Electroweak physics

Nuclear Physics B (Pros. Suppl.) 16 (1990) 71-81North-Holland

ELECTROV='EAK PHYSICS

Riccardo BARBIERI

Dept . of Physics, University of Pisa and '-';4FN, Sezione di Pisa, Italy

1. INTRODUCTIONIn terms of new experimental results relevant to

electroweak physics, this Conference has clearly beenthe most interesting one since quite a few years.On the other hand, at least, but not only, due tothe biginning of LEP operation, it is also evidentthat the time ahead of us promises to be even moicinteresting . This is a first problem that I face inthis talk : appropriate balance must be given to thesummary and comment on new results as well asto perspectives of possible new developments of thefield . Th(- logical and aesthetic motivations to gobeyond the standara model are as significant as thesuccesses of the standard model itself.

A second problem that I have, is related to thevariety of possibilities that aFe discussed for newphysics: an organizing principle is needed . With asubjective choice, , ~' eï order and comment on thedifferent theoretical proposals according to the maxi-mum energy (the cut-of up to which they can be, inprinciple, consistently extrapolates! with the presentknowledge.

The talk is then organized as follows . I will firstsummarize the most precise tests of the standardmodel, in the flavour conserving sector, and I willdiscuss their impact in the comparison with theory .Possible theories are then devided, with respect totheir cut-off A, into three cathegories :

1/2i) A much greater than the Fermi scale, G-Fti250Gev, or infact possible bigger than anyhigher physical scale, with the exception of thePlanck mass. Restricting myself to the latestdevelopments, I will comment on the standard

0920-5632/90/$3.50 © Elsevier Science Publishers B.V .North-Holland

71

Dedicated to the memory ofGiorgio Gamberini

model itself, supersymmetry, neutrino proper-ties, new gauge bosons and, finally, on the pos-sibility of the top quark being anomalous.

ii) A » GF1/2 but, at the same time, A _ Aft,whereAll stands for the scale of flavour physics .This includes theories without scalar fields .

iii) A < 0 (GF1/2) .

This is the case for stronglyinteracting Higgs theories .

2. PRECISION TESTS OF THE STANDARDMODEL (SM)Given all fermion masses and mixings, the EM

is determined by 4 parameters : 2 gauge couplings,the Higgs vacuum exp=station valve and its massin,-, . This means that neutral current processes notinvolving the Higgs or the top, whose mass mt isalso still unknown, are approximately determined interms of 3 parameters, or 3 indep°ndent measure-ments. Apart from the fine structure constant andthe Fermi constant obtained from t1:. 0:fetime, themost significant determination ,~f the riiird parame-ter, before this Conferek-ce, was the v;~iue of the weakmixing angle Ow , mos''Lly coming from deep inelas-tic v -q scattering and !i, Z mzss -neasurementsl.From now on, and presumably for a long time to

come, the role of the third precisely known param-eter in electroweak physics is taken by the Z-mass,whose present average value is2, 3

Alz = 91 .09 f 0.16

Gev

(1)

In this way one is entering the time of the per-rnilictests of the SM .

72

Due to radiative corrections, flavour conservingprocesses not involving the Higgs or the top as ex-

ternal lines are fixed in terms of 3 parameters onlyapproximately. In fact, for a precise determination,radiative corrections bring all the parameters into thegame, as exemplified by the well known equation

1sin' Ow

4rra/fGF)

'!2

=21 -t

-M

1-Ar)z (

with ®r =- Ar (a,GF,MZ,mt,mH). The form of®r actually depends on the precise definition of Owitself. Hereafter 1 will stick to the definition

ç2Or P:~ -Sbp

M2sineOW -1- yn

Z

®f particular significance is the dependence fron .rat of ®r or, more generally, liow r7t t a%ect-- thedetermination of sins Ow from the various neutralcurrent processes . Such dependence is shown inFig.1, taken from Ref.4, for the central values ofs,r' Ow, as extracted -from present data on the vec-tor boson masses (VBM) and on different neutralcurrent processes (see below) . The behaviour ofthe different curves is easily related to the factthat, with the exception of processes with b-quarkexternal legs, the top quark enters in one loopradiative corrections only through vacuum polar-ization diagrams . In fact, for sufficiently largetop quark masses (mt Z Alw), this gives rise toa simple pattern for the mt-dependence both of

®r (s2 =

sinn Ow

,

c2 -cost Ow)5

3G!: m?P 67r2

and of the Z-exchange neutral current amplitudesbetween particles i and j 6

,~(- " 11f2AZ (1j;g2) _ ~n - IL1ZZ

(1+ SP) X

n.J3

(

-2(1+

sc2bp snJem

)c2

J3 - 2 il + ~6P1) S"JPr,~.s

) -

Table 1 contains a summary of the most p"e-cisc and most recent determinations of sine Oiy. The

R. Barbieri/Electroweak physics

50 100 150 200

"nt (GeV)

Figure 1: The dependences on mt of the central val-ues, of sine OW extracted from present data in thedifferent sectors considered : v-q, v-e, e-q and thevector boson masses (VBM). The error on sine Owfrom measurements of Mw/MZ is shown as a verti-cal error oar.

Table 1: Summary of precision tests .

quoted errors include statistica', systematic and the-oretical errors added in quadrature . On the con-trary they dry not include the uncertainty due tomt and MH , which are, rather arbitrarily, fixed tomt = ~d Gev, mH = 100 Gev . !n spite of that,tie theoretical error is still significant in the case ofv - q deep inelastic scattering and domir-int for theAtomic Parity Violation, after the recent measure-ment to 6% accuracy of the weak charge in Cesiumby the Boulder group9. Although the agreementamong the different determinations ofsin20W, is gen-erally very good, a meaningful direct comparison canonly be made between determinations where the rel-ative mt-dependence drops out. This is for exam-ple the case for sine 8W obtained from the A1cvlAfameasurements and from v - q scattering, both al-most it dependent f"om mt.

Allowing for variable nzt and rnH, 2 global fits ofthe data have already been made in Refs.4,13 . Theresults can be summarized as follows :

i) The best fit for the weak mixing angle gives, forarbitrary mt

sin 8w

=

0.226 t 0.005

my < 1 Tev 13

=

0.2276 f 0.004

mH = AJz'1(6)

R . Barbieri/Electroweak physics 7

ii) At 90% confidence level, for mH < 1

ev, theallowed range for the top quark mass is

40 Gev < mt < 210Gev13

(7)

iii) At 1Q level, and for a central fixed value of theHiggs mass mH ® 100 Gev, the fit gives for thetop quark mass

ni t = 140+sâ Gev13

Gev4 (8)

The somewhat smaller errors in the fit of Ref.4mainly reflect a fixed choice for the charmedquark mass, m, = 1.45 Gev, made in theparametrization of the deep inelastic neutrinoscattering data .

Notice that, for the first time, the radiative cor-rections are able to constrain mt also from below.This limit, mainly coming from the comparison ofMZ and 11Iw/MMZ measurements, is logically inde-pendent from the direct lower bound obtained fromthe non observation of the t-p in pg5 collisions (seebelow) . Note also that the expected improved preci-sion in theMZ measurement, to be obtained soon atLEP, will not significantly affect any of the conclu-sions of the fits on mt, since already now the erroron 1fZ is far better than that of any other measuredquantity (apart from a and GF).

The precision tests of the SM are clearly goingto play a significant role in the near future. Theprospects in this area are summarized in Table 2,where I report various planned or proposed high pre-cision electroweak tests . For the various measure-ments I indicate the foreseen experimental uncertain-ties and/or the corresponding errors in sin' ®W . Asin Table 1, these errors do not include uncertainties

due to mt and MH . It should actually be kept inmind that the different tests have different sensitiv-ities to mt , as already seen, and/or to new physics.

3. THE STANDARD MODEL AND BEYOND

(A » GF1lz)3.1 . General remarksThe question of how strongly the SM is sin-

gled out as the theoretical description of all these

Experiment sin' 9W SourceMZ 0.233 f 0.0013 SLC`

0.234 f 0.003 CDF3MW/MZ 0.213 ± 0.015 UA27

0.225 f 0.012 CDF3v - q 0.235 f 0.007 CHARA78

0.227 f 0.007 CDHStV80.239 f 0.011 CCFR8

v - e 0.194 f 0.022 E73480.209 f 0.037 CHARM 180.232 0.014 CHARM âI8

APV 0.217 f 0.019 BOULDER9eD 0.218 f 0.020 SLAC10e+e- 0.225 f 0.021 globall 1,12

()fs'<60Gev)

7

Table 2 : Future of precisinn eleet "oweak tests .

® Z = ±50mev± 20Mev

®(

w/

Z) _ ±0.004± 0.0012

®Alw = ±100RIevv'e

AAFB(bb) = t0.0ÛbAAvot(7) = ±0.011iAALR = ±0.025

± 0.003APV

LEPILEP(pol)

ACOL(2ope-1 )TEV(iooe-1

LEP II(7HARAI II

LANLLEP

0.0ûï4 LEP0.003 I SLC(104Z)0.00031 LEP(pol)0.003 ; BOULDER,

PARISep --> ex

;0.005

;

HERA

0.00050.00040.0070.0020.00060.0060.0020.0009

data is of great importance .

I will not repeathere the logical and aesthetic motivations :o gobeyond the standard model .

Let me restrict first to theories with a possiblecut-off much larger than the Fermi scale or even big-ger than any higher hypothezi,.al physical scale Aph,except for the Planck mass. Notice that this is not agrand-desert hypothesis, since I do not commit my-self to any specific spectrum. One is simply t;yiäegto maximize the predictive power of the theory.

The condition A » GFI1 2 ( or A » Aph) re-quires the use of renormalizable field theory, whosemenu (in 4 dimensions) consists at present of :

i) asymptotically free QCD-like gauge theories,which even admit the limit of infinite cut-off;

ii) infrared free QED-like theories with a finite cut-off A .

It would be nice to have more theories at our dis-posal, for example theories with a non trivial fixedpoint, but this does not seem to be the case atpresent.

Given this general framework, I believe that thefollowing statements are implied:

i) The electroweak interactions are described bya spontaneously broken gauge theory with a


gauge group G containing SIJ(2)xlJ(1) ;

ii) Scalar fields (one or more) are needed to de-scribe the physics of flavour (to distinguish be-tween the electron and the muon).

There is general consensus on the first proposition .On the contrary, not everybody would agree on thesecond statement, which is based on the existenceof no solid counter-example, in spite of the heroicefforts to search for it (See below) .

The minimal theory of this kind, defined as hav-ing the minimum number of degrees of freedom, isthe SM itself.

3.2 .

The missing ingredients in the SMAt this point, a part from a strict Cabibbo-

Kobayashi-Maskawa picture of flavour physics, thestrongest and yet to be verified predictions of theSM are the existence of the top and the Higgs.

The top has been searched at TRISTAN11 ,

SLC2 and at the CERN7 and TEVATRON3 collid-ers with negative results. Assuming the standardbranching ratios for its ieptonic decays, the top is ex-cluded by CDF3 with a mass lower than 77 Gev. Asto the Higgs of the SM . combined studies of rr, K, Band Tdecays strongly indicate a lower bound on mHof about 4 :- 5 Gev, although the searches in thislow mass range should not be abandoned14 . It ischeering to know that the pretended sensitivity lim-its for mt at TEVATRON, with f Gdt = 100pb-1 ,and for rnH at LEP il, with j- Gdt = 500pb-1 are 160

200 and 80 Gev respeUiveiy. The lower figure form. t (160 Gev) makes use of the elt signal from thetop leptonic decays whereas the 200 Gev sensitivitylimit might be reached with the Q + Jet signal, pro-vided the considerable background can be beaten l5 .

An obviously important question is the following:what does the theory itself have to say about rn t andnzH? A quite neat answer can be given if we indeedinsist that the physics of the SM can be extrapo-lated as such up to A » GF`/2 , say A 10 TPvor more . This being the case, thoo allowed region16in the (rnt, mH) plane is drawn in Fig .2, which doesnot show the scales on both axis, since they dependon A.

On the other hand, Table 3 gives, as function of

Figure 2: Allowed region in the (mt, mH) plane inthe SM.

R. Barbieri /Electroweak physics

75

Table 3: Upper bounds on m; and mH as functionsof the cut-off A (all masses in Gev)

A 104 107 1010 10 15

7nH 610I360 300 260mt 460 290 260 230

A, the simultaneous upper bounds on mt and mH(denoted by a circle in Fig.2). These bounds are cal-culated in renormalization group improved perturba-tion theory; with regard to them, however, there isno indication of a failure of the perturbative expan-sion if A Z 10 Tev. A significant feature of Fig.2 isworth mentioning . Independently from the value JA, the lower curve delimiting the allowed region inthe (mt,MH) plane detaches itself from themH = 0axis at mt ^= 80 Gev. For higher m, values, theHiggs potential becomes unstable for large values ofthe Higgs field, unless the quartic Higgs selfcoupling(and so the Higgs mass) is big enough to counteractthe effect of the top Yukawa coupling 17 . Taking,e.g . mt ..� 130 Gev, one has mH Z 40 Gev forAZ10TevormHZ50GevforA=10"Ge_v18 .Finding a Higgs below this bound would at the sametime be an important indication for new physics be-yond the SM (e .g . supersymmetry) .

Based on studies of the one loop renormalizationgroup equations (RGE). the question. has been askedwhether any particular point insidethe Flowed regionof Fig.2 should be prefeo fed .

Disregarding for sim-plicity the small effects due to the electroweak cou-pling constants, the RGE for the strong fire structureconstant a, and for the top Yukawa coupling con-stant at = g,2/4r, (mt = gt(mt) - 173 Gev) can beeasily solved, yelding

2a,(p)s1 'at (Et) - C .l- 9a,W117

where C is an integration constant . This solutionshows a well known19 infrared fixed point of theRCE, a, = 2/9a., which however is never reached in

time (for Zmt , as determined selfconsistently),

unless C is very sma1120 . In probabilistic terms, moreinteresting is an effective infrared fixed point of the

RGE which is obtained for C < 0, or when at(A)

76

is large enough20 . This effective fixed point leads

however to mt (and so for mH) at its maximum

vJue for any given A (the circle in Fig.2), whichseems already excluded from the upper i.-ound on

mt previously mentioned .Let me mention finally that the C =- O solution

in eq.(9) has been advocated in Ref.21 on the basisof a reduction of coupling hypothesis or by requiring asymptotic freedom even in the Yukawa couplingsector (at --+ 0 as o, --> 0) . This appears as a veryfar ultraviolet constraint, not really justifiable . Inany case, with o,(MZ) = 0.11 f 0.01, one wouldget mt = (95 f 10) Gev.

3.3 . SupersymmetrySupersymmetry is among the best motivated ex-

tensions of SM. To some extent, it is implied if: i) thepresent field theory menu is still relevant to describeeven higher phy.;:cal scales than the Fermi scale it-self: A » Aph » GF112 ; ii) scalars are indeedneeded, with a mass m = O (GF1/2) , to describeflavour.

In Table 4, I summarize the present status andthe (not too distant) fut?are of supersymmetry. Thenotation for supersymmetric particles should be obvious. By Xiandx° , I denote fermionic charginosand neutralinos respectively . I have also included theHiggs, H, since supersymmetry generally requires,among a react. Higgs spectrum, at least one lightneutral scalar particle . When needed, the back-ground theory that I have in mind is the minimal su-persymrrietric standard model (:ASSM), as obtainedfrom supergravity22 .

ihe present lower bounds on the various super-particle masses come from CDF (b, q)3, UA2(éf)23

aid TRISTAN (X0 1 1 . The ranges in the presentlower bounds reflect model dependences in the in-terpretation of the data . Column 2 gives the ob-tainable sensitivities at LEP 124 . Their significancerests especially on the fact that they are, in my opin-ion, rather model independent. The TEVATRONsensitivity limits at an integrated luminosity of 100pb'1 are indicated in Column 3 . The many ques-tion marks relative to the nori-strongly interactingparticles reflect partly the considerable backgroundproblems and partly some lack of detailed studies.In Column 4, 1 have finally given indicative tiieoreti-


Table 4: Supersymmetry summary (All masses inGev).

cal upper bounds on the various superparticie massesin the MSSM, as obtained from the naturalness cri-terium . The superp, rticle masses could be made ar-bitrarily heavy by increasingly precise tunings amongthe various physical parameters : the limits shownarise by allowing fine tunings up to 10% only25 .

3.4 .

Neutrino properties

A neutrino with non-standard properties, e.g . ai-.on-zero mass . could signal the presence of a newphysical scale besides GF1/2 . Unfortunately however, no clear indication exists at present of anyanomaly in neutrino physics, except perhaps forthe long-standing solar neutrino problem, on whichI shall come in a moment . Before that, let mequote a new upper limit on the electron neutrinomass, 1n(uF) < 13 .4 et% at 95% c.l ., from the Tri-tium ,ß-decay experiment at Los Alamo..2& . Thisbound, obtained using molecular Tritium gas, con-flicts with the previous ITEP result, which gives 1'eV < m(,.) < 4C eV .

On the solar neutrino problem, a very welcomeresult is the first confirmation by Kamiokande27 ,

using a totally independent method, of the longstanding observation in the Homestake experimentof a solar neutrino flux . In the KamiokandeCherenkov- water detector, one observes tae elas-tic r., - e scattering process, whose directionality al-lows to select events induced by neutrinos comingfrom the sun . For two periods of observation, cor-responding to 2 different electron energy thresholds

Particlemasses

Fmsent Jlowerbounds

LEP 1> 106 Z

TEVA-TRON100pb`1

Theor.upperbounds

m(gl 80 =100 - 200 800m.(q) 100=150 - 200 800tn(él) 30 -40 45 ? 350m(v) - 35--.1-40 - 350

30-1-40 45 50 - 70? 180° ) - 30 -40 50? 90

nt(H) - 30 _40 - 90

Em, one has the following results27 for the measured

0= 0.39 ±0.09 ± 0.06

(10b)

In my opinion the potential significance of these newresults is best appreciated if one considers them inrelation with the Homestake experiment29, whichmakes use of charged current reaction ve + 3'CI -,E- -I- 37Ar at a lower energy threshold Eth(v) = 0.8Mev. In the full period of observation, from 1970 toMarch 1988 (no data are known yet thereafter) theobserved neutrino flux, again normalized to the SSMexpectation, is ¢ = 0 .29 ± 0.03 . Let me recall28that both experiments are mainly sensitive to thehigher energy 8B-neutrinos, whose expected flux isdefinitely more uncertain then for the lower energyneutrinos. More precisely, the Kamiokande experi-ment is only sensitive to the 8 B-neutrinos, whereas inthe Homestake experiment, due to the lower thresh-old, the lower energy neutrinos (from ' Be and ethersources) are expected to contribute for about 25%of the full signal .

Making the assumption that the flux of the lowerenergy neutrinos is well predicted within given e" -rors by the SSM28 , by a simple substraction it ispossible to get the flux of 8 13-neutrinos observedby the Hômestake experiment, 0(6 B)fio,nestak( =

0.09 ± 0.06, still normalized to the SSM predictic .̂for matter of convenience . To the extent that thisnumber does not agree with the direct Kamiokandaobservation, egs.(10), one would conclude that thesolar neutrino problem is not due to a wrong pre-diction of the highly uncertain 8B-n,"trino flux : theview of the solar neutrino problem as a real neutrinoanomaly is then correspondingly strengthened .

It is certainly too early to draw any conclusion .Especially Homestake, but also Kamiokande, are dif-ficult experiments; more data are necded, also to settie the issue of the time fluctuations of the Homes-take results29 . On the other hard, taking also into

R. Barbieri /Electroweak physics 77

Table 5: Maximai effects of new neutral heavy

account that two Gallium experiments are enteringinto operation30 , which are sensitive to the evenlower energy pp neutrinos, one may be confident ona significant progress on the solar neutrino problemin a not too distant future .

3.5 .

New gauge bosonsThe motivations for the existence of new jector

bosons besides W and Z, and correspondingly of agauge group larger than SU(2)xU(1), are not lacking. From an experimental point of view, new vectorbosons could manifest themselves by direct produc-tion (of main interest for the higher energy pp collid-ers) or by mixing effects, modifying the masses andthe couplings of the W/Z (to be looked for in pre-cision experiments mainly at LEP).In the case of aneutral vector boson Z', mixed with the Z by an an-gle 0, the current upper bounds are 8 ,<_ 0.05=0.15rads , MZ, Z, 150 - 400 Gev, depending on the dif-ferent couplings to fermions3l

In Table 5, summarizing part of the results ofRef.32, I give the maximum deviations that couldresult on 4 different LEP observables in 3 typicalmodels, from the mixing of the Z v! - ith a heav-ier neutral boson: L-R, E6 and BESS denote theSU(2)Lx SJ(2)RXU(1) model, a model with an ex-tra U(1) contained in E6 (model B of Ref.31) anda model of composite new gauge bosons33 respec-tively . Also shown are the expected experimentalprecisions (aesp) and the theoretical uncertainties( .~SaFr~) on the different observables due to the un-known top and Higgs masses entering into radia-tive corrections . Also taking into account of pos-sib!e correlations 34 among the different observablesthat can be usefully studied, it is aelieved that, atLEP (, one will be sensitive to mixing angles downto 0.01 - 0.03 rads in all possible cases.

solar neutrino flux, normalized to the expectation of bosons of LEP observables .the standard solar model28 :

i) (from Jan 87 to May 88, Eth = 9.3 Mev) L-R Es BESS aesp LiaRC

0 = 0.46 ±0.13(stat) ± 0.08(syst .) (10a) AAFe 10.015 0.06 -0.015 0.004 0.01AApa!(r) 1 0.07 0.25 -0.015 0.011 0.05

ii)EI (preliminary ; from June 88 to April 89, th = DI'(e+e- ) 13A0 17% 0 2% 2%7.5 Mev) A r(had)_ -4% -5% -3% 1% 1%

78

In a complementary way, the direct production of

new vector bosons is of interest at the TEVATRON .With an integrated luminosity of 100pb-1 , by the

study of pp --> Z' -~e+e' and pp --" W' -~ ev, one

can reach sensitivity limits of about 600 - 700 Gev

in the masses, assuming the same couplings of the

new bosons as those ones of the standard W and Z.Alternative channels to be considered are

PP

7 Z' -+ WW,ZZ

W' ~ WZ

j'

Jets + isolated leptons

Although in this case background problems arein general more severe, this signal might compete,in a mo4el dependent way, with the purely leptonicsignal . For example, this could be the case for com-posite Z', W'35 or for right-handed W-bosons if theleptonic mode, WR --> eVR, is not allowed by phasespace36 .

3.6 .

The top as probe of new physicsBoth on phenomenological and on theoretical

grounds, the arguments for the existence of the topquark are very compelling . However, consistentlywith the present phenomenological constraints, thetop could have anomalous properties . Theoretically,such an anomalous behaviour might even be relatedto the fact that the top is apparently the only quarkwith a mass comparable to the one of the interme-diate vector bosons .

This suggests that appropriate considerationsshould be given to unexpected decay modes of thetop: in particular 2 body decay modes might easilydominate relative to SM ones, which are all 3 bodyfor 7nt S Iv1w .Examples are

j.

H'bt --~ HAc

where H+, H° are charged and neutr? ; Higgs's, t isthe scalar top and X a neutral fermion . All thesemodes can be accomodated, even with dominantbranching ratios, into suitable extensions of the SM .In all These cases, even though an eye must be kepton the issue of the radiative corrections, as I men-tioned, the CDF lower bound, mt Z 7- Gev, is in-valid . MARK II has looked for t -+ H+b and has set


a lower limit, mt Z 41 Gev, for a branching ratio of12 .

Barrying the possibility of Z --, te(fc), whichis unobservably small in the SM, but could besignificant37 in appropriately extended theories38 , at-quark above the Z-threshold, 2m t Z MZ , will haveto be looked for at the TEVATRON. For that pur-pose, in a direct search, one might use the Higgs de-cay modes into is (H+ -), r+v, H° -+ r+T')withbranching ratios of order_ (mT/mb)2 . Alternatively, inar indirect search, one may look for a precise mea-surement of the ratio

a(pp --> W -' ev)

(11)a(pp -' Z -+ e+e-)

whose sensitivity to the top quark mass is wellknown. A 2 - 3% determination of R would beuseful, which is within reach at TEVATRON withf l'.dt = 100pb-1 .

It could also prove possible tokeep at the same level of precision the theoreticalprediction for R, mostly relying on tho measured ra-tio of the deep inelastic structure functions F2/F2.

4.

NO-SCALAR THE0R!ES (A S Afi)Theories witi,out scalars have problems in de-

scribing flavour. The global symmetries of gaugetheories with fermions only, as imposed by renor-malizability, are a very serious obstacle to the con-struction of realistic theories . Abandoning, at leasttemporarily, the requirement of including all phys-ical scales, in particular the flavour scale Afl, be-low the cut-off A, one may consider a theory with(part of) the flavour global symmetries broken byappropriate 4-Fermi interactions . There is no prob-lem, on the other hand, in having the gauge symme-try spontaneously broken by a technicolour fermioncondensate 39 , described by a dynamical momentum-dependent mass ET(k) . Apprc;~ :r. . rte expressionsfor the vector boson and fermion masses are

2 ti922 f kd

22

`-gar

7'(k)A~W,

mfN 1

dk2

(k) .f,

2;. 2

T (12)

The relative size ofmf and A11y is especially sensitiveto the high energy behaviour of ET(k). For

NAF7.(k) - A7-(k/A7,)-y-2

,

AT9

(13)

(7 being the anomalous dimension of the tech-nifermion mass operator) one has

mf ti AT

_Afi -r

Myv ~ Afi CAT) (14)

Ideally, to obtain heavy enough fermion masses with-out having to lower the flavour scale to unacceptablevalues, one would like to have the largest possibleanomalous dimension40. In a QCD-like asymptoti-cally free theory, ET(k) - k-21g k or 7 = 0 , andcorrespondingly, in view of the constraints on Af, ,mf r;;:, 0.1 Mev. This is the heart of the flavour prob-lem in theories without scalars, known as such sincelong time .

In an attempt to alleviate the problem, in latestwork4l one has tried to use the 4-Fermi interactionssitting at the cut-off, not only to break the flavoursymmetries but also to enhance in a dynamical waythe high momentum behavior of the mass operator

ET(k). Qualitatively, the emerging physical pictureis the following . Imagine a 4-Fermi interaction withan attractive channel whose coupling is slightly sub-critical for the formation of the condensate at thecut-off itself42 . This force could affect the high en-ergy behaviour of the condensate, triggered by tech-nicolour, without modifying in a significant way ETat low momenta. To study these effects in a quan-titative way, one uses a simplified Swinger-Dysonequation for ET(k) with a kernel including the 4-Fermi interaction effect4l .

In principle, this is an interesting idea . Dueto the non-linearity of the equations, one has alsosuggested that small differences in the strengthof the various 4-Fermi interactions might give riseto huge differences in the corresponding fermionmasses40, 41 . In practice I find that one is dan-gerously close to giving up the advantages of thedecoupling theorem. Alternatively, to draw any realconclusion, a much better control of the theory atthe cut-off would seem to be needed .

5. STRONGLY INTERACTING HIGGS SECTOR(A = O(GF'l2))On the way of reducing the cut-off (and so the

predictive power) of the theory, one is lead also toconsider theories with strongly interacting Higgs ('s) .

R. Barbieri/electroweak physics 7

In this way one may denote a broad class oftheories,generally characterized by the fact that the gaugesymmetry breaking sector does not give rise to anylight quantum below the Fermi scale other than thelongitudinal components of theWand Z themselves.For example, this could be tire case for the S in thelimit of large Higgs mass or for a technicolour the-ory, as nvively extrapolated for QCD, even though al-ternatives can be envisaged33, 43 in both instances.The problem here is to find signatures alternative tothe production of new particles. Theoretically thistask is made hard by the lack of appropriate com-putational techniques and/or of well defined enoughtheories .

The large Higgs mass limit44, 45 has been ex-tcr-sively studied in the SM . This limit correspondsto the large Higg= self-courting limit At moderately high energies, irfw t i; < mH ,. 1 Tev,one may look for enhancements or structures of ap-piopriately chosen cross sections . Unfortunately, atleast in the calculations made so far44,45, no suchfeature has emerged . This is also a consequence ofthe screening theorern44 , whose validity has beenrecently extended46 to all orders of perturbation the-ory for the leading power in rng.

In a more general approach47 , one applies theconcepts of the chiral Lagrangians to the sponta-neous breaking of the global symmetries (with theelectroweak interactions switched off) which givesrise to the longitudinal W/Z components . Thisseems however more a general parametrization48 ofpossible effects rather than a tool to actually get, stillat moderately high energies, definite predictions .

What th-in if no Higgs is found below or at theFermi scale? Important as it may be, since no onecan reasonably exclude this possibility, this question,I am afraid, has no definite answer. On the positiveside, on the other hand, this is an argument, not theonly one, in favour of large hadron colliders.

6. CONCLUSIONSi s a general conclusion of all the new results

presented at this Conference, the SM appears to bein very good shape. As I said, MZ replaces sin' 8w

as the third precise number 1r, electroweak physics,

other than a and GF. This will be even more true in

30

a short while with the LEP results . The top quark,if standard, is likely to be heavier than about 100Gev. The Higgs, on the contrary, is still basicallyunconstrained.

On the other hand, there are good reasons tothink that the ncar future will be an interesting timefor the development of the fie!~: of the electroweakinteractions . 1 have of course mainly in mind theentering in operation of LEP, as well as the contin-uation of TEVATRON activity. I have mentionedduring the talk the observables which I would watchmore carefully. Ofcourse other sources of potentiallyvery relevant informations e~ist as well . As an ex-ample, I have discussed the solar neutrino problem,whose real nature should also be clarified in a nottoo distant future .

In a minimal scenario, the SM will be tested inmany of its different aspects with a significantly bet-ter precision than now. More optimistically, new discoveries will be made . As I have shown, the chancesare there.

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