We review the current status of precision electroweak measurements and the
constraints they impose on new physics. We perform a model independent analysis
using the STU-formalism of Ref. 1, and then discuss how the Z-pole data from
LEP and SLD can be used to constrain models that are not covered within that
framework.Comment: 1 cover page + 8 pages, 8 postscript figures, LaTeX2e,
  ws-p9-75x6-50.cls, Talk presented at Hadron 13, Mumbai, India, January 14-20,
  199

Grant, Aaron K.

Loinaz, Will

Takeuchi, Tatsu

English

arXiv

We review the current status of precision electroweak measurements and the constraints they impose on new physics. We perform a model independent analysis using the STU-formalism of Ref. 1, and then discuss how the Z-pole data from LEP and SLD can be used to constrain models that are not covered within that framework

Takeuchi, T

Loinaz, W

Grant, A K

CERN Document Server

VPI{IPPAP{99{03hep{ph/yymmdddApril 1999Precision Tests of Electroweak PhysicsTatsu TAKEUCHIa, Will LOINAZbInstitute for Particle Physics and AstrophysicsPhysics Department, Virginia Tech, Blacksburg, VA 24061, USAandAaron K. GrantcPhysics Department, Harvard University, Cambridge, MA 02138, USAWe review the current status of precision electroweak measurements andthe constraints they impose on new physics. We perform a model inde-pendent analysis using the STU{formalism of Ref. 1, and then discusshow the Z{pole data from LEP and SLD can be used to constrain modelsthat are not covered within that framework.Talk presented by Tatsu Takeuchi atHadron Collider Physics 13, Mumbai, India, January 14–20, 1999VPI{IPPAP{99{03hep{ph/yymmdddApril 1999aelectronic address: takeuchi@vt.edubelectronic address: loinaz@alumni.princeton.educelectronic address: grant@gauss.harvard.eduPRECISION TESTS OF ELECTROWEAK PHYSICSTATSU TAKEUCHIyAND WILL LOINAZInstitute for Particle Physics and AstrophysicsPhysics Department, Virginia Tech, Blacksburg, VA 24061, USAAARON K. GRANTPhysics Department, Harvard University, Cambridge, MA 02138, USAWe review the current status of precision electroweak measurements and the con-straints they impose on new physics. We perform a model independent analysisusing the STU–formalism of Ref. 1, and then discuss how the Z–pole data fromLEP and SLD can be used to constrain models that are not covered within thatframework.1 IntroductionThere are two reasons for studying the data from precision electroweak measure-ments. First, we would like to know how well the Standard Model (SM) agreeswith the experimental data: any signicant deviation between the two would be asignal of new physics beyond the SM. Also, since the SM predictions depend on themass of the still unobserved Higgs boson, the value of mH which best reproducesthe experimental data serves as its prediction. Second, we would like to know ifany of the proposed theories of new physics beyond the SM is viable, i.e. does notmake theoretical predictions inconsistent with the experimental data (or perhapsmakes the agreement even better than with the SM).The way to kill these two birds with one stone is to constrain the sizes of radiativecorrections coming from new physics using the precision electroweak data. If thedata prefers a non{zero value for the size of these extra corrections for some choice ofmH , it would signal that: (1) the agreement between the SM and data is not perfectfor that particular choice of Higgs mass, and (2) any new physics which predictssuch corrections would make the agreement between theory and experiment better.2 Constraints on Oblique Electroweak CorrectionsIn order to constrain the size of radiative corrections coming from new physics, wemust rst make some assumptions about the new physics giving rise to them (sinceit is impossible to consider all possible corrections from all possible new physics allat once) and express them in terms of a few model independent parameters.The simplest assumptions that would suciently constrain the number of cor-rections one must consider while still encompassing a large class of models are thefollowing:1. The electroweak gauge group is the standard SU(2)L  U(1)Y . The onlyelectroweak gauge bosons are the photon, the W, and the Z.yPRESENTING AUTHOR.Hadron 13 : Precision Tests of Electroweak Physics 16EnergyCharged Channel Neutral ChannelG αMWMZﬀ -?6?6TSS + U Figure 1. The S, T , and U variables quantify the extra vacuum polarization corrections due tonew physics when relating physics in different channels or physics at different energy scales. Lowenergy and neutral current observables depend only on S and T because α, Gµ, and MZ are usedas inputs to make the SM predictions.2. The couplings of new physics to light fermions are highly suppressed. Since allprecision electroweak measurements only involve four fermion processes withlight external fermions, this means that vertex and box corrections from newphysics can be neglected. Only vacuum polarization (i.e. oblique) correctionsneed to be considered.3. The mass scale of new physics is large compared to the W and Z masses.The rst two assumptions let us focus our attention on just four vacuum polar-ization corrections: WW(q2), ZZ(q2), Zγ(q2), and γγ(q2). Here, XY(q2) isthe transverse part of the vacuum polarization function between gauge bosons Xand Y . The third assumption lets us expand these vacuum polarization functionsaround q2 = 0 and neglect the higher order terms since they are suppressed bypowers of q2/M2new where q2  M2Z for the processes under consideration:WW(q2) = WW(0) + q20WW(0) +   ZZ(q2) = ZZ(0) + q20ZZ(0) +   Zγ(q2) = q20Zγ(0) +   γγ(q2) = q20γγ(0) +   Therefore, we can express the radiative corrections from new physics in terms of justsix parameters: WW(0), 0WW(0), ZZ(0), 0ZZ(0), 0Zγ(0), and 0γγ(0). Of thesesix, three will be absorbed into the renormalization of the three input parametersα, G and MZ , leaving us with three observables parameters which can be takento be: 1αS = 4s2c2[0ZZ(0)−c2 − s2sc0Zγ(0)−0γγ(0)],αT =WW(0)M2W− ZZ(0)M2Z,Hadron 13 : Precision Tests of Electroweak Physics 2Observable SM prediction Measured Value Referenceνe and νe scatteringgeV −0.0365 −0.041 0.015 3geA −0.5065 −0.507 0.014 3Atomic Parity ViolationQW (13355Cs) −73.19 −72.41 0.84 3QW (20581Tl) −116.8 −114.8 3.6 3νN and νN DISg2L 0.3031 0.3009 0.0028 3g2R 0.0304 0.0328 0.0030 3NuTeV 0.2289 0.2277 0.0022 4LEP/SLDΓ‘+‘− 0.08392 GeV 0.08390 0.00010 GeV 5sin2 θlepteff (LEP) 0.23200 0.23153 0.00034 5sin2 θlepteff (SLD) 0.23200 0.23109 0.00029 5W massMW (pp + LEP2) 80.315 GeV 80.39 0.06 GeV 5Table 1. The data used for the oblique correction analysis. The value of sin2 θleptefffor LEP is fromleptonic asymmetries only. The SM predictions for the W mass and the LEP/SLD observableswere obtained using the program ZFITTER 4.9 6. The predictions for the low energy observableswere calculated from the formulae given in Ref. 7. The parameter choice for the reference SM wasMZ = 91.1867 GeV5, mt = 173.9 GeV8, mH = 300 GeV, α−1(MZ ) = 128.99, and αs(MZ) =0.120.αU = 4s2[0WW(0)− c20ZZ(0)− 2sc0Zγ(0)− s20γγ(0)].Here, α is the ne structure constant and s and c are the sine and cosine of theweak mixing angle. Only the contribution of new physics to these functions areto be included. The parameters T and U are dened so that they vanish if newphysics does not break custodial SU(2) symmetry. See Ref. 2 for a discussion onthe symmetry properties of S.The fact that three parameters are necessary to describe the eects of newphysics can also be understood as follows: Since vacuum polarizations modify thegauge boson propagators, their presence can be seen when comparing the exchangeof dierent electroweak gauge bosons, or when comparing the exchange of the sameboson at dierent energy scales. In order to make predictions based on the threeinput parameters α, G, and MZ , which are neutral current{low energy, chargedcurrent{low energy, and neutral current{high energy observables, respectively, onemust compare the theory in the charged (W exchange) and the neutral (Z andphoton exchange) channels, as well as in the same channel at dierent energy scalesas shown by arrows in Fig. 1. New physics eects will manifest themselves in eachof the three arrows shown in Fig. 1. The parameter S quanties the extra correctionfrom new physics one must include when comparing neutral current processes atdierent energy scales while the parameter T quanties the extra corrections thatHadron 13 : Precision Tests of Electroweak Physics 3must be included when comparing charged and neutral current processes at lowenergy. A third parameter, in this case S+U , is necessary to quantify the correctiondue to new physics when comparing charged channel processes at dierent energyscales.This discussion also shows that all low energy and neutral current observableswill receive extra corrections from only S and T . Of all the precision electroweakmeasurements, the only quantity which receives a correction from U is the Wmass. Therefore, the majority of the precision data can be used to constrain justtwo parameters S and T , which in turn can be calculated for each model of newphysics beyond the SM.The details of how to calculate the corrections to various observables from S,T , and U can be found elsewhere1. One obtains expressions such asMW / [MW ]SM = 1 +α2(c2 − s2)[−12S + c2T +c2 − s24s2U],where [MW ]SM is the SM prediction of MW . These expressions can be compareddirectly with the experimental data to place constraints on S, T , and U .In Table 1 we list the data we used in our analysis. The denitions of theparameters geV=A for eν and eν scattering, the weak charge Qw for atomic parityviolation, and g2L=R for ν and ν deep inelastic scattering (DIS) can be found inthe Review of Particle Physics3 from which the data were taken. The quantitymeasured by the NuTeV collaboration4 is a linear combination of g2L and g2R forwhich the uncertainty due to the charm threshold cancels. The rest of the data isfrom Ref. 5.Comparing the experimental data to SM predictions with mt = 173.9 GeV8,mH = 300 GeV, and α−1(MZ) = 128.99, we obtain the constraints shown inFig. 2. Note that Figs. 2d and 2f are drawn at a dierent scale from the otherfour. Fig. 2e shows the 90% condence limits on S and T due to the four classes ofexperiments separately, and Fig. 2f shows the 68% and 90% condence limits fromall experiments combined. As is evident from Fig. 2, the LEP/SLD measurementsprovide the tightest constraints on S and T . All of the other observables combinedhave little eect on the nal result, which isS = −0.30 0.13,T = −0.14 0.15,U = 0.15 0.21.These limits of course depend on the values of mt, mH , and α−1(MZ) used asinput to calculate the SM predictions. The dependence of the limits on these inputparameters is shown by arrows in Fig. 2f. We can see that the current data favoreither a small value of the Higgs mass or a larger value of α−1(MZ).3 Limits on Topcolor Assisted TechnicolorThe limits on S and T are useful in constraining new physics models which satisfythe three initial assumptions but are less useful for other theories. As an example ofHadron 13 : Precision Tests of Electroweak Physics 4Qw(Tl)Qw(Cs)geV geAg2Lg2RNuTeV LEP leptonic asym.SLDMWΓ‘+‘−(a) (b)(c) (d)eνeNQwmtmHα−1(e) (f)Figure 2. The 1–σ limits on S and T from (a) atomic parity violation, (b) eνµ and eν¯µ scattering,(c) νµ and ν¯µ DIS, and (d) LEP/SLD + MW . (e) The 90% confidence contours for the fourclasses of experiments. The LEP/SLD + MW contour is the small shaded area in the middle. (f)The 68% and 90% confidence limits on S and T , all experiments combined. The arrows indicatehow the SM point will move relative to the contours for mt = 173.9 ± 5 GeV, mH = 300+700−210GeV, α−1(MZ) = 128.9± 0.1.such a theory, let us consider topcolor assisted technicolor10 with the gauge groupSU(3)s  SU(3)w  U(1)s  U(1)w  SU(2)LHadron 13 : Precision Tests of Electroweak Physics 5SU(3)s SU(3)w U(1)s U(1)w SU(2)L(t, b)L 3 1 13 0 2(t, b)R 3 1(43 ,−23)0 1(ν , τ−)L 1 1 −1 0 2τ−R 1 1 −2 0 1(c, s)L, (u, d)L 1 3 0 13 2(c, s)R, (u, d)R 1 3 0(43 ,−23)1(ν, µ−)L, (νe, e−)L 1 1 0 −1 2µ−R, e−R 1 1 0 −2 1Table 2. Charge assignments of the ordinary fermions in topcolor assisted technicolor.The coupling constants for the two SU(3)’s and the two U(1)’s are assumed tosatisfy g3s  g3w and g1s  g1w. The charges of the ordinary fermions under thesegroups are shown in Table 2.At a scale of about one TeV, it is assumed that technicolor breaks the twoSU(3)’s and the two U(1)’s to their diagonal subgroups:SU(3)s  SU(3)w ! SU(3)c, U(1)s  U(1)w ! U(1)Y ,which are identied with the SM color and hypercharge groups. Because of the as-sumption g3s  g3w and g1s  g1w, the broken SU(3) gauge bosons (the colorons)and the broken U(1) gauge boson (the Z 0) couple strongly to the third generationfermions but only weakly to the rst and second generation fermions. Coloron ex-change is attractive in both the tt and bb channels, while Z 0 exchange is attractivefor tt but repulsive for bb. The combined strength of the coloron and Z 0 interac-tions is assumed to be strong enough to condense the top but not so strong as tocondense the bottom. As a result, only the top quark becomes heavy.It is easy to see that this model does not t into the STU framework since (1)it has an extra electroweak gauge boson, the Z 0, and (2) coloron and Z 0 exchangecan lead to large vertex corrections for the third generation fermions (b, τ , and ν ).How would we place constraints on such a model?A naive extension of the STU formalism to include the Z 0 vacuum polarizationfunctions turns out to be too complicated to be illuminating. A much better way isto concentrate our attention on the vertex corrections at the Z mass scale, where wehave a wealth of data from LEP and SLD. Recall from our previous discussion thatS and T are relevant only when comparing processes at dierent energy scales or indierent channels. If we only look at the LEP/SLD data, which come from neutralcurrent processes at the Z mass scale, we can make our analysis completely blindto the vacuum polarization corrections and obtain limits on the vertex correctionsonly. Another way to see this is to notice that most of the observables at LEP/SLDare asymmetries and branching fractions which are just ratios of coupling constantsat the Z mass scale. The SM predictions for these observables can be xed by usingonly one of them as input to predict all the others, and any deviations must comeHadron 13 : Precision Tests of Electroweak Physics 6RbR = 0.003RbR = 0.006Figure 3. Limits on κ1 and κ3 from LEP/SLD observables. ∆ parametrizes the size of the top–pion correction to the Zbb¯ vertex. The shaded region is where the combined coloron and Z0interaction can condense the top without condensing the bottom or the τ .from the vertex corrections due to new physics.aSince the details of our analysis has been presented elsewhere12, we give only anoutline here. In the topcolor assisted technicolor model considered above, vertexcorrections come in two classes: (1) gauge boson mixing terms, and (2) propervertex corrections. Gauge boson mixing modies the current to which the Z couplesto from J0Z = JI3 − s2JQ toJZ = JI3 − (s2 + δs2)JQ + J1s.The parameters δs2 and  quantify the amount of Z{photon and Z{Z 0 mixing,respectively. The relevant proper vertex corrections are the coloron and Z 0 correc-tions to the third generation fermion vertices13, the sizes of which we parametrizebyκi =g2is4pi(g2isg2is + g2iw), (i = 1, 3),and a correction to the left{handed coupling of the b to the Z from the top{pionloop14 which we denote .The corrections to various LEP/SLD obserables from δs2, , κ1, κ3, and were calculated and compared to the experimental data. In performing the t, wekept the value of  xed and let the four other parameters and the QCD couplingconstant αs(MZ) float. In Fig. 3, we show only the results in the κ1{κ3 planefor two choices of the value of : 0.003 and 0.006. These correspond to top{pionmasses of m+ = 1000 GeV and m+ = 600 GeV, respectively. κ1 and κ3 must fallinto the shaded region in order for the coloron and Z 0 interactions to condense thetop while not condensing the bottom. Clearly the  = 0.003 case is viable whilethe  = 0.006 case is ruled out.aWe have used a similar technique in Ref. 11.Hadron 13 : Precision Tests of Electroweak Physics 74 ConclusionsPrecision electroweak measurements provide stringent constraints on new physicsbeyond the SM. For models which satisfy the three conditions listed in section 2,the limits can be described in a model independent way using the STU{formalismof Ref. 1. Currently, the tightest limits come from the LEP/SLD observables, withall other observables having little eect. Current data also favors a smaller Higgsmass or a larger α−1(MZ). For models which are not encompassed within the STUframework, in particular, those with extra electroweak gauge bosons and/or largevertex corrections, one can still obtain stringent limits, albeit in a model dependentway, by focussing only on the vertex corrections at the Z mass scale and using theLEP/SLD observables to constrain them.AcknowledgmentsWe would like to thank M. W. Gru¨newald for providing us with the data used inthis analysis. This work was supported in part by the U. S. Department of Energy,grant DE-FG05-92-ER40709, Task A (W.L.), and the National Science Foundation,grant NSF PHY-9802709 (A.K.G.).References1. M. E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990), Phys. Rev.D 46, 381 (1992).2. T. Inami, C. S. Lim, and A. Yamada, Mod. Phys. Lett. A 7, 2789 (1992).3. 1998 Review of Particle Physics, C. Caso et al., Euro. Phys. J. C 3, 1 (1998).4. K. S. McFarland et al., hep{ex/9806013.5. M. W. Gru¨newald, HUB{EP{98/67 and private communication,LEP and SLD collaborations and working groups, CERN{EP/99{15.6. The ZFITTER package: D. Bardin et al., CERN-TH-6443/92.7. W. J. Marciano and A. Sirlin, Phys. Rev. D 22, 2695 (1980); Phys. Rev. D27, 552 (1983); Phys. Rev. D 29, 75 (1984), S. Sarantakos, A. Sirlin, andW.J. Marciano, Nucl. Phys. B 217, 84 (1983), G. Degrassi, A. Sirlin, andW.J. Marciano, Phys. Rev. D 39, 287 (1989).8. S. R. Blusk (CDF and D0 Collaborations) hep{ex/9805035.9. R. Alemany, M. Davier, and A. Ho¨cker, Euro. Phys. J. C 2, 123 (1998),T. Takeuchi, Prog. Theor. Phys. Suppl. 123, 247 (1996).10. C. T. Hill, Phys. Lett. B 345, 483 (1995), G. Buchalla, G. Burdman, C. T. Hill,and D. Kominis, Phys. Rev. D 53, 5185 (1996).11. T. Takeuchi, A. K. Grant, and J. L. Rosner, in the Proceedings of DPF’94, hep{ph/9409211; A. K. Grant and T. Takeuchi, hep{ph/9807413 (unpublished).12. W. Loinaz and T. Takeuchi, hep{ph/9812377 (submitted to Phys. Rev. D).13. C. T. Hill and X. Zhang, Phys. Rev. D 51, 3563 (1995).14. G. Burdman and D. Kominis, Phys. Lett. B 403, 101 (1997).Hadron 13 : Precision Tests of Electroweak Physics 8

Precision Tests of Electroweak Physics

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