Heintz, Ulrich

U., /Boston

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TOP QUARK MASS MEASUREMENTS AT THE TEVATRONU. HEINTZBoston University, Department of Physics, 590 Commonwealth Avenue, Boston, MA 02215, USAThe mass of the top quark has been measured at Fermilab using the Tevatron pp¯ collider to aprecision of less than 1%. I discuss the individual measurements that go into this result andits impact on our understanding of the standard model of the electroweak interactions.The top quark is the most massive fundamental particle that we know today. It is thedominant contributor to radiative corrections for many standard model processes. In order tomake precise predictions based on the standard model we have to therefore know its mass tohigh precision. A well-known example for this is the W boson mass. The dominant radiativecorrections to the W boson mass come from loops containing top and bottom quarks, which areproportional to the top quark mass squared, and from loops containing Higgs bosons, which arelogarithmically dependent on the Higgs boson mass. Thus for every value of the Higgs bosonmass mH , the standard model deﬁnes a unique line in the plane deﬁned by W boson mass andtop quark mass shown in Figure 2. Vice versa, if we measure the W boson and top quark massesprecisely we can constrain the allowed parameter space for the standard model in this plane andtherefore limit the allowed range for the Higgs boson mass.We study top quarks at the Fermilab Tevatron pp¯ collider at√s = 1.96 TeV. The dominantproduction mechanism for top quarks is top-antitop quark pair productions via quark-antiquarkannihilation or gluon fusion. Within the standard model the top quark decays almost exclusivelyto a W boson and a b quark. The decay modes of the W boson then deﬁne the ﬁnal statesignatures. In 6% of all tt¯ decays both W bosons produce electrons or muons in their decay -we call this the dilepton channel. In 38% of all tt¯ decays one W boson produces an electron ora muon in its decay - this is the lepton+jets channel. The remaining 56% of tt¯ decays containno electrons or muons from W decays - we call this the all-jets channel. In addition to the Wbosons, all tt¯ decays also produce b and b¯ quarks that give rise to jets. Since b-ﬂavored hadronsare long-lived, we can identify such jets by the presence of tracks from their secondary decayvertices that do not point back to the primary interaction point. Jets with such tracks or withexplicitly reconstructed secondary vertices likely originate from the fragmentation of a b quarkand are called b-tagged. Requiring at least one b-tagged jet in the event is a good way to increasethe signal-to-background in the data.The measurement of the top quark mass relies on the precise reconstruction of the energy ofits decay products. We calibrate the measurement of the energies of electron and muons usingZ → ee or Z → μμ decays. The calibration of the quark energies is a bigger challenge. Quarksmanifest themselves as jets in the detector and the ﬁrst step is to calibrate the measurement ofthe energy in the jet cone to the energy of all particles from the hadronization of the originalquark in the same cone. The response of the calorimeter to the particles is calibrated bybalancing the transverse momentum in events with a direct photon and a jet. Then MonteCarlo-derived corrections are applied to take this calibration to the parton level. Dijet eventsare used to make the calorimeter response to jets uniform in the calorimeter at all momenta. Wecall this the external jet energy calibration and it is sytematically limited at a precision of about1.7%. Alternatively, we can use hadronic decays of W bosons from top decay to calibrate thejet energy scale with top decay events. This determines an additional overall calibration factorfor jet energies. We call this the in situ calibration. This calibration is presently statisticallylimited by the number of hadronic W decays.Two basic types of algorithms are currently used for the top mass measurements. Thetemplate methods reconstruct one or more observables from each event that serve as estimatorsfor the top quark mass and then compare their distributions to Monte Carlo-derived distributionsfor a range of top quark masses, the so called templates. More recently, methods have beendeveloped that derive a likelihood as a function of the top quark mass for each event. This hasthe advantage that every event can be weighted according to its resolution and probability tobe from tt¯ decays. The most prominant example for the latter is the matrix element methodthat computes the probability for an event to be produced in tt¯ decays as a function of the topquark mass based on inegrating over the tree-level matrix element for tt¯ production and decay 2.It has become standard procedure to calibrate the performance of the measurement al-gorithms using Monte Carlo generated pseudoexperiments. Events are drawn randomly fromsimulated signal and background samples according to the number of events observed in thedata and the expected or observed signal-to-background. Each pseudoexperiment is analyzedwith the same algorithm as the data. The average and root mean square of the measured massesand their pull distribution characterize the performance of the algorithm.Dilepton decays contain two b-jets, two charged leptons and several neutrinos in the ﬁnalstate. This channel has the advantage of a high signal-to-background (3:1) even without using b-tagging. Its disadvantage is that the number of measured quantities in these events is insuﬃcientto constrain the kinematics of the events.D0 uses two diﬀerent algorithms to measure the top quark mass in dilepton events based on1 fb−1 of data. The matrix weighting algorithm ﬁnds for every top mass the possible top andantitop momenta and then assigns a weight to the events based on parton distribution functionsand the lepton energy distribution. The value of the top quark mass at which this weight ismaximized is used as the estimator. Its distribution is ﬁt to templates to extract a top quarkmass of 175.2±6.1(stat)±3.4(syst) GeV. The neutrino weighting algorithm loops over a rangeof pseudorapidities for the two neutrinos and uses a χ2 variable based on the consistency ofthe sum of the neutrino momenta with the observed missing pT as weight. A two dimensionaltemplate ﬁt to the distributions of mean and rms of the weight curves gives a top quark massof 172.5±5.8(stat)±3.5(syst) GeV. Combining the two gives 173.7±5.4(stat)±3.4(syst) GeV 3.CDF use the matrix element method in the dilepton channel. The analysis is carried out on2 fb−1 of data and optimizes the selection with an evolutionary neural network to minimize thestatistical uncertainty. The result is 171.2±2.7(stat)±2.9(syst) GeV 4. CDF also apply the neu-trino weighting method. Based on 1.9 fb−1 and a two-dimensional template ﬁt to the mass withthe largest weight and to the scalar sum of the jet pT s gives 171.6±3.3(stat)±3.8(syst) GeV 5.In lepton+jets decays we measure everything except the component of the neutrino momen-tum along the beam direction. With the two mass constraints on the decay products of the Wbosons and the requirement for both top quark masses to be equal, a kinematic ﬁt with twoconstraints is possible. Signal-to-background is typically 1:2 without b-tagging and 2:1 afterrequiring at least one b-tagged jet.D0 use the matrix element method to measure the mass in the lepton+jets channel. D0integrate over the tree-level matrix elemnts for tt¯-production and for W+jets production tocompute the likelihood that the event originates from either signal or background. The jetsfrom the hadronic W boson decay are used to constrain the jet energy scale calibration. Theresult mt = 170.5 ± 2.5(stat⊕jes) ± 1.4(syst) GeV from the ﬁrst 0.9 fb−1 of data from Run IIhas already been presented at conferences last year. D0 have analyzed an additional 1.2 fb−1 ofdata resulting in mt = 173.0±1.9(stat⊕jes)±1.0(syst) GeV. D0 combine the two measurementsto obtain mt = 172.2 ± 1.1(stat) ± 1.6(syst⊕jes) GeV ?.CDF also use the matrix element method with in situ calibration of the jet energy scale.CDF only integrate over the tt¯-matrix element to compute the likelihood to observe the eventfrom tt¯-production. No integration over the background matrix elements is performed. CDFuse a neural network discriminant to determine an event-by-event signal-to-background ratioand then subtract the bias in the likelihood expected from the background events in the sample.Based on 1.9 fb−1 CDF measure mt = 172.7±1.8(stat⊕jes)±1.2(syst) GeV7. Alternatively CDFalso perform a template ﬁt to the best top quark mass and the best dijet mass from a kinematicﬁt of the event to the tt¯-hypothesis on the same data set. The dijet mass constrains the jetenergy scale. With this analysis CDF measure mt = 171.8 ± 1.9(stat⊕jes) ± 1.0(syst) GeV 5.The all jets channel has the largest branching fraction but also by far the largest background.CDF use events with 6-8 jets, of which at least one has to be b-tagged. They ﬁt the best topquark mass and dijet masses from a kinematic ﬁt of the leading six jets to the tt¯-hypothesis totemplates and obtain mt = 177.0 ± 3.7(stat⊕jes) ± 1.6(syst) GeV 8.We use the BLUE method 9 to combine the best top quark mass measurements from Runs Iand II in each channel by the to experiments, including the correlations between the systematicsuncertainties of these measurements. Fig. 1 compares these measurements and Table 1 summa-rizes the Run II measurements that enter in this combination and their systematic uncertainties.It can be seen that statistical and systematic uncertainties are of similar magnitude and that thelargest source of systematic uncertainty is the jet energy scale calibration. The world averagetop quark mass is mt = 172.6± 1.4 GeV, which is for the ﬁrst time below 1% in precision. Thetop quark masses determined in the three diﬀerent ﬁnal state channels are 169.8 ± 3.1 GeV inthe dilepton channel, 172.4 ± 1.5 GeV in the lepton+jets channel, and 177.3 ± 3.9 GeV in theall-jets channel, all consistent with the overall average 10.The global electroweak ﬁt was repeated with this new world average for the top quark massas input 12. The χ2 is minimized at a value of 17.2 for 13 degrees of freedom, which correspondsto a probability of 19% for a Higgs boson mass of 87+36−27 GeV. The 95% C.L. upper limit forthe Higgs boson mass is 160 GeV. Figure 2 shows the measured values of the masses of the topquark and the W boson 13.In conclusion, we have measured the top quark mass with 0.8% precision to be 172.6±1.4 GeVusing about 2 fb−1 of data from the Fermilab Tevatron collider. By the end of Run II we expectto accumulate a total of around 6-8 fb−1 which will allow us to push the experimental precisionof this measurement below 1 GeV.I would like to thank the organizers for inviting me to present these results at this veryexciting and stimulating conference.Figure 1: Measurements of the top quark mass. Figure 2: W boson mass versus top quark massplane. The shaded band is consistent with the stan-dard model for 114 GeV< mH < 1 TeV.Table 1: Run II top quark mass measurements and systematic uncertainties used in the world average.channel dilepton l+jets all-jets Lxy 11 worldexperiment CDF D0 CDF D0 CDF CDF average∫ Ldt 2.0 1.1 1.9 2.1 1.9 0.7 fb−1result 171.2 173.7 172.7 172.2 177.0 180.7 172.6 GeVjet energy calibration 1.5 3.1 1.5 1.3 2.0 0.3 0.9 GeVsignal model 0.7 0.8 0.6 0.7 0.6 1.4 0.5 GeVbackground model 0.4 0.6 0.6 0.4 1.0 7.2 0.4 GeVﬁt 0.6 0.9 0.2 0.1 0.6 4.2 0.1 GeVMonte Carlo model 0.7 0.2 0.4 0.0 0.3 0.7 0.2 GeVsyst uncertainty 2.8 3.4 1.7 1.6 2.4 8.5 1.1 GeVstat uncertainty 2.7 5.4 1.2 1.1 3.3 14.5 0.8 GeVtotal uncertainty 3.9 6.4 2.1 1.9 4.1 16.8 1.4 GeVReferences1. C Jarlskog in CP Violation, ed. C Jarlskog (World Scientiﬁc, Singapore, 1988).2. V.M. Abazov et al. (D0 Collaboration), Nature 429, 638 (2004).3. D0 Collaboration, D0 notes 5347-CONF, 5463-CONF, 5460-CONF (2007).4. CDF Collaboration, CDF note 9130 (2007).5. CDF Collaboration, CDF note 9206 (2008).6. D0 Collaboration, D0 notes 5610-CONF (2008).7. CDF Collaboration, CDF note 9196 (2008).8. CDF Collaboration, CDF note 9165 (2007).9. L. Lyons, D. Gibaut, and P. Cliﬀord, Nucl. Instrum. Meth. A270 110 (1988).10. TeV Electroweak Working Group, FERMILAB-TM-2403-E (2008).11. A. Abulencia et al. (CDF Collaboration), Phys. Rev. D 75, 071102(R) (2007).12. M. Gru¨newald, private communication.13. http://lepewwg.web.cern.ch/LEPEWWG/plots/winter2008/.

Top quark mass measurements at the Tevatron

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Top quark mass measurements at the Tevatron

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