Internal consistency of the most sensitive electroweak measurements within
the standard model framework is examined. Confirming an earlier observation on
the separation of Z-pole asymmetry measurements into {\em hadronisation-
free}and {\em hadronisation-sensitive}, the electroweak mixing angle derived
using the former is in perfect agreement with the precision W mass. These two
complimentary measurements of weak radiative corrections, when combined with
the lower limit on Higgs mass, are incompatible with the measured top quark
mass. To overcome this inconsistency, a scenario readily testable in Run-II at
Tevatron is envisaged: an upward shift of the top quark mass by about 10 GeV
($\sim 2\sigma$). If, however, the improved top quark mass remains at its
current value or the lower limit on Higgs mass moves up substantially, then
abandoning the SM may become inevitable.Comment: 7 pages, 4 figure

Aziz, T.

Gurtu, A.

English

arXiv

Internal consistency of the most sensitive electroweak measurements within the standard model framework is examined. Confirming an earlier observation on the separation of Z-pole asymmetry measurements into {\em hadronisation- free}and {\em hadronisation-sensitive}, the electroweak mixing angle derived using the former is in perfect agreement with the precision W mass. These two complimentary measurements of weak radiative corrections, when combined with the lower limit on Higgs mass, are incompatible with the measured top quark mass. To overcome this inconsistency, a scenario readily testable in Run-II at Tevatron is envisaged: an upward shift of the top quark mass by about 10 GeV ($\sim 2\sigma$). If, however, the improved top quark mass remains at its current value or the lower limit on Higgs mass moves up substantially, then abandoning the SM may become inevitable

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHAugust 29, 2001Precision testing the Standard ModelT. Aziz?, a and A. Gurtu?, bEP Division, CERN, 1211 Geneva 23, SwitzerlandAbstractInternal consistency of the most sensitive electroweak measurements within the standardmodel framework is examined. Conrming an earlier observation on the separation ofZ-pole asymmetry measurements into hadronisation-free and hadronisation-sensitive, theelectroweak mixing angle derived using the former is in perfect agreement with the pre-cision W mass. These two complimentary measurements of weak radiative corrections,when combined with the lower limit on Higgs mass, are incompatible with the measuredtop quark mass. To overcome this inconsistency, a scenario readily testable in Run-II atTevatron is envisaged: an upward shift of the top quark mass by about 10 GeV ( 2σ).If, however, the improved top quark mass remains at its current value or the lower limiton Higgs mass moves up substantially, then abandoning the SM may become inevitable.To be submitted to Phys. Lett. B?On sabbatical leave from Tata Institute of Fundamental Research, Mumbai, India.a e-mail: Tariq.Aziz@cern.chb e-mail: Atul.Gurtu@cern.ch1CERN-OPEN-2001-06729/08/2001Over the last several years the Standard Model (SM) of electroweak interactions has beensubjected to precision tests through a variety measurements at LEP, SLC and Tevatron.While the measurements at Z pole are sensitive to the presence of top quark and Higgsboson via weak radiative corrections, the direct measurement of top quark mass at Teva-tron and W boson mass at LEP2 and Tevatron, along with the lower bound on Higgsmass at LEP2, provide a detailed set to test the validity of SM. These measurements,which are now nal or almost nal, have reached a precision where it is possible to verifytheir self-consistency within the SM framework. In case of serious inconsistency eitherthis framework collapses or the data have to be re-looked. In this paper we examine theself-consistency of these data and discuss their implications.The important weak radiative corrections that aect Z ! ff (f: fermion) widths andasymmetries [1] appear as propagator correction, ρ, sensitive to both top and Higgsmasses, and Z! bb width where there is an additional vertex correction, δvtb, sensitiveonly to top quark mass. All those measurements where ratio of widths are involved, likeR` and σpeak, the ρ sensitivity is practically lost and whatever top dependence one seesis due to indirect eect of δvtb in Z! bb width. Thus the only sensitive measurements totest ρ are fermion asymmetries leading to eective weak mixing angle1, sin2 θlepteff , andthe total Z decay width, ΓZ . The ratio Rb = (Z! bb/Z! hadrons) is a clean measureof δvtb and practically independent of the Higgs mass. We will restrict ourselves to onlythose measurements whose sensitivity for weak radiative eects is well above the mea-surement uncertainties. On the Z pole these are sin2 θlepteff , Rb and Γz. The rst two arefree from αs uncertainty, the last one requires αs for its interpretation.Observations on the measurements of asymmetries and hence sin2 θlepteff over the years haveshown a clear pattern and several years ago it was pointed out [2] that all asymmetry mea-surements should be placed in two classes. Class A measurements where hadronisationeffects are not relevant for the nal result and class B measurements where hadronisa-tion effects cannot be avoided and can only be corrected with whatever understanding ofthese phenomena we have. In class A measurements are forward-backward asymmetry ofleptons e, µ, τ at LEP and left-right asymmetry at SLC. In class B are measurements ofall quark asymmetries as well as τ polarisation asymmetry measured through hadronicdecays. The two class of measurements were found to be more than 3 σ apart alreadyin 1997 [2]. It was also pointed out that the measured W mass was in favour of class Ameasurements, though W mass was much less precise than now. With increased precisionof the W mass with time, its consistency with class A asymmetry measurements andincompatibility with class B measurements has become even more pronounced.Meanwhile the lower limit on Higgs mass from direct searches at LEP has increasedconsiderably: it is now 114.1 GeV [3] (with even a  2σ hint of Higgs at 115 GeV).This increase in lower bound on Higgs mass along with the improvement in W masshelps signicantly in testing the self-consistency of data. The latest compilation of allthe electroweak measurements from LEP, SLC and Tevatron is taken from [4]. With theabove mentioned classication of asymmetry data, the average sin2 θlepteff for the two classesof measurements from LEP and SLC are: 0.23098 0.00023 for class A (hadronisation-free: SLD-dominated) and 0.23206  0.00024 for class B (hadronisation-sensitive: LEP-1In terms of vector and axial vector couplings gV f , gAf , the definition of the effective weak mixingangle is sin2 θlepteff =14 (1 − gV/gA)2Class AClass BMW (GeV)Sin2θ eff0.2290.230.2310.2320.23380.2 80.4 80.6 80.8Figure 1: Dependence of sin2 θlepteff on MW . The band around central line corresponds touncertainty in α(MZ)dominated) and these are 3.3σ apart. The measured W mass from LEP and Tevatronhas improved considerably and the current average value is 80.451 0.033 GeV. The topmass measured at Tevatron is 174.3 5.1 GeV and the lower bound on Higgs boson massis 114.1 GeV at 95% CL from LEP2 searches.The simplest consistency test of data is provided by comparison of sin2 θlepteff measure-ments with the W boson mass, as both are aected by weak radiative eects arising fromtop and Higgs and provide a complementary measure of the same weak corrections. Thesemeasurements are compared in gure 1. This gure clearly illustrates the dierence be-tween the Class A and Class B measurements of sin2 θlepteff as well as a strong preferencefor Class A due to pretty precise W mass. Thus, as already emphasised earlier [2], forfurther consideration we prefer sin2 θlepteff from class A measurements only and suggest thattill a better understanding of class B measurements is found, they be kept aside.As the next step we study the consistency of sin2 θlepteff or MW with that of the measuredtop quark mass. This is shown in gure 2. One sees explicitly the eect of the recentLEP lower limit on the Higgs mass: it is clear that for MHiggs > 114.1 GeV the presentvalue of top quark mass is not sucient to drive the radiative corrections to explain either3Mtop (GeV)Sin2θ effM H = 1000 GeVM H = 114 GeV0.230.2320.234150 200 250Mtop (GeV)MW (GeV)M H = 1000 GeVM H = 114 GeV8080.2580.580.75150 200 250Figure 2: Dependence of sin2 θlepteff on Mtop (left) and MW on Mtop (right). The band aroundcentral line in both corresponds to Higgs dependence. The edges corresponding to Higgs massof 114 GeV and 1000 GeV are indicated. The central line corresponds to a Higgs mass of 300GeV in both.sin2 θlepteff or MW . It seems impossible to satisfy all the measurement constraints, sin2 θlepteff ,MW , Mtop and MHiggs > 114.1 GeV simultaneously within the SM framework. One hasto make a choice: either one goes beyond the scope of the SM and formulates a modelin which all the existing data can be explained, or one can examine the data criticallyand see if a reasonable change in one of the measurements would remove the discrepancywithin the SM. There have been recent approaches using the rst option [5]. In this pa-per we explore the second alternative. We note, rstly, that two precise and independentmeasurements, sin2 θlepteff and MW , are self-consistent within the SM framework. Secondly,in relative terms Mtop is presently the least accurately determined data point, being de-termined to an accuracy of 2.9%, whereas sin2 θlepteff and MW are determined to 0.1% and0.04% respectively. Thus the minimal change in data which may make it consistent withinthe SM is an upward movement of Mtop. We now try to estimate how much change in itis required for everything to t together.To arrive at a quantitative estimate of required increase in Mtop to explain the data, wehave taken the most sensitive and clean measurements that are indicative of weak radia-tive eects. These are the sin2 θlepteff = 0.23098 0.00023 from class A (hadronisation-free)measurements, Rb = 0.21646  0.00065 and ΓZ = 2.4952  0.0023 GeV at the Z pole,MW = 80.451  0.033 GeV and the lower bound of 114.1 GeV on the Higgs mass. All416018020022010 10 2 10 3Excluded by direct searchesfor Higgs at LEPHiggs-top SM bandMtop=174.3±5.1 GeVMHiggs(GeV)Mtop (GeV)Figure 3: Mtop as function of Higgs mass for which fit to data give minimum χ2. The bandHiggs-top SM band corresponds to 1σ fit uncertainty and the central line as the best value. Themeasured top mass (174.35.1 GeV) is depicted as a band parallel to Higgs axis. The Higgsmass excluded region below 114.1 GeV is also indicated.in association with the MZ = 91.1875  0.0021 GeV, α(MZ) = 1/(128.945  0.052)2and αs(MZ) = 0.1181 0.0020 [8] as inputs and ZFITTER (version 6.36) [9] as the SMpackage. A t to these data is performed to extract top quark mass for various Higgsmasses in an extended range, from 10 { 1000 GeV. Fit results for a few representativevalues of the Higgs mass are given in table 1 and in gure 3 the variation of the topquark mass is shown as a function of the Higgs mass for which the χ2 is minimum. Theband indicated as the Higgs-top SM band along with the central line in gure 3 indicatesthe best line with 1σ t error where weak radiative eects balance each-other to get theminimum χ2. The band with central line parallel to Higgs-axis indicates the measuredtop quark mass with its errors. The broad band parallel to top-axis is the lower bound onHiggs from LEP2 searches [3]. Given the Higgs-bound of 114.1 GeV, the only reasonableoption to gain self-consistency of data within the SM is to move top quark mass up byabout 10 GeV to 184 GeV. This represents a 2σ shift upward from the current value of2This corresponds to the best measured value of ∆α(5)had(MZ) = 0.027610.00036 as determined usingBES collaboration data [6, 7].5Table 1: Result of the t using data most sensitive to radiative corrections. The Higgsmass has been varied starting from the lower bound and top mass has been extracted.Fit Parameter MHiggs(GeV)114.1 200 300 450 1000Mtop(GeV) 184 4 190 4 195 4 200 4 211 4χ2/DOF 4.3/4 6.0/4 7.5 9.2/4 13.8/4(Prob %) 36.7 20.0 11.4 5.5 0.8174.35.1 GeV, which does not seem dramatic. However, this would suce only if theHiggs is indeed around the corner. In case the lower bound on the Higgs mass increasessubstantially beyond the current value, the change in Mtop required for SM consistency ofdata would be much more and would become increasingly unrealistic. In such a scenariothe SM would really have to be abandoned. Indeed, the variation of χ2 with Higgs massin table 1 indicates that data favour a light Higgs.Run-II at the Tevatron will play a crucial role in clarifying the situation: the error onthe top mass is expected to be reduced considerably and on the W mass to some extent.The lower bound on Higgs mass may also be improved or, if nature is kind, it may bediscovered.We conclude that the present measurements on W mass, sin2 θlepteff and lower Higgs-boundare not compatible with the present value of the top quark mass within the standardmodel framework, the incompatibility being driven by the recent LEP2 result on thelower Higgs-bound. The simplest way to restore compatibility, without resorting to newphysics, would be to move the top quark mass up from its present value of 174 GeV toa higher value of 184 GeV or so. If the Higgs lower bound does not move very muchupward, this required increase of about 10 GeV is essentially a 2σ increase and can betested soon in Run-II at the Tevatron. In case the top quark mass remains at its presentvalue and the measurement uncertainty goes down to 3 GeV or better, or if the lowerlimit on the Higgs mass increases substantially, that will be the real beginning of the endof the standard model.References[1] M. Consoli, W. Hollik and F. Jegerlehner in: Z Physics at LEP 1, eds. G. Altarelli,R. Kleiss and C. Verzegnassi, CERN 89-08 (1989), vol. 1, p 7.[2] T. Aziz, Mod. Phys. Lett. A12 (1997) 2535Indications of such pattern were noticed even earlier:ibid: Mod. Phys. Lett. A9 (1994) 1857.[3] ALEPH, DELPHI, L3 and OPAL Collaborations and the LEP working group forHiggs Boson searches, CERN preprint CERN-EP/2001-055 (2001).6[4] Results and description from Winter 2001:The LEP Collaborations ALEPH, DELPHI, L3, OPAL, the LEP Electroweak Work-ing Group and the SLD Heavy Flavour and Electroweak Groups, LEPEWWG/2001-01, 31 May 2001Results from Summer 2001:S. Mele, Combined t to Electroweak data and constraints on the Standard Model,talk at Intern. Europhysics Conf. on High Energy Physics, Budapest, 12-18 July2001,J. Drees, Review of Final LEP Results or A Tribute to LEP, talk at Lepton Photonconference, LP01, Rome, 23-28 July 2001.[5] some recent examples:M. Chanowitz, hep-ph/0104024, LBNL-47684, 2 April 2001 (revised 27 May 2001).G. Altarelli et al, hep-ph/0106029, CERN preprint CERN-TH/2001-145, (2001).[6] G. Huang, Measurement of R in 2-5 GeV with BES II at BEPC, talk at XXXVIthRencontres de Moriond, Electroweak Interactions and Unied Theories, Les Arcs,France, 10-17 March 2001.[7] H. Burkhardt and B. Pietrzyk, Phys. Lett. B 513 (2001) 46.[8] PDG Collab., D.E. Groom et al. Euro. Phys. Jour. C 15 (2000) 1.[9] D. Bardin et al, Z. Phys. C 44 (1989) 493; Comp. Phys. Comm. 59 (1990) 303;ZFITTER v.6.21: DESY 99-070 (1999) [hep-ph/9908433].7

Precision testing the Standard Model

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