In this paper, we report on the most recent measurements of the top quark
mass, performed by the CDF and D0 collaborations at the Fermilab Tevatron. The
CDF collaboration has performed measurements of the top quark mass in three
decay channels from which the top quark mass is measured to be 175.6 +- 6.8
GeV/c^2. The D0 collaboration combines measurements from two decay channels to
obtain a top quark mass of 172.1 +- 7.1 GeV/c^2. Combining the measurements
from the two experiments, assuming a 2 GeV/c^2 correlated systematic
uncertainty, the measurement of the top quark mass at the Tevatron is 173.9 +-
5.2 GeV/c^2. This report presents the measurements of the top quark mass from
each of the decay channels which contribute to this measurement.Comment: To be published in the 33rd proceedings of the Recontres de Moriond,
  Les Arcs, France, March 21-28, 1998. 6 pages, 3 figure

Blusk, Steven R.

English

arXiv

The first evidence and subsequent discovery of the top quark was reported nearly 4 years ago. Since then, CDF and D0 have analyzed their full Run 1 data samples, and analysis techniques have been refined to make optimal use of the information. In this paper, we report on the most recent measurements of the top quark mass, performed by the CDF and D0 collaborations at the Fermilab Tevatron. The CDF collaboration has performed measurements of the top quark mass in three decay channels from which the top quark mass is measured to be 175.5 {+-} 6.9 GeV=c{sup 2}. The D0 collaboration combines measurements from two decay channels to obtain a top quark mass of 172.1 {+-} 7.1 GeV/c{sup 2}. Combining the measurements from the two experiments, assuming a 2 GeV GeV/c{sup 2} correlated systematic uncertainty, the measurement of the top quark mass at the Tevatron is 173.9 {+-} 5.2 GeV/c{sup 2}. This report presents the measurements of the top quark mass from each of the decay channels which contribute to this measurement

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F Fermi National Accelerator LaboratoryFERMILAB-Conf-98/151-ECDF and D0Measurement of the Top Quark MassSteven R. BluskFor the CDF and D0 CollaborationsUniversity of RochesterRochester, New York 14627Fermi National Accelerator LaboratoryP.O. Box 500, Batavia, Illinois 60510May 1998Published Proceedings of the XXXIIIrd Rencontres de Moriond, QCD and High Energy HadronicInteractions, Les Arcs, France, March 21-28, 1998Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United States Department of EnergyDisclaimerThis report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any oftheir employees, makes any warranty, expressed or implied, or assumes any legal liability orresponsibility for the accuracy, completeness, or usefulness of any information, apparatus,product, or process disclosed, or represents that its use would not infringe privately ownedrights. Reference herein to any specic commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the United States Government or any agencythereof. The views and opinions of authors expressed herein do not necessarily state or reectthose of the United States Government or any agency thereof.DistributionApproved for public release; further dissemination unlimited.Copyright NoticationThis manuscript has been authored by Universities Research Association, Inc. under con-tract No. DE-AC02-76CHO3000 with the U.S. Department of Energy. The United StatesGovernment and the publisher, by accepting the article for publication, acknowledges thatthe United States Government retains a nonexclusive, paid-up, irrevocable, worldwide licenseto publish or reproduce the published form of this manuscript, or allow others to do so, forUnited States Government Purposes.MEASUREMENT OF THE TOP QUARK MASSSTEVEN R. BLUSKDepartment of Physics and Astronomy,University of Rochester,Rochester, NY, 14627for theCDF and D0 Collaborations            The rst evidence1 and subsequent discovery2;3 of the top quark was reported nearly 4 yearsago. Since then, CDF and D0 have analyzed their full Run 1 data samples, and analysistechniques have been rened to make optimal use of the information. In this paper, we reporton the most recent measurements of the top quark mass, performed by the CDF and D0collaborations at the Fermilab Tevatron. The CDF collaboration has performed measurementsof the top quark mass in three decay channels from which the top quark mass is measuredto be 175:5  6:9 GeV=c2. The D0 collaboration combines measurements from two decaychannels to obtain a top quark mass of 172:1  7:1 GeV=c2. Combining the measurementsfrom the two experiments, assuming a 2 GeV GeV=c2 correlated systematic uncertainty, themeasurement of the top quark mass at the Tevatron is 173:95:2 GeV=c2. This report presentsthe measurements of the top quark mass from each of the decay channels which contribute tothis measurement.1 IntroductionThe top quark is dened as the I3 = +1=2 member of a weak SU(2) isodoublet that also containsthe b quark. In pp collisions, top quarks are produced primarily in tt pairs and are expected todecay through the electroweak interaction to a W-boson and b-quark. In the standard model,the branching fraction for t!Wb is expected to be nearly 100%. The decay width4 is calculatedto be 1:6   1:7 GeV for masses between 150   180 GeV=c2. The top quark mass is sucientlylarge that top-avored hadrons are not expected to form 5.The top quark mass,Mtop , is an important parameter in calculations of electroweak processessince its mass is approximately 35 times larger than that of the next heaviest fermion. Like otherfermions, its mass is taken to be an unpredicted parameter of the standard model 6. Calculationsof electroweak radiative corrections relate the top quark and the W-boson (MW ) masses to thatof the Higgs boson. Precision measurements of Mtop and MW can therefore aid in searches forthe Higgs boson.2 Overview of Top Quark Mass MeasurementInps = 1:8 TeV pp collisions, top quarks are expected to be produced in pairs mainly throughthe subprocess qq ! tt. At the Tevatron, both CDF and D0 select samples of events which areconsistent with containing a tt pair. Since each W-boson may decay leptonically or hadronically,this leads to three categories of events. Events which have 2 high PT isolated leptons (bothW-bosons decay leptonically), missing transverse energy (6ET ) 7 and two or more jets (from theb-quarks) are classied as Dilepton events. Events which have one isolated high PT lepton, 6ET ,and 4 or more jets are referred to as l+jets events. Events containing 6 or more jets and no highPT isolated leptons are classied as All-hadronic events. Neither CDF nor D0 try to reconstructthe top mass from candidate tt! +X events. Ignoring nal states containing  's, the branchingratio for tt into these three decay channels is 5%, 30%, and 44% respectively.Both CDF and D0 have measured the top quark mass in the Dilepton and l+jets channels.CDF has also made a measurement of the top quark mass in the All-Hadronic channel. Ageneral procedure is used for extracting the top quark mass. For each decay channel, we choosea variable (or a set of variables) which can be measured in the data sample, and is highlycorrelated with Mtop . Examples of such variables include event-by-event top mass, jet ET,6ET , total scalar ET, etc. The distribution of a given variable is modelled using Monte Carlo(MC) simulations of tt signal and background. The tt signal distributions are modelled usingthe HERWIG8 MC simulation and are produced for a wide range of input top quark masses,ranging from 120 to 220 GeV=c2. Background distributions are derived from a combinationof Monte Carlo and/or data, depending on the channel. The modelled signal and backgrounddistributions are generically referred to as templates. The top quark mass is extracted from amaximum likelihood procedure which compares the observed data distribution(s) to the tt signaland background templates. Assumptions made in the modelling of signal and background areincluded as sources of systematic uncertainty.3 Top Quark Mass Measurement in the Dilepton TopologyBoth CDF9 and D010 have reported measurements of the top quark mass in the Dilepton decaytopology. Because these events are presumed to have two neutrinos, the kinematics of the ttsystem (including the top quark mass) cannot be uniquely determined. A measurement of the topquark mass can however be made by comparing the measured observables with the expectationfrom tt and background. Each experiment employs two techniques to measure the top quarkmass from their respective samples.3.1 CDF Dilepton Mass MeasurementsThe rst Dilepton mass measurement uses the energies of the 2 highest ET jets in the can-didate events as a discriminator for the top quark mass measurement. From a sample of 8events, with an expected background of 1.10.3 events, the analysis yields a top quark mass of15923(stat)11(syst) GeV=c2. A second analysis exploits the fact that, in the W-boson restframe of the t!Wb decay, the top quark mass can be related to the invariant mass of the b-jetand lepton (Mlb) to which it decays. Among the two possible pairings of the 2 leptons with the 2highest ET jets, the pair with the smaller sum of invariant masses is chosen. From this analysis,the top quark mass is measured to be 16320(stat)6(syst) GeV=c2. The jet energy scale, andsignal and background modelling dominate the systematic uncertainty. The two measurementsare combined taking into account the correlations in uncertainties to obtain a top quark mass of16117(stat)10(syst) GeV=c2.3.2 D0 Dilepton Mass MeasurementsBoth techniques which D0 employs uses MC simulations to calculate a probability that the ob-served kinematics of the event are consistent with top of an assumed mass. This probability ismapped out as a function of assumed top mass in the range from 80 to 280 GeV=c2. The proba-bility in the rst technique is based on: (a) the probability for the charged leptons to have comefrom tt decay at the assumed mass, and (b) the probability for the event to have been producedby valence quarks with momentum fractions f(x) and f(x). The second technique calculates aprobability based on the dierence between the measured and calculated 6ET in the event. Thecalculation of the 6ET is facilitated by assuming values for the pseudorapidity of the two neutri-nos (1 and 2), and then integrating over the 1, 2 phase space. For both techniques, detectorresolution eects are included as well as trying both lepton-(b-quark) combinations. Based onthe data sample of 6 events and an expected background of 1.42 events, the mass is measured tobe 168.112.4(stat)3.6(syst) GeV=c2 using the rst technique, and 169.914.8(stat)3.6(syst)GeV=c2 using the second technique. The dominant systematics are the same as those mentionedfor the CDF dilepton analyses. The measurements are combined to obtain a top quark mass of168.412.3(stat)3.6(syst) GeV=c2.4 Top Quark Mass Measurement in the l+jets TopologyBoth CDF11 and D012 have measured the top quark mass in the l+jets topology. The l+jetsdecay channel currently allows for the most accurate determination of the top quark mass. Themeasurement benets from a relatively large branching ratio and the ability to fully reconstructthe top mass on an event-by-event basis. The momentum of all nal state particles are assumedto be measured, with the exception of the unobserved neutrino, . The transverse momentumcomponents of the neutrino however can be inferred from the 6ET in the event, leaving only itsZ-component unmeasured. Three kinematic constraints are implied by the tt ! lqqbbX decayhypothesis. Namely, we require that Ml = MW , Mjj = MW , and Mlb = Mjjb, where b =b or b jet, j=non-b jet, MW=W-boson mass, and Mxx(x) are invariant masses formed from thereconstructed 4-vectors of the indicated objects. Because tt events are expected to contain 2 b-quarks, as compared to only a few percent for background events, identifying b-jets improves thesignal to background ratio (S/B). B-jets are tagged by either reconstructing the secondary decayvertices of B-hadrons (SVX tagged jet), or by identifying charged tracks which are consistent withcoming from semileptonic b-hadron decay (SLT tagged jet). Each event is t to the tt! lqqbbXtopology, requiring b-tagged jets to be assigned to b-quarks, All allowable permutations aretried, and the top mass corresponding to the solution with the lowest 2 < 10 is taken as thereconstructed top mass (Mrec) for a given event. The ensemble of reconstructed masses (one perevent) are t using a likelihood procedure to extract the best estimate of the top quark mass.4.1 CDF l+jets Mass MeasurementThe initial sample selection requires 1 isolated lepton with PT > 20 GeV=c, jj < 1, 6ET >20 GeV,  3 jets with ET > 15 GeV, jj < 2:0, and a fourth jet with ET > 8 GeV and jj < 2:4.After applying these selection criteria and the 2 cut on the kinematic t, the sample consists of151 events, of which 35% are estimated to be from tt. Motivated by the dierent S/B and topmass resolution for events with SVX, SLT, or no tags, MC simulations were used to determinean optimal way to partition the sample as to obtain the best precision on the top quark massmeasurement13. Studies showed that an optimal partitioning consists of subdividing the eventsinto the four statistically independent categories shown in Table 1. The table shows the numbersof events in each subsample, the expected background fraction14 xb, and the tted top mass.Data Sample #Events xb(%) Top Mass (GeV=c2)SVX Double (2 SVX tagged jets) 5 5+4 2 170:1 9:3SVX Single (1 SVX tagged jet) 15 13+5 4 178:0 7:9SLT tagged (1 SLT tagged jets, no SVX tags) 14 40+9 9 142:1+33 14No Tags (4 jets with ET > 15 GeV, jj < 2:0) 42 56+14 17 180:8 9:0Combined 76 - 175:9 4:8Table 1: Subsamples used in the top quark mass analysis, expected background fractions, and the measured topquark mass in each sample. The last line shows the results from the combined likelihood t to all four subsamples.Reconstructed Mass (GeV/c2)Events/(10 GeV/c2 )Mtop (GeV/c2)-∆log(L)BackgroundSignal+Background05101520100 150 200 250 300 350125 150 175 2000510Figure 1: The results of applying the like-lihood procedure to the combined subsam-ples. The gure shows the data (points), t-ted background (light shaded region), and t-ted signal plus background (darker shaded re-gion). The inset shows the shape of   logLversus the generated top mass from which weextract the best estimate of the top mass andthe statistical uncertainty.Since the four subsamples are statistically inde-pendent, the joint likelihood for the 76 events isgiven by the product of the four subsample like-lihoods. Each subsample likelihood uses parame-terized signal and background probability densities,along with a constraint on the the background frac-tion (see Table 1), to evaluate the likelihood for ob-serving the measured set of masses as a function ofthe top mass. The results of the likelihood t foreach subsample and the combined result are shownin Table 1. The results of the combined t forthe 76 data events and are shown in Fig. 1. In-cluding the systematic uncertainties presented inTable 3, the top quark mass is measured to be175.94.8(stat.)4.9(syst.) GeV=c2 for events inthe l+jets topology.4.2 D0 l+jets Mass MeasurementThe event selection for the D0 analysis is similar toCDF. The main dierences are a larger jj cut forthe charged lepton (from the W-boson decay) andall four jets are required to have ET > 15 GeV. After the event selection criteria and thekinematic 2 cut, 77 events remain of which 5 are SLT tagged (D0 did not have a silicon vertexdetector in Run 1). D0 extends the likelihood procedure by including an additional variable D0123456789Fit top quark mass (GeV/c2)datafitbkgd(a)0100246∆ ln L80 120 160 200 240 280(b)Fit mass100 260LBNN(c)150 200True massFigure 2: The t results from the LB andNN likelihood procedures applied to the 77event data sample. (a) Events which haveDlb > 0:43 and (b) Dlb < 0:43. The his-togram shows the data, and the points arethe MC t results. (c) shows the t to  logLvs top mass for the two methods.which provides discrimination between signal andbackground events. Two versions of the discrim-inant are tried. The rst is a low-bias versionDlb, and the second, DNN , was the output from aneural network trained on tt signal and backgroundevents. Both discriminants provide similar levelsof discrimination between signal and backgroundevents. Two-dimensional signal templates of D vsMrec are generated for many input values for the topmass and a single template for the background. Foreach top mass value, a likelihood is minimized withrespect to the number of signal and backgroundevents. The corresponding negative log-likelihoodvalues are t to a quadratic function of top mass,and the measured top mass is taken to be where thefunction is a minimum. The ts to the data are pre-sented in Table 2 and shown in Fig. 2 For illustrativepurposes, the data sample is separated into (a) sig-nal depleted and (b) signal enhanced subsamples.Also shown are the likelihood ts for the two meth-ods. Including the systematic uncertainties shownin Table 3, the top quark mass is measured to be173.35.6(stat.)5.5(syst.) GeV=c2.Method Mtop (GeV=c2) Fitted Ns Fitted NbLB 174.05.6 248 5310NN 171.36.0 299 4810LB+NN 173.35.6 - -Table 2: Fit results using the low-bias (LB) likelihood, then neural-network (NN) method, and the combinedresult. Shown are the tted top quark masses, and the tted number of signal (Ns) and background (Nb) events.5 CDF All-Hadronic Top Mass MeasurementThis measurement15 requires 6 or more jets with ET > 15 GeV, and jj < 2, and at leastone b-tagged jet. Additional cuts, based on MC simulations, were employed to improve theS/B ratio. An event-by-event top mass is evaluated using the measured jet energies and thekinematic constraints mentioned previously. All thirty combinations are tried, and the top masshaving the lowest 2 < 10 is taken as the top mass for the event. The data sample consists of136 events, of which 1089 events are expected to come from background sources. A likelihoodprocedure (with a gaussian background constraint) was used to extract a measured top mass of18610(stat.)12(syst.) GeV=c2. The systematic uncertainties are dominated by the jet energyscale signal modelling, and the tting method.6 Combining the top mass measurementsThe measurement in each decay topology may be combined to improve the resolution on the topquark mass measurement. Each experiment combines their measurements into a single measure-ment, taking into account correlations in uncertainties between the measurements. Combiningthe three CDF measurements, the top quark mass is measured to be 175.66.8 GeV=c2. The twoD0 measurements yield a top quark mass of 172.17.1 GeV=c2. These two mass measurementsSource CDF D0Energy Scale 4.4 4.0Signal Model 1.8 1.9Background 1.3 2.5Noise/M.I. - 1.3b-tagging bias 0.4 -Likelihood Method - 1.3Total 4.9 5.5Table 3: Main systematic uncertainties (GeV=c2) inthe l+jets top quark mass measurement for each ex-periment. (M.I.=Multiple Interactions; PDF's = Par-ton Distribution Functions)are combined assuming a 2 GeV=c2 correlatedsystematic uncertainty. The top quark massat the Tevatron is therefore measured to be173.95.2 GeV=c2. The values of MW ver-sus Mtop for several (standard model) Higgsmasses are shown in Fig. 3 The data tend tofavor a mass below 500 GeV=c2, but clearlymore data is needed to reduce the uncertainties. In Run 2, we expect to measure Mtop to within1-2 GeV=c2 and MW to within 40 MeV=c2. This will clearly narrow the search window for futureHiggs' searches.I would like to thank my collaborators at CDF for their assistance in preparing this talk.I would also like to thank the D0 top group, particularly Scott Snyder and Erich Varnes foranswering questions regarding their top mass analyses.8080.180.280.380.480.580.6130 140 150 160 170 180 190 200Mtop (GeV/c2)MW (GeV/c2 )1002505001000Higgs Mass (GeV/c2 )World AverageCDFD0Figure 3: MW versusMtop for various choicesof the Higgs mass. Shown are the CDF andD0 averages, as well as the world average.References1. F. Abe et al., Phys. Rev. D 50, 2966 (1994). Phys. Rev. Lett. 73, 225 (1994).2. F. Abe et al., Phys. Rev. Lett. 74, 2626 (1995).3. S. Abachi et al., Phys. Rev. Lett 74, 2632 (1995).4. M. Jezabek and J. H. Kuhn, Phys. Rev. D 48, 1910 (1993); Erratum, ibid. Phys. Rev. D49, 4970 (1994)5. I. I. Bigi, Yu L. Dokshitzer, V. A. Khoze, J. H. Kuhn, and P. Zerwas, Phys. Lett. B181,157 (1986).6. S. L. Glashow Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264(1967); A. Salam, in Elementary Particle Theory: Relativistic Groups and Analyticity(Nobel Symposium No. 8), edited by N. Svartholm (Almqvist and Wiksell, Sweden,1968), p367.7. The missing ET, 6ET is dened to be the magnitude of the vector sum of the transverseenergy of all calorimeter towers.8. G. Marchesini and B. R. Webber, Nucl. Phys. B310, (1988), 461; G. Marchesini et al.,Comput. Phys. Comm. 67, 465 (1992).9. F. Abe et al. Phys. Rev. Lett. 80, 2779 (1998)10. S. Abachi et al. Phys. Rev. Lett. 80, 2063 (1998)11. F. Abe et al., Phys. Rev. Lett. 80, 2767 (1998).12. S. Abachi et al., Phys. Rev. Lett. 79, 1197 (1997).13. K. Tollefson, Ph.D. Thesis, University of Rochester (1997).14. The background fractions, xb, are dened as the expected number of background events ina given subsample divided by the total number of events in that subsample.15. F. Abe et al. Phys. Rev. Lett. 79, 1992 (1997).

Measurement of the Top Quark Mass

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