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distribution as a function of |*i — *21 is shown in Fig. (3c and d). The J PC agreement between the data and theory is excellent. Similar conclusions arise for the The JPC = 2~+ states, the r?2(1645) and /i(1420). 772(1870), are predicted to be produced poIn passing, the resulting analysis of axial meson production 65 implies that the /i(1285; 1420) are members of a nonet with 7/0/700 are spatially extended KK molecules, (with r.m.s. radius R > 0(AgJ 7Z? )), then the The radiative decays of the <j> —• 7/0 (980) high momentum region of the integration in 75 77 and 700 (980) have long been recognised as refs. ' is cut off, leading in effect to a form 2 75 79 a potential route towards disentangling their factor suppression, F (R) < l ' . The differences in absolute rates are thus intimately nature. In this section I we note that linked to the model dependent magnitude of isospin mixing effects could considerably alter 2 some predictions in the literature for T((f> —> F (R). 7/o(980)) and T((/> -> 7a 0 (980)), and I show that new data from DA$NE promise to rePrecision data on both /o and 00 proveal their nature. duction are now available from DA$NE 5 0 . Before discussing this, there are two particThe magnitudes of these widths are pre- ular items that I wish to address concerning dicted to be rather sensitive to the funda- the current predictions. One concerns the abmental structures of the /o and ao, and as solute branching ratios, and the second concerns the ratio of branching ratios where, if /o such potentially discriminate amongst them. and OQ have common constituents (and hence For example, if / 0 (980) = ss and the dominant dynamics is the "direct" quark tran- are "siblings") and are eigenstates of isospin, + sition (j>(ss) —> 7 0 + + ( s s ) , then the pre- then their affinity for K K~ should be the 338 = io'2(f>*, hU'D'E
larised. Helicity 2 is suppressed by Bose symmetry 60 and has been found to be negligible experimentally 67 . The structure of the cross section is then predicted to be dominantly in helicity-one. The helicity zero distribution is as for the 0 h case,
/ i ( 1 2 8 5 ) ~ \nn) - 0.5|ss) /i(1420) ~ \ss)
da dt\dt2d(f>
+0.5\nn)
(nn = {uu + dd)/y/2). DELPHI 66 have measured the production rate < n > of these states per hadronic Z decay and find
*i*2 sin 2 (
and hence suppressed for M > IGeV as was the case for the 0 _ + . The dominant helicity 334
Prank E. Close
0)
"llilnn
0.1 GeV
Light Hadron Spectroscopy
f^Sn ^ r n
o O D
In Iln
u
10 '
it 0.1
if
Deg
In contrast to the 0 v case, where parity forbade the LL amplitude, in the 0 + + case both TT and LL can occur. Hence there are two independent form factors 5 5 A T T ( * i , i 2 , M 2 ) and ALL(tut2,M2). For 0 + + and the helicity zero amplitude of 2 + + (which experimentally is found to dominate 6 8 ) the angular dependence of scalar meson production has the form 6 1
b)
Itl
0.2
0.3
u 0.4
GeV!
Figure 4. a) The <$> and b) the \t\ distributions for the ij2(1645) for the data (dots) and the Monte Carlo (histogram).
aT/aL cos((/>)]2
which successfully predicts that there should be significant changes in the distributions as t varies 5 7 . one: is as the 1 + + case except for the important and significant change from sin2((/>'/2) to cos2\cj)'i'2).
The overall
=
0++ a n d 2++
Here we find that the production topologies do depend on the internal dynamics of the produced meson and as such may enable a distinction between qq and exotic, glueball, states.
335
H e a v y Flavours a n d Light Scalars
The working hypothesis is that the qq nonet, mixed with a glueball, is realised above 1 GeV
Light Hadron Spectroscopy
Prank E. Close
0.3
0.25
-
f
0.2
0.15 0.1
\^r #v-p
°(i37)A
a j f
0.25
k a j _ f0(i500)
clear scalar, and this state could be sought in D3 —> ixKK with enough statistics (in E687 72 the K*K band contaminates the 1710 region of the Dalitz plot). The momentum transfer in Ds —> 7r/o(1710) is small enough that a non-relativistic calculation of the transition amplitude (cs^ So)\ir(k)\ss(3 Po)) may be reliable. In particular this could distinguish between the /o(1710) as a radially excited state, for which there is significant suppression, and a pure ss(l3Po) for which the rate would maximise. Quantifying this rate could be a challenge for high statistics data e.g. with FOCUS. The major signal in the E687 data is the TTTTK the /o(980) is very prominent, together with the /o(1370) and a possible (though unclaimed) hint of a shoulder that could signal the /o(1500). Dunwoodie's analysis of i\) —• JTTTT shows structure around 1400 MeV and with better statistics from BES and Cornell this should be verified and attempts to resolve it into /o(1370) and / 0 (1500) made. The strength of/o(1710) in these data should also be determined.
b)
0.2
0.15 0.1
0.05
0.05 50
100
f 3 (1270)
0.3
150
50
C
\
0.3
'L
100
i, f 2 (l950)
150
d)
0.25
0.25 0.2
0.2
0.15
0.15
0.1
0.1
0.O5
0.05
0
50
100
0
150
ip
50
100
150
Deg
Figure 5. The
and we now need to determine the flavour content of these states. In addition we need to confirm the picture of the / 0 (980) and light scalars below 1 GeV. Novel probes are provided by the decays of heavy flavoured states. They can provide important information about the enigmatic 0 - + and 0 + + light flavoured states in particular. The nature of the rj — rj' system remains an important open question with an impact on heavy flavour decays. The D and B meson decays into final states containing rj or T?' continue to challenge theoretical predictions. Further experiments can test the nature of these 0 *" states, e.g. D+ versus Ds —> j]{vl)e+v and B° versus Bs —>
ij) —> 77T7T compared with Ds —> ITITIT, and ip —> -yKK compared with Ds —> irKK provide complementary entrees into the light flavoured 0 + + mesons. Comparison with Dd -> 7r.fi:* (1430) then enables us to "weigh" the flavour content of the nonets. In ip ~* -yKK Dunwoodie 70 finds the / 0 (1710) as
One clear message from the E791 data is that /o(980) has strong affinity for ss in its production; it decays into TTTT as the KK channel is closed. This brings us naturally to new information, presented to this conference, which may at last help to solve the conundrum of the nature of the /o(980). We argued earlier that the /o(980) and ao(980) have strong affinity for a fourquark composition, the question at issue being whether they are compact qqqq or meson molecules. The emerging picture from phenomenology 48 ' 49,50 and theory 5 1 is that both components are present.
336
There is a large amount of data on the
Light Hadron Spectroscopy
Prank E. Close production of the Jo (980) which require in some cases a strong affinity for ss (e.g. the Ds decays already ), or for nn (the production in hadronic Z decays has all the characteristics associated with well established nn states 66,71 ) and also data that require both components to be present (ip —» ufo versus if) —» 0/o) • There are new data that touch on the relationship between these states.
0.25
a)
Hr
^\
0.2
0.15
^
v
^>-=H
0.1
0.05
0.35
c)
0.3
0.25
First I summarise arguments that the /o and ao are mixed. Then I shall review ideas on
4-1
/o do mixing in central production
Fig 6c) and d) show the xp distributions for the ag(980) and a£(1320) formed in pp -> ppao,2- The distribution for the 02(1320) is similar to that observed for the a^(1320) whereas that for the a()(980) is significantly different and peaks at xp = 0. Indeed this is the only state with 1=1 that is observed to have a XF distribution peaked at zero 74 , and moreover the distribution for the ag(980) looks similar to the central production of states that are accessible to P P fusion, in particular P P—> / 0 (980). In the process pp —> p(nn0)p, P P fusion will feed only 1 = 0 channels, such as the /o(980) and / 2 (1270); one would not expect this to affect ao,2 production unless isospin is broken. The a o (980)/a 2 (1320) ratio in the WA102 data is relatively large and the xp distribution of the ao(980) production is, within the errors, identical to that of the /o(980)
337
0.2
0.15 0.1
0.05
-t-
~~*~
Figure 6. The
t
distributions a) for the reaction b) for t h e /o(980) compared to distributions c) for the reaction d) for t h e /o(980) compared to
(see fig. 6d) and the
Frank E. Close
Light Hadron Spectroscopy
Other lines of study are now warranted. Experimentally to confirm these ideas requires measuring the production of the r]ir channel at a much higher energy, for example, at LHC, Fermilab or RHIC where any residual Reggeon exchanges such as pco would be effectively zero and hence any ao(980) production must come from isospin breaking effects. On the theory side, detailed predictions are needed in specific models in order to resolve precisely how the KK threshold relates to the / 0 (980)/a 0 (980) states. Other "pure" flavour channels should now be explored. Examples are Ds decays where the weak decay leads to a pure 1=1 light hadron final state. Thus 7T/O(980) will be (and is 7 3 ) prominent, while the mixing results suggest that irao should also be present at 8 ± 3 % intensity. Studies with high statistics data sets now emerging from E791, Focus and BaBar are called for, and also studies of J/ip decays at Beijing, in particular to the "forbidden" final states uao and (f>ao where ref48 predicts branching ratios of O(10 - 5 ).
dicted b.r.(
b.r.{
where F2(R) = 1 in point-like effective field theory computations, such as refs. 76 ' 78 . (The range of predicted magnitudes for the branching ratios reflects the sensitivity to assumed parameters, such as masses and couplings that vary slightly among these references). By contrast, if the /o(980) and a 0 (980) 4.2
Prank E. Close
Light Hadron Spectroscopy
same and S o 7 6 , 7 5 ' 7 8
r(
There is some uncertainty about the former, which needs to be experimentally studied further. In particular, an analysis of Fermilab E791 7 3 data, which studies the /o(980) produced in Ds decays, even suggests that
(2)
2
9 n L
There are reasons to be suspicious of the predictions in both eqs. (1) and (2). I frame these remarks in the context of the KK molecule, but they apply more generally. If in the KK molecule one has
|/o) = cos6\K+K-)
+ sin9\K°K°)
(3)
and \a°0) = sin6\K+K-)
- cos9\K°K°)
(4)
then the branching ratios <j> —> 7/0(700) found in ref.75 can be summarised as follows
as
b.r.{4> -> 7/0 : 7ao) = (4 ± 1) x 10~ 4 x(cos29 : sin29)
X(
Q.^GeV2
)
F
W
-^~ 0.02 ± 0.04 ± 0.03 (GeV) 2 , hence consistent with zero! However,it should be noted that only the TTTT decay mode of the /o(980) has been studied in this experiment and hence the coupling to K+K~ is only measured indirectly. With such uncertainties in the value of this coupling strength, predictions of absolute rates for
As shown in ref.75, the analytical results of point-like effective field theory calculations (e.g. refs. 76,78 ) can be recovered as R —> 0, for which F2(R) —+ 1. In contrast to the compact hadronic four quark state, the KK molecule is spatially extended with r.m.s. R ~ l / y m ^ e , where e is the binding energy and F2(R) < 1, the precise magnitude depending on the KK molecular dynamics. It is clear also that the absolute rate above is driven by (i) the assumed value for = 0.58 GeV 2 , and (ii) the further assumption that the /o and ao are KK states with / = 0,1: hence 9 = 7r/4.
With the basis as defined in eqs. (3) and (4), the ratio of production rates by P P(isoscalar) fusion in central production will be a{PP - a0)/a(PP - /„) = £ f & § Ref.48 found this to be (8 ± 3) x 10" 2 . Hence if we assume that the production phase is the same for the two, then within this approximation the relative rates are predicted to be 4 9 r(<£ - 7/0) cot29 = 3.2 ± 0.8 T(4> -> 7a 0 )
(5)
9sK + 4 /~
339
This is far from the naive expectation of unity for ideal isospin states and is a rather direct
Frank E. Close
Light Hadron Spectroscopy
consequence of the isospin mixing obtained in ref. 48 . In order to use the data to abstract magnitudes of F2(R), and hence assess how compact the four-quark state is,a definitive accurate value for gl^nl^ will be required. If for orientation we adhere to the value used elsewhere, g2tKK/k-K ~ 0.6 GeV 2 , and impose the preferred 9, then the results of ref. 75 are revised to
lfo) + b-r.(4>
7a0)<(4±l)(10-
4
) (6)
and
b.r.{
6 . r . ( 0 ^ 7 / o ) = (2.4±O.l)lO- 4 b.r.(4>-> ja0) = (0.6±0.05)10" 4
(10) (11)
which imply F2(R) ~ 0.7 ± 0.2, supporting the qualitative picture of a compact qqqq structure that spends a sizeable part of its lifetime in a two meson state, such as KK. An important feature of this also is that there is a significant isospin mixing at work, driven by the K+K~-K°K° mass difference. A subtle and unexplained violation of isospin has already been noted in the ratio 4> —> K+K~ /K°K°81, whose origin may also touch on these issues.
(7)
6.r.(
5
T h e
£( 2 - 2 )
There is a tantalizing signal that has been claimed 82 as evidence for a tensor glueball. I have severe doubts about this state, but first let me present the "case for the prosecution". It is narrow (~ 20MeV) and seen in a glueball favoured production channel: ip —> j£ where £ —> K+K~;
K°K0,TT+IT~
,pp, according to
82
It is therefore most interesting that data presented here find 50
r(0 -+ 7/o)
cot26 = 4.1 ± 0 . 4
(9)
consistent with the predicted ratio in eq. (6). The individual rates may therefore be used as a measure of F2(R). Branching ratios for which F2(R) « 1 would imply that the K+K~0++ interaction is spatially extended, R > 0{KQ1CD). Conversely, for F2(R) - • 1, the system would be spatially compact, as in qqqq. The data from KLOE are 50 340
BES . In each channel the effect is ~ 4
Light Hadron Spectroscopy
Prank E. Close plies a large intrinsic production: br.(ip —> 7£) > 1 0 - 3 . Such a magnitude would be in line with expectations for a tensor glueball if Ttot ~ 20MeV55, but at the price of having detected only a limited fraction of the decay channels. A further piece of evidence has been presented to this conference from L3. They find no signal in 77 and place an upper limit: T(£ - • -ry)b.r.(£ -> KSKS) < lAeV86. So, we appear to have a large production in the glueball friendly ip decay and a strong suppression in the "anti-glueball" 77 channel, which leads some to assert that the 2 + + glueball is the £. The problem, in my opinion, is that the claims for glueball are based on what is not being seen! Furthermore, there is no convincing signal for £ in any other experiment. There is another possible interpretation of the LEAR and L3 non-observations: the £ does not exist! If it does exist, another solution is that the KK decay is dominant (as in the Mark 3 data) and that, in aprticualr, pp is suppressed. The LEAR limit would then be less restrictive, and allow br.(tp —> 7^) ~ 10~ 4 . The true £ could then be a broader state ( as seen elsewhere, for example WA102 87 , DM2 84 and 88 ) and with br.(ip —> 7^) ~ 10~ 4 be compatible with a qq state 5 5 . If this state has a significant ss content, an excited tensor with width ~ lOOMeV, then it is probably compatible with the L3 77 limit. This is clearly a question that needs to be pursued with high priority at an upgraded BES and at a downgraded (in an energy sense!) CESR. High statistics and independent analyses should determine whether this state is real or not. If it is confirmed with the above properties then it will be rather compelling; however, at the present time I am of the opinion that absence of evidence may be evidence of absence. The challenge for the new facilities will be to settle this question.
341
6
Summary and Prospects
Establishing that gluonic degrees of freedom are being excited is now a real possibility and centres on understanding (a) the scalar mesons (b) being able to distinguish between hybrids and molecules or compact four-quark states for exotic Jpc = 1 l". A "pure" molecule would be produced and decay in the mesons that make it; a compact four quark or hybrid would show up in channels driven by the flavour spin clebsches. Furthermore, the latter configurations will be in nonets (any other representation would immediately eliminate hybrid) and the mass dependent pattern will in general be different for qq /hybrid and (qq)3(qq)3- So, unless Nature is malicious, it will be possible to answer this puzzle definitively. The scalars below 1 Gev are too light to enable a simple distinction between loose molecules and compact four-quarks states to be felt in decays (except perhaps for the ao(980) where the KK and r/7r both couple strongly and point to a significant compact four-quark feature). However, the production dynamics and systematics of these states is interesting and full of enigmas, which may be soluble if one adopts the four-quark/molecule picture. Ds decays into 7r/o clearly point to an ss presence in the /o- However, the production in Z decays is rather non-strange-like 71 . ip to uifo and
Prank E. Close
Light Hadron Spectroscopy
the exotic J = 1 _ + now seen in various channels and more than one experiment (ii) with 0~ + and 1 signals in the 1.4 - 1.9GeV region that do not fit well with conventional Whenever S-wave dynamics can play a quarkonia and show features predicted for hyrole it will overide P-waves; so one expects brids (iii) in the form of the scalar glueball KK S-wave production to drive the /o/«o mixed in with quarkonia in the 1.3 - 1.7 Gev whenever allowed. This is indeed what hap- mass range. Theoretical questions about the pens in the
Knowledge on the 77 couplings is lacking and better data would be useful. We know that for the 2 + + 77 reads the compact qq flavours; there is no 2-body S-wave competition in the imaginary part as pp etc are too heavy. I would expect that for the 0 + + the KK will dominate the 77 if there is a KK component in the wavefunction. At the other extreme; were the state a pure compact four quark, then higher intermediate states KK, KK*,KK** etc - would all be present. Achasov76 has discussed these and a precise calculation has many problems, but the RATIOS of 77 to fo/ao would probably be sensitive and more reliable. The theoretical frontier suggests that one can divide the phenomenolgy of scalars into those above and those below 1 GeV. I suspect that much of the confusion will begin to evaporate if one adopts such a strating point. Empirically,signs of gluonic excitation are appearing (i) in the form of hybrids with
Tau-Charm-Factories. At lower energies, VEPP and DA$NE can study the 1.41.7GeV region where light flavour hybrid vectors may occur. High statistics studies of radiative decays of such states into the /o(980); /i(1285); / 2 (1270) could teach us much 90 . HERA can also investigate the production mechanism, Q2 dependence etc of the vectors in hope of distinguishing radial excited quarkonia from hybrids. (ii) Photo and electroproduction of hybrids ~ 2GeV mass can be studied at Jefferson Lab, via 7r and u> exchange. The vector nature of the photon, and its mixed isospin content, can access the exotic quantum numbered "golden" hybrids, such as 1 •". In any event, the properties of the newly-sighted 1 _ + around 1.4 - 1.6Gev should be investigated. The moderate energies available here can actually be an aid. (iii) 77 couplings give rather direct information on the flavour content of C = + states. 342
Frank E. Close
Light Hadron Spectroscopy
Such information on the scalar mesons will be an essential part of interpreting these states. (iv) Heavy flavour decays, in particular Ds and D into IT and associated hadrons can access the scalar states. Precision data are needed to disentangle the contributinos of the various diagrams, whereby the flavour content of the scalars can be inferred. There is also a tantalising degeneracy between the 7r9(1.8) and the D, which may radically affect the Cabibbo suppressed decays of the latter. Hence precision data on such charm decays is warranted. (v) Central production need now to be studied at higher energies, at RHIC, Fermilab and possibly the LHC. The 0 ~ + glueball should be manifested once the t\t2 —> 0 kinematic suppression is overcome. The systematica of scalar and tensor production, with their cf> and dkr dependences, need to be understood. (vi) Tau Charm Factories may at last appear. Obtaining a well defined universally accepted data-set on ip decays is needed; a problem for phenomenology is that data from different experiments do not always agree. Clarifying the status of £(2.2) is needed from independent experiments, such as BES and CESR should provide. Finally, \ decays offer an entree into light flavoured states; the excitement about the scalar glueball mixing with the quarkonia nonet began when the precision data from pp annihilation at LEAR first emerged. Data at rest were beautiful and well analysed. Data in flight however tend to be more problematic, not least as one cannot so easily control knowledge of the incident partial wave. \ decays can access these phenomena, at c m . energies up to 3.5GeV, and from well defined initial Jpc states. In particular, the 1 + + decay into IT + X probes X = 1~ + in S-wave. I hope that this talk has shown some 343
ways in which current and future experiments can impact on the physics of light flavours, and of glue. A TCF promises to be an important feature in this field; hopefully, together with BEPCII, That's Cornell's Future. Acknowledgements This is supported, in part, by the EU Fourth Framework Programme contract Eurodafne, FMRX-CT98-0169.
Light Hadron Spectroscopy
Frank E. Close References 1. G.Bali et al SESAM Collaboration; NucLPhys.ProcSuppl. 63 209 (1997) 2. The Science Driving the 12 GeV Upgrade of CEBAF Jefferson Lab report 2001 (eds L.Cardman, R.Ent, N.Isgur et al), pp.19-22 3. S.Godfrey and N.Isgur, Phys.Rev. D 32 189 (1985) 4. S.Godfrey and J.Napolitano, Rev. Mod. Phys. 71 1411 (1999) 5. Y.Nambu Univ of Chicago report No.7070 (1970) (unpublished); lectures at Copenhagen Summer Symposium (1970) (unpublished) 6. N. Isgur and J. Paton, Phys. Rev. D 31 2910 (1985). 7. N.Isgur, R.Kokoski and J.Paton, Phys. Rev.Lett. 54 869 (1985) 8. G. Bali et al. (SESAM), heplat/0003012; Phys.Rev. D 62 054503 (2000). 9. M. Luscher, Nucl.Phys. B180 317 (1981) 10. F.E.Close and P.R.Page, Nucl.Phys. B 443 233 (1995) 11. G.Bali et al Phys.Lett. B309 378 (1993) 12. J.Sexton et al. (IBM Collaboration) Phys. Rev.Lett. 75 4563 (1995) 13. F.E. Close and M.J. Teper, "On the lightest Scalar Glueball" Rutherford Appleton Laboratory report no. RAL96-040; Oxford University report no. OUTP-96-35P 14. C.J.Morningstar and M.Peardon, Phys.Rev. D 56 4043 (1997) 15. D. Weingarten, Nucl. Phys. Proc. Suppl. 53 (1997) 232; 63 (1998) 194;73 (1999) 249. 16. C. Amsler and F.E. Close Phys. Lett. B 353 (1995) 385. 17. V V Anisovich Physics- Uspekhi 41 419 (1998) 18. C.Mc Neile and C.Michael, 344
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Frank E. Close
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58. D. Barberis et al, arXiv:hep-ex/0001017 To be published in Phys. Lett. 59. D. Barberis et al, Phys. Lett. B 462 (1999) 462. 60. F.E. Close and G.A. Schuler, Phys. Lett. B 458 127 (1999). 61. F.E. Close and G.A. Schuler, Phys. Lett. B 464 279 (1999). 62. A. Donnachie and P.V. Landshoff, Nucl. Phys. B 231 189 (1983). 63. F.E. Close, Phys. Lett. B 419 387 (1998). 64. D. Barberis et al, Phys. Lett. B 440 (1998) 225; P.Chauvat, Phys.Lett. B 148 (1984) 382; P.Schlein, private communication. 65. F.E.Close and A.Kirk, Z.Phys C 76 469 (1997) 66. M. Chapkin et al DELPHI 2001-063 CONF491 this conference. 67. W A 2 - + 68. D. Barberis et al, Phys. Lett. B 453 305 (1999); D. Barberis et al, Phys. Lett. B 453 316 (1999). 69. H J Lipkin, remarks at this conference. 70. W. Dunwoodie, Proceedings of Hadron 97, AIP Conf. Series 432 (1997) 753. 71. G Lafferty, comment at this conference 72. P Frabetti et al (E687 Collaboration) Phys.Lett. B 351 591 (1995) 73. E Aitala et al (E791 Collaboration) Phys.Rev.Lett. 86 765 (2001) 74. A.Kirk, Phys. Lett. B 489 29 (2000) 75. F.E. Close, N. Isgur and S. Kumano, Nucl Phys. B 389 (1993) 513 76. N. Achasov and V. Ivanchenko, Nucl.Phys. B 315 (1989) 465 77. N. Brown and F.E.Close, in The DA&NE Physics Handbook, L. Maiani, G.Pancheri and N.Paver, eds.; INFN Frascati (1995) 78. J.L. Lucio and J.M. Pestieau, Phys. Rev. D 42 3253 (1990) 79. N.N. Achasov and V.V.Gubin, hep-
Frank E. Close
Light Hadron Spectroscopy
ph/0101024 T.Barnes, Phys.Lett. B 165 434 (1985) A.Bramon et al. Phys.Lett. B 486 406 (2000) BES Collaboration, Phys.Rev. Lett. 76 3502 (1996) Mark 3 Collaboration, Phys.Rev.Lett. 56 107 (1986) DM2 Collaboration, Phys. Rev.Lett. 60 2238 (1988) PS185 Collaboration P.Barnes et al. Phys.Lett. B 309 469 (1993) J.Alcaraz (L3 Collaboration), submitted to this conference D.Barberis et al (WA102 Collaboration), Phys.Lett. B 453 462 (1999) S.Godfrey, R.Kokoski and N.Isgur, Phys.Lett. B 141 439 (1984) R Barate et al (ALEPH) Phys.Lett. B 472 189 (2000) F E Close, A.Donnachie and Yu Kalashnikova (in preparation)
346
EW Physics and Beyond
E W Physics and Beyond Session Chair: R. Cashmore Scientific Secretaries: S. Braccini H. Pichl J. Drees J. Ellis
Review of final LEP results Beyond the Standard Model
Session Chair: H. Chen Scientific Secretaries: R. Paramatti A. Denig F. Zwirner J. Miller G. Hanson
The Higgs puzzle: experiment and theory The Muon anomaly: experiment and theory Searches for new particles
348
R E V I E W OF FINAL LEP RESULTS OR
A T R I B U T E TO LEP J. DREES CERN/University Wuppertal E-mail: Jurgen.Drees @cern.ch After a comment on the performance of L E P some highlights of the L E P l and LEP2 physics programmes are reviewed. The talk concentrates on the precision measurements at the Z resonance, two fermion production above the Z, W+W~ production, ZZ production, indirect limits on the Higgs mass, LEP contributions to the exploration of the CKM matrix, and on the L E P measurements of as.
1 1.1
Introduction A comment on the machine and the detectors
LEP delivered the last beam on November 2 n d 2000. By now the storage ring and the detectors are dismantled. What remains is the LEP saga and a rich harvest of physics results. So far more than 1100 scientific papers have been published covering an enormous range of physics. The main topics centre on the study of the properties of the gauge and scalar bosons, on heavy fermions and on searches for the Higgs boson and for new physics. Many analyses are still continuing, 220 papers have been submitted to this symposium by the LEP collaborations. The performance of LEP during the 12 years of operation can best be illustrated by showing in Fig. 1 the integrated luminosity as a function of time for each year. During the phase 1 where LEP operated in the vicinity of the Z resonance luminosities up to 65 pb"1 have been reached. After raising the energy the luminosity increased to more than 200 pb~l per year. The total luminosity delivered per experiment above W+W~ production threshold was about 700 pb-1, while only 500 pb-1 had been hoped for. In the hunt for the Higgs boson higher and higher energies were achieved in 2000 which was a particularly good year for LEP. As shown in Fig. 2 a record beam energy
349
of 104.4 GeV was reached, much more than originally foreseen. In 200 days of running more than 130 pb'1 above 103 GeV were delivered to the experiments, 110 pb~x in the last 110 days mainly at beam energies above 103 GeV. Crucial for the success of LEP2 have been the superconducting cavities. Let me quote here S. Myers 1 : For superconducting cavities the power needed is only proportional to the 4th power of energy. To operate LEP at 103 GeV with copper cavities (where the power would be proportional to E%eam) would have needed 1280 cavities and 160 MW of power! Impossible for many reasons. At the time when plans for superconducting cavities were developed little was known about their performance 2 . The final success was due to a long term development programme, which started already in 1980 together with outside laboratories, pursuing the goal to reach thermal stability for 350 MHz niobium coated copper cavities at reduced costs. In 2000 a total of 272 Nb film and 16 Nb bulk cavities were installed. At 104 GeV beam energy an average accelerating field of 7.5 MV/m at a quality factor of Q > 3 x 109 at 4.5 K was achieved, much better than the design value of 6 MV/m. More than 80% of the superconducting cavities had Q > 2.5 x 109 even at 8 MV/m. Fig. 3 shows a 4 cell cavity with its typical rounded structure.
J. Drees
Review of Final LEP Results or A Tribute to LEP
Integrated luminosities seen by experiments from 1989 to 2000
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350
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Review of Final LEP Results or A Tribute to LEP
Figure 3. A 4 cell Niobium coated cavity in the clean room.
A word on the four LEP detectors ALEPH, DELPHI, L3, OPAL. All collaborations improved their detectors substantially during the years of data taking, the most important improvements being: 1. The development of silicon micro vertex detectors for high resolution secondary vertex measurements. The installation of these detectors greatly improved the quality of heavy flavour physics. 2. All experiments replaced their first luminosity detectors by new high-precision detectors capable of measuring small angle Bhabha scattering with an accuracy well below 0.1 %. The LEP Collaborations also created a new style of working together, the LEP Working Groups, of which the Electroweak Working Group (EWWG) is best known. These groups have the task to combine the results obtained by the four LEP Collaborations and also by the SLD Collaboration working at the SLAC e+e~ linear collider SLC taking proper account of all systematic correlations between the data. 351
Figure 4. The final hadronic cross-section as measured (solid line) and QED deconvoluted (dotted line).
2 2.1
Precision at the Z Determination Parameters
of the Z Resonance
If one asks the question, what are the most important results from LEP1, the answer has to be: the precision electroweak measurements at the Z resonance. During the data taking periods from 1990 to 1995 the four experiments collected 15.5 million Z decays into quarks plus 1.7 million decays to charged leptons corresponding to an integrated luminosity of 200 pb~l per experiment. Fig. 4 shows the hadronic cross-section measured by the four collaborations as a function of the centre-of-mass energy. Also shown is the cross-section after unfolding all effects due to photon radiation. Radiative corrections are large but very well known. At the peak the QED deconvoluted cross-section is 36% larger and the peak position is shifted by -100 MeV. The figure illustrates the difference between the measurements and the so-called pseudoobservables like mz, Tz, &lad which are averaged by the Electroweak Working Group.
J. Drees
Review of Final LEP Results or A Tribute to L E P The ratios of the Z partial decay widths:
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Figure 5. mz combined by E W W G for the different periods of data taking.
The most impressive final result of the Z lineshape studies is the 2 x 10~ 5 accuracy for one of the most fundamental constants of nature, the Z mass:
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(7) Details on the final combination and an extended list of references can be found in 3 . mz = 91.1874 ± 0.0021 GeV. (1) The final measurements of Z line shape and This precision cannot be exceeded by any one of the leptonic forward-backward asymmeof the future machines, not even with a GigaZ tries performed by the four LEP Collabora5,6 7 8 linear collider. Two essential points have to tions are documented in ' ' . The measurements of the r polarisation are obtained by be mentioned: - The beam energy measurement using the the four collaborations by studying five r de9 10 11,12 . technique of resonant spin depolarisation plus cay modes ' ' Before summarizing the final results for careful control of all machine parameters. the effective lepton couplings and the still Still the beam energy contributes 1.7 MeV to the total uncertainty of mz- Fig. 5 shows preliminary results for the quark couplings I the consistency of the energy calibration for would like to mention two measurements of special interest. One of the questions asked the different data taking periods. - The close cooperation with theory groups by the LEPC before recommending approval essential for understanding radiative correc- of the experiments was: What is the expected accuracy for neutrino counting? I will come tions with the necessary accuracy. The full set of nearly uncorrelated back to the answer given in 1982 a t the end pseudo-observables used to describe the pre- of the talk but here is the final measurement. cise electroweak measurements on the Z res- The present best value results from the accurate measurement of rj r a „/r;; divided by onance and combined by EWWG includes: ^wl^u, the latter evaluated from the Stan- The total Z width: dard Model ( Tinv = Tz - Thad - TU{Z -5T), 5T corrects for the r mass effect): Tz = 2.4952 ± 0.0023 GeV. (2) Nu = 2.9841 ± 0.0083.
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z 352
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Review of Final LEP Results or A Tribute to LEP
tion of a new object to the invisible width of T?„„ = -2.7+H MeV. The second special quantity is the Veltman p-parameter. Assuming lepton universality p can be determined from the measured leptonic width: p' e # = 1.0050 ± 0.0010.
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By combining the measurements of the partial decay width of the Z boson, which is proportional to the sum of the squares of the vector and axial-vector couplings, with asymmetry measurements the vector and axial-vector couplings can be determined separately. For the three charged leptons the final results are presented in Fig. 6. It has to be noted that many data enter this analysis. LEP contributes the measurements of the three partial widths Fa, the forward-backward asymmetries at the Z (which yield ^4e,^4M,^4T), and the r polarisation (AT,Ae). SLD contributes the asymmetry for left and right handed e~ polarisation (yielding the most precise individual measurement of Ae)13 and the left-right forward-backward asymmetry for the three leptons (Ae, A^, AT)14. Assuming lepton universality the result presented by the solid ellipse in Fig. 6 is found. The comparison with the Standard Model prediction shows the preference of the combined lepton data for a low value of the Higgs mass. 2.3
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Information on the b and c quark couplings is obtained from three types of observables: The ratios R% = Tbl/Thad and R°c = ^cc/^had, which are measured by the LEP
353
Figure 6. The effective vector and axial-vector couplings for leptons. The shaded area shows the prediction of the SM for mt0p = 174.3 ± 5.2 GeV and ran = 300ljgg GeV. The arrows indicate increasing values of mtop or mu.
Collaborations and by SLD, the forwardbackward asymmetries ApB and Ap°B, which are measured at LEP, and the direct measurements of At, Ac by SLD. Though the measurement of Rf, and Rc is conceptually simple, one has to separate an enriched sample of b or c quark events from the bulk of the hadronic events, some problems have been experienced in the past. A measurement of Rt,, for instance, requires extremely high quality of b tagging, one has to know the tagging efficiency and the background with sufficient precision and one must control the correlations between the two event hemispheres. The most precise measurements use double or multi tag methods which allow the simultaneous experimental determination of the tagging efficiency and the b quark rate. Combining the results of the five experiments results
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J. Drees
Review of Final LEP Results or A Tribute to LEP
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The most recent i?& work of the collaborations, all using a lifetime tag based on micro vertex detector information plus additional information from high pr leptons and the hadronic structure of the event, can be found in references iMMT.is.i^ An updated comparison with the SM expectation is shown in Fig. 7. Obviously the new Ri, and Rc data agree with the prediction. This is not the case for the b forwardbackward asymmetries. Two new analyses of the pole asymmetry A°pbB by ALEPH 20 and by DELPHI 21 have been submitted to this conference. These measurements are notoriously difficult. One not only has to produce a high purity b quark sample, accurately control the background and understand the hemisphere correlations, one also has to know whether a b quark or an anti-6 was produced in the forward hemisphere. Both collabora-
Figure 8. The differential forward-backward b asymmetry as function of the polar thrust angle. The line is the result of a fit with its statistical error indicated as a band.
tions made optimal use of neural networks. ALEPH used a neural network 6-tag based on lifetime measurement, highpx leptons and event structure and obtains finally a 30% increase in the data sample. The b hemisphere charge is estimated by an optimal merging of the information from the primary and secondary vertex charge, leading kaons and the jet charge. Their final result is:
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DELPHI uses a very high purity b sample (96%), and a neural network tag for the hemisphere charge combining the information from vertex charge, jet charge, and from identified leptons and kaons. Self calibration from double tagging is used to measure the probabilities for b or anti-& tagging. The still preliminary result is: A°/B = 0.0997 ± 0.0042.
(12)
Fig. 8 shows the differential b quark forwardbackward asymmetry from the DELPHI single and double tag data. The analysis includes all data collected from 1992 to 1995. These two measurements improve the accuracy of sin26^ff evaluated from ApB.
354
J. Drees
Review of Final LEP Results or A Tribute to LEP
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However, as in the past 22 , there is still a significant deviation of 3.3 a from the sin29eff value determined from the lepton asymmetries. One then has to ask two questions: 1. Are all LEP measurements consistent? This is clearly the case as demonstrated in Fig. 9, where the pole asymmetries as measured by all LEP collaborations using different analysis methods are collected. It should be remarked that the numerical ApB values quoted in Fig. 9 correspond to the measurements at the Z peak only. They do not include measurements above and below the Z peak whose results are included in Eq. (11). Including the off peak data the average LEP value is: A°/B = 0.0990 ± 0.0017.
(13)
The error is dominated by statistics, the statistical error alone being ±0.00156. The dominant contribution to the systematic uncertainty is due to internal effects uncorrelated between the experiments, the correlated systematic uncertainty is only ±0.00039.
355
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iA" 2. Is the LEP result on Ab 3Ae consistent with the direct measurements of Ab from the polarised b quark forwardbackward asymmetry? The results are Ab{LEPonly) = 0.891 ± 0.022 (last year 0.890±0.024) and Ab(SLD) = 0.921 ± 0.020. Both agree within 1 standard deviation. Using the information from all b quark data, Rb, ApB, and Ab, one can separate the vector and axial-vector couplings gvb, 9Ab or the right and left handed couplings gm,, QLI respectively. They are related by
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The results are presented in Figures 10 and 11. Compared to the Standard Model prediction the data show a deviation of about 3 standard deviations. The strong anticorrelation in Fig. 10 is due to the constraint on the sum of the squares from the precise Rb measurement. Fig. 11 shows that the deviation from the SM is mainly for gmAn update of the measurements of
Review of Final LEP Results or A Tribute to LEP
J. Drees
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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
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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
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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
J. Drees
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
366
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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-
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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/.
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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-
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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
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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.
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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
. =
lll.(lll-
in
-H.iOeV..; il
•
•-•;«•$••>''
100
^lfl%«l 100 200 300 400 500 600 700 800
mm (GeV) 200
>
o 100
100
200
300 400
500
600
700
800
m]/2(GeV)
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 .
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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
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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
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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.
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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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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
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John Ellis
Decline and Fall of the Standard Model? can (B = 30 , u > 0
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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.
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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
(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
+ YlciOi(
(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-
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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
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.
.
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Standard ModeT~—^^ .
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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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