments. It has the great advantage that the recoil electron direction is strongly correlated with the direction of the incident neutrino (and hence the direction of the Sun). In addition, this reaction has sensitivity to all neutrino flavors. For ve's, the elastic scattering reaction has both charged and neutral current components, making the cross section for ^ e 's 6.5 times larger than that for u^s or
Figure 1. Diagram of SNO Detector.
trator, which increases the photocathode coverage to nearly ~ 55%. The front-end discriminator thresholds are set to fire on 1/4 of a photoelectron of charge. Outside the PMT support sphere is another 7 ktons of light water shielding. The detector is also equipped with a flexible calibration system, capable of placing sources almost everywhere in either the x — z or y — z plane. The sources that can be deployed include a diffuse multi-wavelength laser for measurements of optical parameters and PMT timing, a 16 N source which provides a triggered sample of 6.13 MeV 7's, and a 8 Li source delivering 0's with an endpoint near 14 MeV. In addition, high energy energy (19.8 MeV) 7's are provided by a 3 H(p,7) 4 He ('pT') source 13 and neutrons by a Cf source. Some of the sources can also be deployed on vertical axes within the light water volume between the acrylic vessel and PMT support sphere. 3
(ES) (CC) (NC)
SNO R e a c t i o n s
SNO can provide direct evidence of solar neutrino flavor change through comparisons of the interaction rates of three different pro471
The deuterium in the heavy water makes the second process possible: an exclusively charged current (CC) reaction which (at solar energies) occurs only for i/e's. In addition to providing exclusive sensitivity to ve 's, this reaction has the advantage that the recoil electron energy is strongly correlated with the incident neutrino energy, and thus can provide a good measurement of the 8 B energy spectrum. The CC reaction also has an angular correlation with the Sun which falls as (1 — 0.340cos(# Q )) 14 , and has a much larger cross section (~ 10 times larger) than the ES reaction. The third reaction—also unique to heavy water—is a purely neutral current process. This has the obvious advantage that it is equally sensitive to all neutrino flavors, and thus provides a direct model-independent measurement of the total flux of neutrinos from the Sun. For both the ES and CC reactions, the recoil electrons are directly detected through their production of Cerenkov light. For the NC reaction, the neutrons are not seen directly, but are detected in a multi-step process. When a neutrino liberates a neutron from a deuteron, the neutron wanders within
Joshua R. Klein
Solar Neutrino Results from the Sudbury Neutrino Observatory
the D2O and is eventually captured by another deuteron, releasing a 6.25 MeV 7 ray. The 7 Compton scatters an electron and it is this secondary particle which is detected. Although the data we present here were acquired with the acrylic vessel filled with pure D2O, the detector is now running with NaCl added to the heavy water. The addition of the salt provides chlorine which has a larger capture cross section (and hence a higher detection efficiency) for the neutrons. The capture on chlorine also yields multiple 7's instead of the single 7 from the pure D2O phase, which aids in the identification of neutron events. Eventually, discrete He 3 proportional counters will be added which will count neutrons exclusively. To determine whether neutrinos which start out as ue's in the solar core convert to another flavor before detection on Earth, we have two choices: comparison of the CC reaction rate to the NC reaction rate, or comparison of the CC rate to the ES rate. The former has the advantage of high sensitivity— we compare the total flux to the ve flux and therefore expect to see a large difference if the true neutrino flux agrees with standard solar models (which predict a total flux two to three times larger than previous measurements). In addition, uncertainties in the cross sections for the two processes will largely cancel. The second comparison has the advantage that both the CC and ES recoil electrons provide neutrino spectral information. The spectral information can ultimately be used to show that any excess in the ES reaction over the CC reaction is not caused by a difference in the energy thresholds used to analyze the two reactions. The CC-ES comparison also has the advantage that the strong angular correlation with the Sun demonstrates that any excess seen is not due to some unexpected non-solar background. Lastly, the CC-ES comparison can be made with fairly high precision despite the small ES reaction
cross section, because the Super-Kamiokande collaboration has already made a precision, high statistics measurement of the ES rate 5 . For the results presented here, only the CCES comparison will be described. 4
Data Analysis
The goal of the data analysis is the determination of the relative sizes of the three signals (CC, ES, and neutrons) and ultimately the comparison of the rates. In the pure D2O detector configuration—the configuration with which these data were taken—we cannot separate the signals on an event-by-event basis. Instead, we 'extract' the signals statistically by using the fact that they are distributed distinctly in the following three derived quantities: the kinetic energy of the recoil electron or capture 7 ray (T), the reconstructed radial position of the interaction (R3), and the reconstructed direction of the event relative to the Sun
(COS#Q).
Figure 2 shows these distributions for each of the signals. The top row of Figure 2 plots the different energy distributions for the three signals. We see in the figure that the strong correlation between the electron energy and the incident neutrino energy for the CC interaction produces a spectrum which resembles the initial 8 B neutrino spectrum, while the recoil spectrum for the ES reaction is much softer. The NC reaction is—within the resolution smearing of the detector— essentially a 5-function, because the 7 produced by the neutron capture on deuterium always has the same 6.25 MeV. The bottom row of Figure 2 shows the reconstructed direction distribution of the events. In the middle of that row we see the familiar peaking for the ES reaction, pointing toward the Sun. The ~ 1 — 1/3 cos 6Q distribution of the CC reaction is also clear in the left hand side of the bottom row. Not surprisingly, the NC reaction shows no correlation with the solar direction—the 7 ray from
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Solar Neutrino Results from the Sudbury Neutrino Observatory
CC
ES
this is that the capture cross section for neutrons on deuterium is very small—the neutron wanders around long enough inside the D2O that it may leak outside and be captured by hydrogen in either the acrylic vessel or the light water. Such hydrogen captures produce a much lower energy 7 ray (~ 2.2 MeV), below the analysis threshold. Therefore the acceptance for events which are produced near the edge of the volume is reduced, because the probability of leakage there is correspondingly higher than for events produced near the center.
NC
R' (AV rodii)
-1
0
1
u
- , cosOsun
Figure 2. The energy (top), radial (middle), and directional (bottom) distributions used to build pdfs to fit the SNO signal data.
the captured neutron knows nothing about the incident neutrino. The distributions of reconstructed event positions is shown in the middle row of Figure 2. These distributions are plotted as a function of R3, with R3 = 1 occurring at the radius of the acrylic vessel (the edge of heavy water volume). We see here that the CC reactions—which occur only on deuterons—produce events distributed uniformly within the heavy water, while the ES reaction (which occurs on a n y electron) produces events distributed uniformly well beyond the heavy water volume. The small leakage of events just outside the heavy water volume for the CC reaction is due to the resolution tail of the reconstruction algorithm. The NC reaction, however, does not have a uniform distribution inside the heavy water like the CC reaction, b u t instead monotonically decreases from the central region to the edge of the acrylic vessel. The reason for 473
One last point needs to be made regarding the distributions labelled ' N C in Figure 2: they represent equally well the detector response to all neutrons, not just those produced by neutral current interactions, as long as the neutrons are produced uniformly in the detector. For example, neutrons produced through photodisintegration by 7 rays emitted by U or Th chain daughters inside the D2O will have the same distributions of energy, radial position, and solar direction as those produced by solar neutrinos. In the analysis described here, no separation is done between these neutrons and those from the NC reaction. To determine the size of the three signals, then, we use these nine distributions to create probability density functions (pdfs) and perform a generalized maximum likelihood fit to the same distributions in the data. There are, however, two principal prerequisites that must be satisfied before we can even begin this 'signal extraction' process. First, we need
