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PROBING NEW GAUGE BOSON COUPLINGS AT

arXiv:hep-ph/9206258v1 26 Jun 1992PROBING NEW GAUGE BOSON COUPLINGS ATHADRON SUPERCOLLIDERSTHOMAS G. RIZZOHigh Energy Physics Division, Argonne National Laboratory , Argonne,Illinois 60439, USAandAmes Laboratory and Department of Physics, Iowa State University , Ames,Iowa 50011, USAABSTRACTOnce it is discovered, the determination of the various couplings of a newneutral gauge boson at a hadron supercollider will not be an easy task. Wereview several recent studies that have begun to examine this issue for boththe SSC and LHC.1.IntroductionIf a new neutral gauge boson(Z2) is discovered at either the SSC or LHC we willwant to know more about it than the fact that it exists.

Since many models in theliterature predict such particles, we will want to know which Z2 we have discovered.To accomplish this goal one must probe the couplings of the Z2. This will not be aneasy task since only a few of the properties of the Z2 are easily measurable at hadronsupercolliders.

During the past 1-2 years there have been some initial attempts toaddress this problem and they will be reviewed in the discussion below.2.Observables and AnalysesNeither the SSC or LHC detectors will have much difficulty in making cleanmeasurements of the mass(M2), width(Γ), production cross section(σ), and forward-backward asymmetry(AF B) for a Z2 in the TeV mass range1 via the lepton-pair pro-duction channel. If this is the only information available then identifying the Z2 willbe difficult but not impossible provided that certain theoretical prejudices are indeedrealized in nature and sufficient statistics are available.

Within a given extended gaugemodel, Γ (and, hence σ) will be sensitive to what final states are kinematically allowedin Z2 decay since such models require the existence of exotic particles in addition tothose present in the Standard Model(SM). If one assumes that the Z2 can decay onlyto the SM particles it is possible to get an excellent handle on the nature of the Z2couplings using the above data alone2.

However, such an analysis could be spoiled bythe potential contributions of these exotics to Γ or by the influence of a small mixing

between the Z2 and the SM Z. One can show that for a class of models, the proba-bility that some of these new degrees of freedom contribute substantially to Γ is smallsince it is very likely that they are more massive than M2/2 and are thus kinematicallyforbidden to appear as decay products.

Fig. 1a shows this explicitly for the case ofthe exotic fermions in E6 Effective Rank-5 Models3.

Since the exotics and the Z2 havetheir masses generated by the same vev and all of the particle couplings are determinedonce the E6 angle −90o ≤θ ≤+90o is fixed, the only free parameter for each exoticparticle is the size of its Yukawa coupling. This can be bounded in the usual way bydemanding tree-level unitarity in exotic particle scattering amplitudes mediated by Z2exchange.

One then can determine what fraction of the allowed range for the Yukawacouplings will permit the exotics to participate in Z2 decay resulting in Fig. 1a; com-parable bounds are obtainable for the exotics in other models.

Generally, however, theexistence of additional Z2 decay modes remains a concern for analyses using only theobservables listed above.Fig. 1.

(a)Probability that a Z2 can decay into the exotic fermions h,E,Sc(solid), N(dash-dot), or N c(dash) in E6 models. (b)χ2 fit to the value of θ for the model discussed in thetext; the solid(dashed) curve corresponds to a Z −Z2 mixing angle of 0.01(-0.01).Similarly, it can also be shown that if the magnitude of the Z −Z2 mixing angle issmall(≤0.01, as might be expected for a heavy Z2), then this will have little effect onour ability to determine extended model couplings using only the data above3; this isdemonstrated by an explicit example in Fig.

1b for an E6 model Z2 with θ = 0(model ψ)and a M2=3 TeV at the SSC for an integrated luminosity of 10fb−1. Here, we performa χ2 fit to determine the value of θ obtainable from the above data using the propertiesof the SDC detector1 assuming the absence of mixing when it is in fact present andassuming decays to SM fermions only.

(We remind the reader that, once specified, thevalue of θ uniquely fixes all of the Z2 couplings.) We see that the best-fit value of θ aswell as its 95% CL allowed range(corresponding to the gap between the curves alongthe dotted line) are only slightly altered by mixing angles as large as 0.013.

We notethat other models show more or less the same sensitivity to finite mixing.In order to circumvent the potential problems in coupling determinations associ-ated with theoretical uncertainties in the value of Γ we must search for new observables

which are insensitive to this quantity. One possibility is to examine 3-body decays suchas Z2→W ±l∓ν and Z2→Zl+l−or Zν¯ν4,5.

For a relatively light Z2 with a mass less than1-2 TeV, the number of events of this type is generally in the range 102−104 at both theSSC and LHC so that significant statistics can be accumulated once SM backgroundsare removed5. The ratios of the number of these kinds of events to ordinary lepton-pairevents is thus not too small and is Γ independent.

In particular, one defines5 the ratiosrlνW = Γ(Z2→W ±l∓ν)/Γ(Z2→l+l−) and rννZ = Γ(Z2→Zν¯ν)/Γ(Z2→l+l−) whose val-ues are shown for a number of different models in Fig. 2a assuming M2=1 TeV and noZ −Z2 mixing.

(For a discussion of the individual specific models shown, see Ref. 4.

)Most models predict values for these ratios that lie along the solid line provided the Z2has generation-independent couplings and its corresponding generator commutes withthose of SU(2)L; this is indeed the case for most GUT-inspired models. By satisfyingthese two conditions one finds that rlνW and rννZ become simultaneously correlatedand bounded.

Scenarios not satisfying these conditions will lie elsewhere on the plot.Fig. 2.

(a)rlνW and rννZ for several different extended gauge models as discussed in the text. (b)rlνW including the effects of Z −Z2 mixing as described in the text.If mixing does occur these conditions are no longer satisfied as the generatorcoupling to the Z2 now has a small piece proportional to T3L.

This does not significantlyinfluence the resulting value of rννZ, but rlνW can be greatly modified since mixing turnson an additional resonant diagram involving the now non-zero Z2W +W −coupling. Thiscan result in a substantial increase in the value of rlνW as shown in Fig.

2b for theE6 model case as a function of θ (x-axis) and the ratio of the two Higgs-doubletsvevs, tanβ (y-axis) assuming M2=1 TeV. Here we see that mixing can induce valuesfor rlνW of order unity or larger for a broad region of parameter space.

The result ofmixing for a model lying along the solid curve in Fig. 2a would then be a shift to theright without any appreciable shift up or down.

While discovering a Z2 whose valuesof these ratios place it in the lower right-hand part of Fig. 2a would be difficult tointerpret (something exotic and/or non-zero mixing), a value of rννZ ≥0.06 would be aclear indication that something unusual has been found.

(Unfortunately, rννZ has a veryserious SM background from 2Z production that is very difficult to deal with5.) A studyof the SM backgrounds for the above 3-body channels, including the decays of the final

state W and Z, has recently been done by del Aguila et al.6 for a number of differentextended models. These authors conclude that the Z2→e¯µ plus missing energy finalstates are reasonably sensitive to Z2 couplings and are statistically powerful providedthat M2 is less than about 1.5 TeV.As a last point we mention that in some extended models the Z2 is accompaniedby a W2 with a comparable mass; in a large fraction of cases the two particles arealmost exactly degenerate so that W2 cannot participate in Z2 decay.

(Of course, themere observation of a W2 will tell us a great deal about the nature of the extended modeland in most cases the W2 production cross section is larger than that of the Z2 makingit likely that W2’s might be observed first as was the case for the SM gauge bosons. )In the Left-Right Symmetric Model(LRM) however, there is a region of parameterspace which allows Z2→W +2 W −2 the rate for which depends on the nature of SU(2)Rbreaking and the ratio of the SU(2)L and SU(2)R coupling constants, κ.

A somewhatlarger range of parameters allows for the corresponding 3-body decay Z2→W ±2 l∓ν. Anobservation of either of these modes will provide us much needed information on theextended gauge sector.

For a further discussion of these possibilities see Refs. 4 and 7.Fig.

3. (a)τ polarization asymmetry, A, as a function of θ for the case discussed in thetext.

(b)Left-right asymmetry, ALR, at the SSC for both the E6 model with M2=1(solid) or2(dotted) TeV and the LRM for M2=1(dashed) or 2(dot-dashed) TeV as discussed in thetext.Another possibility, which has a long history and has been recently resurrected8,is to measure the polarization asymmetry, A, of taus coming from the decay Z2→τ +τ −.The advantage of this observable is that, in the narrow-width approximation, it directlyprobes the leptonic Z2 couplings and is very insensitive to structure function andluminosity uncertainties: A = −2vτaτ/(v2τ + a2τ). Fig.

3a shows the strong sensitivity ofA to the mixing parameter θ discussed above for E6 models. Unfortunately, observingτ pairs at hadron supercolliders is difficult due to substantial backgrounds from t¯tand W +W −pairs as well as conventional QCD 2-jet production all of which must bedrastically reduced before the value of A can be reliably determined; this problem hasbeen recently addressed for the SDC by Anderson et al8.

These authors have shown (fora Z2 arising from the E6 model discussed above with M2=1 TeV) that a judicious choice

of cuts can reject as much as 97% of the background and provides a determination ofA at the 10% level assuming a luminosity of 10 fb−1. (After these cuts only 6% of theτ-pairs from Z2 decay remain but, since event rates are high, enough statistics remainsavailable.) Unfortunately, for a heavier Z2 it is unlikely that τ polarization data willbe very useful as the signal to background ratio is substantially smaller even if largerluminosities were available.

These authors8 hypothesize that a better choice of cutsmay help this situation; clearly more work on this observable is needed.If polarized proton beams become available at either the SSC or LHC, then otherasymmetries such as the left-right asymmetry, ALR (defined in a manner similar towhat is discussed for e+e−collisions), can be constructed9 which are comparable inmagnitude to the more conventional AF B. Fiandrino and Taxil9, have recently shownthat such asymmetries are quite sensitive to the choice of extended model as well thevalues of model parameters, such as θ in the E6 scenario, as shown in Fig. 3b.

(In thisplot, β = 90o −θ and α is related to the parameter κ of the LRM.) Unfortunately, evenif such asymmetries were reliably determined for the dilepton invariant mass regionnear M2 they would be difficult to interpret in terms of model couplings in a morethan a qualitative fashion due to the very large uncertainties currently present in thepolarized parton densities.

The authors of Ref. 8 are optimistic, however, that newpolarized scattering data anticipated from RHIC may alleviate at least some of thesedifficulties.3.ConclusionsAs can be seen from the discussion above, the identification of new Z2 gaugebosons at hadron supercolliders remains a serious problem especially if the mass of thisparticle exceeds 2 TeV.

Clearly, much more work will be needed to address the issuesraised here before hadron supercolliders are turned on later in the decade.References1. SDC Technical Design Report, E. Berger et al., SDC-92-201 (1992); GEM Letterof Intent, R. Steiner et al., (1991); ASCOT Expression of Interest, P.R.

Nortonet al., (1992); CMS Expression of Interest, M. Della Negra et al., (1992); EAGLEExpression of Interest, P. Jenni et al., (1992); L3+1 Expression of Interest, S.C.C.Ting et al., (1992).2. J.L.

Hewett and T.G. Rizzo, Phys.

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Hewett and T.G. Rizzo, Argonne National Laboratory report ANL-HEP-PR-92-34 (1992).4.

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Lett. B192 (1987) 125; J.L.

Hewett and T.G. Rizzo, ArgonneNational Laboratory report ANL-HEP-PR-92-33 (1992).5.

M. Cvetic and P. Langacker, University of Pennsylvania report UPR-0487-T (1991).6. F. del Aguila et al., Universidad de Granada report UG-FT-22/92 (1992).7.

M. Cvetic, P. Langacker, and B. Kayser, Phys. Rev.

Lett. 68 (1992) 2871.8.

H. Haber in Proceedings of the 1984 Summer Study on the Design and Utilizationof the Superconducting Super Collider, ed. R. Donaldson and J.G.

Morfin (1984),p. 157 ; J.D. Anderson, M.H.

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