Top Quark Mass Measurement by Dynamical Likelihood Method
in the lepton+jets with SECVTX btag events

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- Authors - Kohei Yorita

The University of Chicago

Kunitaka Kondo

Waseda University, Japan

Measurement of the top quark mass obtained by DLM (Dynamical Likelihood Method) in the lepton+jets channel with SECVTX b-tagged events is described. The DLM defines a likelihood for each event based on the ttbar differential cross section as a function of the top quark mass. In particular, the parton kinematics is statistically reconstructed by (a) generating the vitual mass squared of W-boson in the leptonic channel, Sw, according to the Breit-Wigner form, (b) identifying momenta of electron or muon with the measured values, and the neutrino transverse momentum with the measured transverse energy flow, and (c) generating momenta of jets with the transfer function (TF). TF w(x,y) correlates between the parton and observed variable sets, denoted by x and y respectively, and is obtained from the ttbar Monte Carlo simulation. The z-component of the neutrino momentum is given with a two-fold ambiguity by solving equation Sw = (l+nu)^2. With an inferred set of x and Sw, parton kinematics is determined, and its likelihood as a function of M_{top} is calculated by
where the normalization factor N is a constant for a given event, independent of M_{top}. Integers I_t and I_s are numbers to sort parton-jet assignments and two neutrino solutions, respectively. This process is repeated and summed for each event, typically fifty thousand times, until the likelihood value converges. A joint likelihood is formed by multiplying the event likelihoods together. We take into account the presence of of background events by modelling the effect of the background as a shift on the top quark mass and making an appropriate correction (mapping function). Using 63 events with the exactly 4-tight-jets of the data, where 9.16 events is expected from background, which corresponds to an integrated luminosity of 318 pb-1 in Run II, we measure the top quark mass to be 173.2 +2.6/-2.4 (stat.) ± 3.2(syst.) GeV/c².

Description	gif	eps
Expected Number of Background Events Expected number of background events of each source in exactly 4 tight jets bin. 9.16 events out of 63 observed events are expected to be backgrounds (14.5%).		eps
Mapping Function Reconstructed mass shift due to background. Background fraction is varied from 0% to 50%. Each point is obtained by Pseudo experiments (PE) with Poisson fluctuation for signal and background events. The total number of events are 63 for each PE.		eps
Each background effect on top mass Individual backround effect on reconstructed top mass(M=178GeV) as a function of background fraction. Mistag, Wbb and nonW(QCD) background are very similar which are dominant background sources(~90%). Single top effect is relatively small while diboson is a little large. Expected background fraction is 14.5% in data.		eps
Slope and Constant term of Mapping function The slope and constant from linear fit of mapping function are very stable at least up to background fraction of around 50%. These are used to correct the measured top mass to get "right top mass" ("background free mass").		eps1 eps2
Sanity Check with backgrounds(9.2 ev) The sample includes 9.2 event(Poisson) out 63 total number of events. Even if the sample contains background, The top mass can be reconstructed correcly by applying mapping function.		eps
Center and Width of Pull distribution The check of center and width of pull distribution with 9.2 bacground events as a function of input top mass. Pull width is measured to be 1.04, therefore 4 % correction is applied to statistical uncertainty for 68% coverage of top mass fluctuation.		eps1 eps2
Joint Likelihood of 63 observed data 63 events in data (at least one btag jet, and exactly 4 jets) joint likelihood. Maximum likelihood gives 171.8 +2.18-2.02 GeV. This value is affected by background (14.5%(9.2 event) expected). Therefore we apply mapping function at 14.5% and statistical errors are also scaled by the slope of mapping function. The final (corrected) value is 173.2 +2.6 -2.4 GeV.		eps
Center Valie Shift Center value change as a function of background fraction. Background fraction uncertainty is assigned as ±5.6%, and added to systematic uncertainty.		eps
Expected Statistical Uncertainty A plot shows a comparison between data and Monte Carlo simulation using M=175 GeV sample. Black arrow indicates the one from data. A probability of having smaller uncertainty is 18%.		eps
Systematic Uncertainties Summary The summary of systematic uncertainties.		eps
Each Event Likelihood distribution Event likelihood is defined as Li = ∫ L(M)dM in one event (Integral region [155,195] GeV). Agreement between data and Monte Carlo is quite good. The plot is showing log of event likelihood.		eps
Per-Event Top Mass at Maximum Likelihood for each event Per-Event top quark mass at maximum likelihood. Data and Monte Carlo (M=175 GeV for signal) agree nicely.		eps
Per-Event W(jj) Mass at Maximum Likelihood for each event Per-Event hadronic W mass at maximum likelihood where W mass constraint is removed in the likelihood, instead, top mass is constrainted to be 175 GeV for both data and MC.		eps
Transer Function chacks by comparing data and MC outputs Plots of transfer(response) variable for b jets (left) and w jets (right), where likelihood gets maximum in each event. There are two entries in each event, so 63 events give 126 jets. Note that each time we calculate a likelihood, each jet is assigned as each parton and has response variable from trasnfer function. Therefore b (or w) jets in the plots are not necessarily b (or w-daughter) quark. They includes mis-assignments and gluon contamination.		bjet (eps) wjet (eps)
Consistency check Comparisons of (1) lepton type (electron vs muon), (2) lepton charge (+ vs -), (3) 1 btag vs 2 b tag, (4) Spliting run range A and B. (Rnage A corresponds to a previous dataset which has integrated luminosity of 162 pb-1.)		eps
Each event likelihood distribution for 63 observed data 63 event-by-event likelihood distrobutions are showed in the range of 75-275 GeV. Blue and red line are 1 btag and 2 btag events respectively. Black line in each distribution corresponds to the measured value of 173.2 GeV.		eps