I une 1992CERN -TH.6525/92

Les Arcs, Savoie, F rance, 15-22 March 1992Elecrroweak Interactions and Unified Theories

XXVIIth Rencontres de Moriond onTalk given at the

of Electroweak DataToward a Model Independent AnalysisExtended Gauge ModelsIntroduction

CONTENTS

1211 Geneva 23, SwitzerlandTheory Division, CERN

G. Altarelli

AND CONSTRAINTS ON NEW PHYSICSPRECISION ELECTROWEAK DATA

C ZX OCR OutputPnaaezavn

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CERN_TH.6525/92/ /BERN LIBRHRIES, GENENF?

presented at this Conference. We take the combined values of mz and the Z—widths OCR Outputupdate here the results of those papers also including the latest experimental resultswill heavily refer to refs.[7] and [17], respectively, for notations and discussions, while wedescribe the more model independent approach of ref.[17]. For absolute lack of space wealso in connection with LEP results, in particular by our group in refs.[6,7]. Then we willmodels with an extra U(1), which recently have been extensively discussed in the literature,

In the following we will first discuss the case of extended gauge models, especially

vacuum polarization effects or other similar ones.models are disfavoured) can be obtained directly with no assumptions like dominance ofinteresting constraints on models of new physics (e. g. the result that simple technicolourphenomenologically satisfactory compromise at this stage.We shall see that most of thethe optimum number of variables that one can control) which we consider as apragmatic point of view (roughly it is the quality and the nature of the available data that fixobservable which is considered. We have recently proposed [17] an approach based on aindependent an infinity of parameters would be necessary, or at least one for each newanalysis in terms of 4 variables S, T , S', T`. Clearly if one really wants to be modelbased on hypotheses formulated within an operator expansion approach, they propose anthat the above assumptions are only plausible in models with no decoupling, otherwise,(or S, T and U [15]) are implied by the same assumptions. Still other authors [16] arguedpolarisation diagrams. Others [14] pointed out that in general three parameters e;,eg and E3

based on the assumption that new physics effects arise dominantly from vacuum[10-13] have argued for model·independent analyses in terms of two variables S and Tcorrections with respect to the SM predictions in a wide class of models. Some authorsunaffected by our ignorance of mt, sensitive to the Higgs sector, likely to receive largephysics. For example, one is interested in constnrcting measurable quantities relativelymodel in mind one can still be interested in a strategy for increasing the sensitivity to newon tgB and m A from the Higgs searches [9]). On the other hand even without a specifiedmany new parameters for a complete study (but important limits are for example obtainedwith interesting results for extended gauge models [6,7] while the MSSM contains tooparameters (as functions of mt and mg). A general analysis of this type has been performedparameters). In principle one can repeat a similar fit as above and obtain limits on the new

Minimal Supersymmetric Standard Model (MSSM) [8] (which leads to Q 4-5 new

simplest case of a single additional U(l) factor introduce Q 2 new parameters) or the

generalisation of it. Typical examples are extended gauge models [5-7] (which in theintermediate cases). On one hand one can imagine replacing the SM with some specific

Beyond the SM two extreme situations can be contemplated (with a variety of

is larger, mt ; 175 GeV for heavy Higgs (ml.; = 0.5-1 TeV).The central value of mt is smaller, mt ·; 135 GeV, for light Higgs (mg =50- 100 GeV) whilethe CDF limit on mt [4], what theoretical errors are assigned to some quantities and so on.value of ots(mZ) is assumed (I have taken or.S(mz)=0.12T0.01), what weight is assigned to

GeV. The precise result of the fit depends on exactly what set of data is included, whatpresented at this Conference [3] I obtain ml = 155f 30 GeV for mH in the range 50 - 1000vN scattering, mw/mz ..... with the corresponding data. From the combined results

,Bol EBcomparing the SM predictions for the measured observables FZ, Ph, I"`], A:, Ag, Ahadronic final states) and ends up with allowed ranges for mt and mH obtained byfrom the known input parameters ot, Gp , mz, (mmtgm and 0ts(mZ) (the latter only for

In the Standard Model (SM) the analysis of precision electroweak data [1,2] starts

the running of ot due to known physics is extracted from (1-Ar) = (1- A0t)(l— Arw).In OCR Output

Here ot(mZ) = or/(l—A0t) is fixed to the conventional value 1/128.8 [18] so that the effect of

mi mi x/-2Gpm;(1—Arw)(1 ) _ (1)

ww mum;)2 2 mm

following. First we introduce Arw as obtained from mw/mz by the relation:

Ak', which contain thesmall effects one is trying to disentangle, and are defined in the

we can isolate the corresponding dynamically significant corrections Arw, Ap andAim

measured, each of them probing qualitatively different dynamics. From mw/mZ_ I`] and

quantities at qz = m; are very simple (e.g. not involving 0tS(mZ)), cleanly defined and

data no deviation is observed) and l refers to the charged lepton average. These three

mw/mZ_1"] and Aim where lepton universality is assumed (within the precision of present

set of input parameters ot, 0ts(mZ), Gp , mz, mf, mH we consider the basic observables

In the following we do not assume the validity of the SM from the start. Given the

Toward a Model Independent Analvsis of Electroweak Da

least favourable instances. Similarly 0< 6pM < 0.75%.

most cases IQI < 1% is implied for all values of mt, mH and ots(mz). with IQI < 2.5% in the

left—right symmetric model. We see that the constraints on Q and 5pM are very strong. Indirectly to the updated results in figs 1, 2 for the class of models based on E6 and for the

]ld1)sin2Q. More details can be found in ref.[7]. Here for lack of space we go(mg/mi

lowest state down. If the ZH mass was known 5pM and sin2Q would be related: 8pMSU(2) is induced by Higgs doublets). One has 5pM > 0 because the mixing pushes the

ldcos29w = ma,/(mip) with p = 1 + 8pM (we assume that the breaking of the ordinarysinQZN. 8pM describes the shift induced at tree level in the p parameter by the mixing:

light (ZL). Observed at LEP, and the heavy (ZH) mass eigenstates, e.g. ZL = cosQZs +

Q defmes the mixtures of the standard (ZS) and the new (ZN) vector boson that make up the

(namely of the heavy ZH mass) 2 new parameters are introduced, tgQ and 5pM. The anglecoupling of the new (old) U(1)), irrespective of assumptions on the new Higgs sectorthe associated neutral vector boson ZN (it is assumed that g"=g', with g" (g') being the

For a specified definition of the extra U(1), i.e. for given couplings to fermions of

Exten Model

and Agn = 0.094 T 0.014 (corrected for BB mixing).

which can also be derived from his talk: ALB = (1.74 T 0.30) 10*2, Agol = 0.140 T 0.024explicitly given by J.Nash [3] and the following values of the asymmetries at ~/E = mz ,

eg = (-0.02 1* 0.56) 10*

eg = (-0.7lT 0.83) l0‘ (3) OCR Output

8] = Ap = (O.I5'!' 0.41) IO'

Given the present values of mw/mz, I`] and ALB we obtain:

convenient starting point for a model·independent analysis of the data.important input data with respect to the sensitivity to new physics so that they represent aThe epsilons are useful in that they provide a very efficient parametrization of the most

These definitions are quite general and do not commit us to any particular model.

needs better measurements of mw/mz.TeV)[l7] .Note that LEP1 directly measures cl and eg while to really improve on eg one

realistic values of mt. In the SM E3 = +0.3 10*2 (+0.55 l0·2) for mH = 50 GeV (mg = 1but are also present in t-:3. Actually E3 tums out [17] to be almost independent of mt for

The leading terms for large Higgs mass, which are logarithmic, are mainly contained in el

Clearly eg and sg no longer contain terms of order Gpmf but only logarithmic terms in mt.

eg = cg Ap +(cg - sg) Ak'

(co — s 0)(2)c2=c0Ap+ ·—-2s5 Ak'

2 sg Arw

81 = AP

thus introduce the following linear combinations [14,17]]:

while trading Arw and Ak` for two quantities with no contributions of order Gpmf . We

be disentangled if not masked by large conventional mt effects, it is convenient to keep Ap

Arw ~ -c§sgAp ~ (cg - sg )/sg Ak' (see, e.g. ref. [18]). As new physics can more easilym;_ are all dominated by quadratic terms in mt of order Gpmf [22] and in this limit one has

GeV). As is well known, in the Standard Model Arw, Ap and Ak' , for sufficiently large

given by sg cg : mm;)/(~J§opm;> with cg :1- sg (sf, : 0.23145 for mz :91.175shell Z [18-21], while sf] is the corresponding quantity before non-pure QED corrections,

Q(1 + %) and gi = 1 — 4 5%, = 1 - 4 (1 + Ak') sg. Here sg] is an effective sin26w for on·gand Agn as exact. In terms of gv and gA_ Ap and Ak' are given by [14] gA = - {Q =

and gA of the on-shell Z to charged leptons defined by taking [17] the Bom formulae for I`;

order to define Ap and Ak' we consider the effective vector and axial-vector couplings gv

Fl,/Ph). For these reasons we restrict our attention to Al`§B at this stage.Note that there is a OCR Output

[23] makes the relation with the epsilons strongly mt dependent (as is also the case forrange measured at LEP. But the presence of large vertex corrections in the Z->bb vertex

and/or the total width FZ, for ocS(mZ) varying in a specified interval, for example in the

hadronic quantities at the Z pole. At this point one could also include the hadronic width Th

The assumption of quark-lepton universality of new physics is needed to add

83 = (-0.01 1* 0.51) l0·

(4)E2 = (-0.72 T 0.82) l0‘

8] = Ap = (0.16 TO.4l) IO'

information on ALJ . At this stage the results are not much changed (iig.3b):

Essentially one only needs to assume charged lepton universality in order to add the

can be derived at each stage.with an increasing number of particular assumptions and we examine the conclusions that14]. In the following we sketch how the analysis of present data can be performed in stagesis weak enough for all second and higher order derivatives in q2 to be safely neglected [10with the assumption that the qz-dependence of the relevant vacuum polarisation amplitudesFor example, we could restrict ourselves to the case of new physics in oblique correctionsneutrino-nucleus scattering, v-e scattering and atomic parity violation in atomic physics).

asymmetries, or to observables measured at low qz, far from the Z pole (e. g. deep inelasticthe epsilons to observables involving quarks or neutrinos,like the hadronic widths orStronger hypotheses about possible forms of new physics are needed if one wants to relatedisentangled if we only consider on-shell Z properties in the charged lepton sector.universal for all charged lepton flavours. These two kinds of contributions cannot beof the form AVp_(Z*>l+1- ) = u (Agp, 75 + Agv) Yuu with Agv and Agp, real form factors

occur either through vacuum polarisation terms [10-14] and/or in Z->l+l· vertex correctionsasymmetry ALR. This is true in all models where the contributions of new physics only

mind, apart from I`] and Ai,B, the 1:-polarisation asymmetry ASM and the left-right

charged leptons at the Z pole are uniquely determined by the ai. For example, we have in

First, very mild assumptions are required in order that all other observables related towhich are needed in order to relate the epsilons to a progressively larger set of observables.hierarchy of simple and rather general assumptions [17] valid in large classes of models

In order to include other measurements in the analysis, one can formulate a

favoured.

As a consequence, models of new physics that correct E3 in the negative direction are

somewhat smaller than implied in the Standard Model by the measured central value of

independent stage. We realize that this result arises because the central value of I`; is

value of E3 is below the Standard Model range is already obtained at this completely model

functions of mt and ml.; is shown in tig.3a. We see that the famous result that the centralThe corresponding 10 ellipse in the plane 83 — cl compared with the SM predictions as

Standard Model being verified with increasing precision it becomes less and less plausible OCR Outputof large vacuum polarization effects is only likely in models with no decoupling. With thedominance of oblique corrections as were made in previous discussions. In fact dominanceparameters el, eg and eg following a general definition independent of assumptions like the

Summarising, we have shown that it is possible and indeed useful to introduce the

corrections from new physics, while the epsilon parameters can be defined more in general.T and U are well defined only in the specific context of dominance of vacuum polarisationthe Standard Model at some reference mt and mg. Note, however, that in refs.[l0-13] S,

-0tU/(4s;) and Aeg = 0tS/(4s$), where Ae= s—eS[(m[,mH) with es; being the prediction of

leptons then these particles should be discovered at LEP200.unchanged (that is of decreasing 2:3). If the small value of 2-:3 is due to charginos and s

induced, which automatically go in the right direction of decreasing I`] while leaving A

It has been shown in ref.[29] that for light charginos and s-leptons sizeable effects arecharginos, neutralinos and s-leptons could be light, with masses in the range 50-200 GeV.MSSM approaches that of the Standard Model for a relatively light Higgs [29]. However,supersymmetric particles are sufficiently heavy the pattem of radiative corrections in thesplitting is small and their average mass is large this effect is not particularly large. If allnon decoupling effects are those associated with s-top and s-bottom scalar quarks. If theirthe MSSM have been studied in detail in ref. [29]. As well known, the only possible newdepartures from the Standard Model predictions on the epsilon parameters that can occur inNote that corrections to eg can be negative in models with an exu·a U(1) [28]. Recently the

are mainly those on I`] and A;:B and, with smaller weight, those on Cs parity violation.

N·y(;=4 discussed in refs.[l0-14,17,27], also shown in tig.3d. The data that push eg down

sg is predicted are discouraged, as is the case for the class of technicolour models with

still rather large error (fig.4). Clearly, models where an additional positive contribution toStandard Model prediction.The values of eg are consistent with the Standard Model, with a

As seen from fig.3d, the central value of E3 is negative and about lo away from the

:-:3 = (0.00 T 0.43) l0‘

(6)t-:2 = (-0.72 T 0.79) l0‘

8] = Ap = (0.16 TO.32) 10'

energy results with the rest of the data (as done in ref.[l7]) one finds (fig.3d):inelastic scattering [25] and parity violation in Cs atoms[l3,26]. By combining the lowStandard Model, is to include the low energy data, in particular neutrino—nucleus deep

The next step, valid if the effects of a large q2 difference can be described as in the

E3 = (0.02 T 0.48) l0‘

(5)1-:2 = (-0.73 T 0.82) l0‘

8] = Ap = (0.16 T 0.40) l0‘

taking this effect into account we obtain for the epsilons (fig.3c):

QCD effect [24] in AER : (AgB)mcas = (Agn) Ew( 1-0.79 <xS(mZ)/rt) = 0.97 (AQ,) Ew. After

than in the Standard Model (although compatible with it). OCR Output

data on I"; given Agn and on parity violation in atomic Cesium favour values of 83 smaller

Higgs sector and likely to collect large conuibutions in models with no decoupling. Presentparticularly interesting, being independent of ml with very good accuracy, sensitive to themt and mg and the associated theoretical errors were extimated [17]. eg turns out to be

concentrated in el. The epsilons have been studied in the Standard Model as functions of

of new physics effects, because the uncertainties due to our ignorance of mt aremass scale (beyond the input parameter mz). 82 and eg are good indicators of the presence

different information and are the most precisely measured observables defined at the W/Z

of three parameters is related to the fact that mw/mz, I`; and Agn carry qualitatively

similar footing. Thus our approach in terms of the epsilons is more flexible. The presencea few TeV's). In models with decoupling, in general all kinds of diagrams contribute on athat such large effects are present (assuming the existence of new physics at a scale of order

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REFERENCES

which are available at present. OCR Output1000 GeV) with the experimental result in Eq. (6), obtained from all the data

Fig. 4: eg vs. mt in the Standard Model for different values of my.] (ml.; = 50,100, 500,

technifamily) [10-13,17, 27] are also shown for comparison.d). The predictions of QCD-like versions of technicolour (with N·[·(;=4 and oneAbpg is added in c). All data, including low energy experiments, are included inAlpg. In b) the data on ATDO; have been also taken into account . The result forCases a) to d) correspond to different input data. a) is obtained from I`; and

1000 GeV, and the dots mark values of mt in the range mt= 50-270 GeV).(The four solid lines are for different values of mg, mg = 50, 100, 500,shown. The Standard Model prediction is also displayed for reference purposes

Fig. 3: Data on sl and 2:3. The lo ellipses and their projections on the 21, E3 axes are

those of ref.[7].corresponding bounds for L-R models are also indicated. These figures updateof the extra U(l) in E6), for mmp=mHgggS= 100GeV and otS=0.12. The

Figs. l and 2: Allowed ranges (90%CL) of ApM and Z; versus 92 (defining the embedding

OCR OutputFIGURE CAPTION