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## Measurements of the top-quark mass using charged particle tracking

Ford Garberson, Joe Incandela, Sue Ann Koay, Roberto Rossin
UCSB
Christopher Hill
University of Bristol

 Top Mass Results with 1.9 fb-1 of Data: 170.7 ± 6.3 (stat) ± 2.6 (syst) GeV/c2, for the combined measurement 166.9+9.5-8.5 (stat) ± 2.9 (syst) GeV/c2, for the decay length measurement alone 173.5+8.8-8.9 (stat) ± 3.8 (syst) GeV/c2, for the lepton transverse momentum measurement alone

Internal webpage (password protected)
The publication draft.
Phys.Rev.D71:054029,2005. Presented first feasibility studies of the decay length technique at the Tevatron and the LHC, and proposed the transverse momentum of the leptons as a possible second variable.
Phys.Rev.D75:071102,2007. First publication of a top mass measurement using the decay length with 695 pb-1 of CDF data.
Public webpage for the 700 pb-1 analysis.

### Abstract:

We present two measurements of the top quark mass in the lepton plus jets channel with approximately 1.9 fb-1 of data using quantities with minimal dependence on the jet energy scale. One measurement is of the SecVtx transverse decay length of b-tagged jets (Lxy), and the other is of the transverse momentum of the lepton. Both these quantities are roughly linearly proportional to the top mass. Since the quantities have approximately the same statistical resolution in top mass determination, and since the quantities are approximately uncorrelated to one another, the statistical uncertainty in the mass measurement is significantly reduced by combining the results. Results are shown below. Since many of the systematic uncertainties are statistically limited, these results are expected to improve significantly if more data is added at the Tevatron in the future, or if the measurement is done at the LHC.

### Event Selection:

The data are collected with an inclusive lepton trigger that requires an electron or muon with ET > 18 GeV (PT > 18 GeV/c for the muon). From this inclusive lepton dataset we select events offline with a reconstructed isolated electron ET (muon PT) greater than 20 GeV.

The total missing transverse energy (MET) in the event is required to be greater than 20 GeV, and a minimum of three jets must also be identified with reconstructed transverse energies greater than 20 GeV. b-jets are identified (tagged) using the SecVtx algorithm. In order for the event to pass selection, at least one jet must be tagged as a b for events with four or more jets of ET greater than 20 GeV, and at least two jets must be tagged as a b for events with exactly three jets of ET greater than 20 GeV.

### Event Composition:

#### QCD background:

QCD events may enter the selection when a jet fakes a lepton and the missing transverse energy is misreconstructed. The QCD background is evaluated from data by altering the lepton selection criteria to make the events much more likely to contain fake leptons. The new event selection is such that identified events do not overlap those selected from data for the analysis, and the selection is tuned to reduce bias in either Lxy or Lepton Pt compared to the standard event selection.

#### W+jets background:

The W+jets sample represents the largest background. It is evaluated from ALPGEN events that are showered using Pythia. When heavy flavor quarks are produced from the Pythia shower, events are only kept if the opening angle between the quarks is less than $0.4$ in $\eta\phi$ space. Similarly, events with heavy flavor production from ALPGEN are rejected if quarks from the heavy flavor pair have an opening angle that is less than $0.4$. In this manner double counting of events between Pythia and ALPGEN is avoided.

#### Single Top Sample:

we do not really treat the single top distribution as a background. Rather, we parameterize the shape of the single top Lxy and Lepton Pt distributions according to top mass so that we can find the mean values for an arbitrary mass point. Distribution shapes were determined from the four mass points for which single top Monte Carlo samples were available (MT = 165, 170, 175, and 180 GeV/c2).

#### Corrections to the ttbar sample:

Various corrections were applied to the signal sample including PDF reweightings, gluon fraction reweightings, and decay length corrections. The decay length correction is the most complicated of these, as it must be parameterized as a function of jet energy, which leads to our development and calibration of an algorithm for measuring jet energy using tracking. See the publication draft for details.

### Method:

For each event passing selection, the Lepton Pt value is recorded, as is the Lxy of the two leading SecVtx tagged jets. Signal and background distributions for top mass hypotheses similar to the measured results area shown below.
 Signal, background, and data for the Lxy distribution, using hypothesis top mass M=168 GeV/c2 Signal, background, and data for the Lepton Pt distribution, using hypothesis top mass M=173 GeV/c2

To evaluate the top mass results for each individual measurement (before Lxy and Lepton Pt are combined), the means and RMS's of the pseudoexperiment results are determined and are fit to quadratic polynomials as shown below. Given the mean Lxy and Lepton Pt in data, the corresponding x-values of the central fit give us our expected mass, and the value of the shifted fits give us our ± one sigma asymmetric statistical uncertainties.

 Expected central values and one sigma confidence intervals of Lxy mean results depending on top mass. Solid lines show the plus and minus one sigma statistical uncertainties from data. Expected central values and one sigma confidence intervals of Lepton Pt mean results depending on top mass. Solid lines show the plus and minus one sigma statistical uncertainties from data.

### Combination

A joint top mass measurement using both the Lxy and Lepton Pt is also performed using pseudoexperiments. Given the two observed means in data, a likelihood distribution is determined and fit to a Gaussian to determine the mass results and one sigma statistical errors as shown below. See the publication draft for details.
 Likelihood fit results for data.

### Systematic Uncertainties:

Our largest systematic uncertainty is due to the background distributions. We describe the conservative manner in which we estimate this systematic below. There are many other categories of systematic uncetainties we consider for this measurement. Some, relating to the uncertainties on the properties of the tracking based jets we use for our decay length calibration, are unique to our measurement. Our studies have demonstrated that our measurement is almost completely independent of calorimeter based jet energy uncertainties, and that the uncertainties on our tracking based jet energy measurements are almost completely independent of the calorimeter based ones. We are also the only measurement to include an uncertainty on the differences between b-jets and light flavor jets in terms of the fraction of the jet energy that flows out of the jet cone and fails to be reconstructed. Until conventional top mass measurements account for this potentially large uncertainty, it becomes difficult to make any meaningful comparison between our results and theirs. For further details please see the publication draft.

#### Background Uncertainty:

To evaluate the systematic uncertainty on the background means, a direct comparison with the data was performed. We evaluate the mean Lepton Pt and Lxy for data and compare to our background estimations in the one and two jet bins as cross checks for our signal sample. These bins are both dominated by background events, in roughly the same proportion as in the signal region of our event selection. To be conservative, we take the larger of the shifts between the signal and the background for the one jet and two jet bins as our systematic uncertainty. The distributions in these cross check bins are shown below.
 Background predictions compared with data in the one jet control region for Lxy and Lepton Pt Background predictions compared with data in the two jet control region for Lxy and Lepton Pt