Standard Model fits are performed on the most recent leptonic and b quark Z
decay data from LEP and SLD, and FERMILAB data on top quark production, to
obtain $m_t$ and $m_H$. Poor fits are obtained, with confidence levels $\simeq$
2%. Removing the b quark data improves markedly the quality of the fits and
reduces the 95% CL upper limit on $m_H$ by $\simeq$ 50 GeV.Comment: 6 pages 3 tables i figur

A. Gurtu

C. Caso

F. Abe

G. Degrassi

G. Rodrigo

J. H. Field

J.H. Field

M. Schmelling

M.S. Chanowitz

S. Abachi

S. Dittmaier

S. Eidelmann

English

arXiv

Standard Model fits are performed on the most recent leptonic and b quark Z decay data from LEP and SLD, and FERMILAB data on top quark production, to obtain $m_t$ and $m_H$. Poor fits are obtained, with confidence levels $\simeq$ 2%. Removing the b quark data improves markedly the quality of the fits and reduces the 95% CL upper limit on $m_H$ from 169 GeV to 110 GeV

Field, J H

CERN Document Server

UGVA-DPNC 1998/10-181 October 1998hep-ph/9810288The Indirect Limit on the Standard Model Higgs Boson Mass from thePrecision FERMILAB, LEP and SLD Data.J.H.FieldDe´partement de Physique Nucle´aire et Corpusculaire, Universite´ de Gene`ve24, quai Ernest-Ansermet CH-1211 Gene`ve 4.E-mail: john.field@cern.chAbstractStandard Model fits are performed on the most recent leptonic and b quark Zdecay data from LEP and SLD, and FERMILAB data on top quark production, toobtain mt and mH . Poor fits are obtained, with confidence levels ’ 2%. Removingthe b quark data improves markedly the quality of the fits and reduces the 95% CLupper limit on mH by ’ 50 GeV.PACS 13.10.+q, 13.15.Jr, 13.38.+c, 14.80.Er, 14.80.GtKeywords ; Standard Electroweak Model, LEP, SLD and FERMILAB data,Z-decays, b quark couplings, top quark and Higgs boson masses1Since the discovery of the top quark by the CDF and D0 Collaborationsat FERMILAB [1] and the determination of its mass with a precision of’ 3% [2], an important goal of the analysis of the precision electroweak datafrom LEP and SLD [3, 4] has been to establish indirect limits on the mass,mH , of the Standard Model (SM) Higgs Boson from the measurement of theeect of quantum corrections in Z decays. A 95% condence level (CL) lowerlimit on mH of 89.8 GeV has also recently been set in the direct search for theHiggs Boson by the 4 LEP experiments [5]. The consistency, or otherwise, ofthe indirect and direct limits for mH constitutes an important test of the SM.Measurents of the same electroweak observables by dierent experimentsare combined by the LEP-SLD Electroweak Working Group (LSEWWG) [3],but still, in the global ts to the data used to obtain the indirect limit on mH ,a large number of dierent ‘raw’ observables are included in the χ2. Theseobservables vary widely both in experimental precision and in sensitivity tomH . They may, however, be further combined, using only very weak theo-retical assumptions (lepton universality and the validity of perturbative QEDand QCD corrections) to yield a much smaller number of parameters thatcontain all precise experimental information on mH . Fitting these parame-ters to the SM prediction, as is done below, rather than the raw observables,as in the LSEWWG ts, results in much sharper test and, as will be seen,clearly pin-points possible anomalies or inconstencies in the data. There areessentially four such independent parameters, which may be chosen to be theeective weak coupling constants (vector and axial vector, or right-handedand left-handed) of the charged leptons and b quarks. The eective couplingconstants of the other quarks have a similar theoretical status but, becauseof their much larger experimental errors, have a negligible weight in the de-termination of mHa. Actually, in the SM, although all four parameters aresensitive to mt given the present experimental errors, the sensitivity of theb quark couplings to mH is extremely weak. The method of extraction ofthe eective coupling constants from the raw observables as been describedpreviously [6, 7, 8]. In order to simplify the tting procedure it is convenientto use, instead of the eective vector (axial vector) coupling constants vf (af)(f = l, b) the equivalent quantities, with uncorrelated experimental errors, Af ,sf dened by the relations:Af 2(√1− 4µf)rf1− 4µf + (1 + 2µf)r2f, (1)whererf  vf/af ,andsf  (af)2(1− 6µf) + (vf )2. (2)aAlthough the direct measurement of the W mass is expected, in the future, to provide valuable infor-mation on mH , the present experimental error is too large to be competitive with Z decay measurements.2The parameter µf = (mf(MZ)/MZ)2 where mf (Q) is the running fermionmass at the scale Q, can be set to zero for f = l to sucient accuracy,while for b quarks (mb(MZ)/MZ)2 = 1.0  10−3 [9]. The values of Al, sl,Ab, sb extracted from the most recent compilation of electroweak data [4] arepresented in Table 1 where they are compared with the SM prediction formt = 174 GeV, mH = 100 GeV. The SM predictions used here are derivedfrom the ZFITTER5.10 program package [10], which includes the recentlycalculated O(g4m2t/M2W ) two-loop corrections [11]. Good agreement is seen forall parameters except Ab, which diers from the SM prediction by 3.0 standarddeviations. The CL that all four parameters agree with the SM is only 1.0%(χ2/dof = 13.2/4). This apparent anomaly was already apparent in the 1996LSEWWG averages [12], and has been extensively discussed [6, 7].The right-handed (R) and left-handed (L) eective couplings of the b quarks: gRb =(vb − ab)/2, gLb = (vb + ab)/2 are found to have the values:gRb = 0.1050(90), gLb = −0.4159(24)as compared with the respective SM predictions of 0.0774 and -0.4208. Thelargest anomaly is in gRb (3.1σ) rather than gLb (2.0σ).The purpose of this letter is twofold: (i) To recall that only one parameter,gRb , among the four that contain all the high precision information on quantumcorrections in Z decays shows a large deviation from the SM prediction [6]. (ii)To point out that the values of the limits on mH depend strongly on inclusionor exclusion of the b quark data. Using only the leptonic data, that agreeswell with the SM prediction, leads to signicantly lower values of mH .The results of SM ts for mH and mt to the parameter sets Al, sl, mt andAl, sl, Ab, sb, mt are presented in Table 2. The recent CDF, D0 average [2, 4]:mt = 173.8  5.0 GeV and the xed value αs(MZ) = 0.120, consistent withthe world average 0.118(5) [13, 14] is used in the ts. For each parameterset three ts are performed for dierent values of α(MZ), corresponding tothe experimental value: α(MZ)−1 = 128.896(90) [15], and  1σ variations onthe value. The tted value of mH is seen to be very sensitive to α(MZ). Allts give a very stable value of mt of ’ 171.2 with a maximum variation of0.7 GeV, much smaller than the typical t error of ’ 3.7 GeV. On the otherhand, large variations are seen in mH both as a function of α(MZ) and onthe inclusion or exclusion of the b quark data. For α(MZ)−1 = 128.896 the texcluding the b quark data gives mH = 38.0+30.5−19.8 and a 95% CL upper limitof 94 GeV; including the b quark data gives mH = 77.8+38.6−26.2 and an upperlimit of 150 GeV. The CLs of the SM ts to the lepton data and mt are in therange 24%− 57%, whereas when the b quark data is included, the CLs dropto only 1.7% − 1.8%. The results on the indirect Higgs Boson Masss limitsare summarised Table 3, where the variations due to the experimental erroron α(MZ) and  1σ variations in the tted value of mt are also presented.When the b quark data is included, the ‘maximum’b 95% CL upper limit onmH is found to be 278 GeV, in good agreement with the LSEWWG valuebGiven by adding linearly the shifts generated by the experimental error on α(MZ) and the fit erroron mt.3of 280 GeV [4]. Excluding the b quark data, which is incompatible, at the3σ level, with the SM, reduces the tted value of mH by a factor two, andlowers the 95% CL upper limit by 56 GeV. Taking into acccount the strongdependence of the limit on α(MZ) and mt (see Table 3), this is still quiteconsistent with the direct lower limit of 89.9 GeV [5]. It should be stressedthat the shift in the value of mH is generated due to the high sensitivity of Alvia correlations ( A0,bFB = 3AlAb/4) and not by any variation in the quantityAb, which is quite insensitive to mH . This point is made clear by Figure 1,AlAb SMAFB0,b99%95%68%0.80.820.840.860.880.90.920.940.960.9810.14 0.145 0.15 0.155 0.16Figure 1: The cross-hatched bands show the1σ limits for the quantities Al(LEP + SLD),Ab(SLD). and A0,bFB(LEP). The cross shows the best t to Al and Ab, togther with 68%,95% and 99% CL contours. The narrow cross hatched rectangle shows the SM predictionfor mH = 100 GeV and mt = 174 5 GeV. The open arrow shows the SM prediction formH = 100+200−50 GeV and mt = 174 GeV. The arrow points in the direction of increasingmH .which shows a two dimensional plot of the LEP+SLD average value Al andAb(SLD). The diagonal band shows the LEP A0,bFB measurement. Also shownare the 68%, 95% and 99% CL contours of the best t to Al and Ab usingall three data, as well as the prediction of the SM that lies just outside the99% CL contour. The shift towards higher values of mH caused by the A0,bFBmeasurement as well as poor agreement of the t with the SM are evident.None of the above conclusions were reported when the results of global SMts by the LSEWWG to the same data set used in this letter, were presentedat the recent Vancouver conference [4]. This is because no attempt was madeto extract the eective couplings of the b quarks, and the SM t was performed4on a large number (20) of raw electroweak observables, many of which havelarge errors and/or are relatively insensitive to mH or the b quark couplings.In fact it is clear from inspection of Figure 1 that the 3 largest ‘pulls’ c in theglobal EW t shown in Ref.[4](due to Ab(SLD), A0,bFB and sin2 lepteff derivedfrom ALR), are all correlated to the large deviation of the best t value ofAb from the SM prediction. These three data alone contribute 11.1 (or 65%)out of the total χ2 of 17.0 for 15 dof . The 3.1σ deviation of gRb from theSM is not revealed in the SLEWWG t. Instead smaller deviations appearin the correlated quantities Ab(SLD), A0,bFB and Rb. It is interesting to notethat the 17 data whose pulls are least eected by the deviation in the b quarkcouplings give an anomalously low contribution to the χ2 (χ2/dof = 5.9/17,CL=99.45%) indicating that, on average, the errors for these quantities maybe overestimated by a factor of ’ 1.7. The very low contribution from thesedata hides the large positive contribution resulting from the deviation in Abwhen only the global χ2 is considered. A similar criticism may be made ofanother recent global analysis [16] based on the data set used in this letter. Inthis case the global χ2 contained 42 data t to 6 parameters (including mt andmH) yielding a χ2/dof = 28.8/36 (CL = 80% ). It is stated, in consequence,that: ‘The t to all precision data is perfect’. Although it is true that, asin the SLEWWG t, ‘None of the observables deviates from the SM bestt prediction by more than 2 standard deviations’ it also remains true thatan anomalously large contribution to the χ2 comes from the b quark data,where the eective couplings do deviate from the SM at the 3σ level. This iscompletely hidden by the good ageement with the SM of 39 out of the 42 datathat are tted!Finally, it may be mentioned that none of the previous discussions in theliterature of the sensitivity of mH to dierent data sets [17, 18, 19] pointedout either the sensitivity of the limit to the b quark data, or the poor over-all condence levels of SM ts to the eective couplings when the latter areincluded. A more detailed discussion of this previous literature is given inRef.[8].AcknowledgementsI thank M.Dittmar for discussions, and his encouragement for the pursuit ofthis work.ci.e. (measurement-fit)/error5References[1] F.Abe et al. The CDF Collaboration, Phys. Rev. D56 5919 (1974), Phys.Rev. Lett. 74 2626 (1995). S.Abachi et al. The D0 Collaboration, Phys.Rev. Lett. 74 2632 (1995).[2] Review of Particle Properties, Particle Data Group, C.Caso et al. Eur.Phys. J. C3 1 (1998).[3] The LEP Collaborations ALEPH, DELPHI, L3, OPAL, the LEPElectroweak Working Group and the SLD Heavy Flavour Group.LEPEWWG/97-01 (1997).[4] M.Gru¨newald and D.Karlen, in proceedings of the XXIX InternationalConference on High Energy Physics, UBC, Vancouver, BC, Canada, July23-29 1998.[5] ALEPH, DELPHI, L3 and OPAL Collaborations, ‘Lower bound on theStandard Model Higgs boson mass from combining the results of the fourLEP experiments’, CERN-EP/98-046.[6] J.H.Field, Mod. Phys. Lett. A, Vol. 13, No. 24, 1937 (1998).[7] J.H.Field, Phys. Rev. D58 093010-1 (1998).[8] J.H.Field ‘Z-decays to b Quarks and the Higgs Boson Mass’ UGVA-DPNC1998/09-179 September 1998 (hep-ph/9809292). Submitted to Phys. Rev.D.[9] G.Rodrigo, Nucl. Phys. B (Proc. Suppl.) 54A, 60 (1997).[10] D.Bardin et al. FORTRAN package ZFITTER, Preprint CERN-TH6443/92.[11] G.Degrassi, P.Gambino and A.Vicini, Phys. Lett. B383, 219 (1996),G.Degrassi, P.Gambino and A.Sirlin, Phys. Lett. B394, 188 (1997),G.Degrassi, et al. Phys. Lett. B418, 209 (1998).[12] The LEP-SLD Electroweak Working Group (see Ref.[3]), CERN-PPE/96-183 (1996).[13] M.Schmelling in Proceedings of the 28th International Conference on HighEnergy Physics, Warsaw 1996, Eds. Z.Ajduk and A.K.Wroblewski.[14] P.N.Burrows, Talk presented at the 3rd International Symposium on Ra-diative Corrections, August 1-5 1996, Cracow, Poland. Pre-print: SLAC-PUB-7293.[15] S.Eidelmann and F.Jegerlehner, Z. Phys. C67, 585 (1995).[16] J.Erler and P.Langacker ‘Status of the Standard Model’ Pre-print UPR-0816-T, (hep-ph/9809352).[17] A.Gurtu, Phys. Lett. B368, 247 (1996).[18] S.Dittmaier, D.Schildknecht and G.Weiglen, B385, 415 (1996).[19] M.S.Chanowitz, Phys. Rev. Letters 80, 2521 (1998), and pre-print LBNL-42103 (hep-ph/9807452).6leptons b quarksAl sl Ab sbMeas. 0.1492(18) 0.25243(30) 0.878(19) 0.3662(14)SM 0.1467 0.25272 0.9347 0.3647Dev.(σ) 1.4 -1.0 -3.0 1.1Table 1: Measured values of Af and sf (f = l, b) compared to SM predictions for mt =174 GeV, mH = 100 GeV. Dev(σ) = (Meas.-SM)/Error.Fitted Quantities α(MZ)−1 mt (GeV) mH (GeV) C.L.(%)128.986 171.5 3.8 73.8+46.5−29.4 [166] 24Al, sl, mt 128.896 170.7 3.8 38.0+30.5−19.8 [94] 28128.806 172.0 3.8 19.6+18.1−8.0 [54] 57128.986 171.9 3.6 124.7+58.7−40.9 [234] 1.8Al, sl, Ab, sb, mt 128.896 171.4 3.6 77.8+38.6−26.2 [150] 1.7128.806 171.3 3.6 44.1+22.5−19.6 [87] 1.8Table 2: SM ts to dierent data sets. 95% C.L. upper limits for mH are given in thesquare brackets.Fitted Quantities mH (GeV) 95 % CL upper limit on mH (GeV)Al, sl, mt 38+31+36+17−20−18−9.5 94+72+34−40−23Al, sl, Ab, sb, mt 78+39+47+24−26−34−17 150+84+44−63−33Table 3: Summary of SM t results for mH . The errors on mH are, in order: the 1σ terror, and the changes produced by 1σ variations in α(MZ)−1 and mt. The errors onthe upper limit are those due to 1σ variations in α(MZ)−1 and mt.7

The Indirect Limit on the Standard Model Higgs Boson Mass from the Precision Fermilab, LEP and SLD Data

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Indirect limit on the standard model Higgs boson mass from the precision Fermilab, LEP, and SLD data

The Indirect Limit on the Standard Model Higgs Boson Mass from the
  Precision FERMILAB, LEP and SLD Data

The Indirect Limit on the Standard Model Higgs Boson Mass from the Precision FERMILAB, LEP and SLD Data

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