We present a novel method to measure the top quark mass using the transverse decay length of b-hadrons from top decays. This technique relies solely on tracking and thus avoids the jet energy scale uncertainty that is common to all other methods. We apply our new method to the lepton+jets sample corresponding to 695 pb^{-1} and extract a measurement of m_{t} = 180.7^{+15.5}_{-13.4} (stat.) ± 8.6 (syst.) GeV/c^{2}. While this is not a competitive measurement of the top quark mass by itself, since the decay length technique is uncorrelated with other methods, this result will help to reduce the overall uncertainty on the top mass in combination with other CDF results.
The top quark's mass therefore (to the extent that the threshold approximation holds) is strongly correlated with the boost given to the b-quark and the subsequent b-hadron after fragmentation. Thus, the average lifetime of the b-hadrons resultant from top decays can be used to statistically infer the mass of the top quark. In this analysis, rather than measuring the average lifetime, we simply measure the experimentally more accessible transverse decay length of the b-hadrons. This correlation is illustrated in the following Figure, which plots the generator level transverse decay length of b-hadrons from top quarks with varied mass. We use the sample mean as an estimator of the slope of the exponential distribution, from which we deduce the top quark mass.
This technique relies on tracking to precisely determine the decay length. It does not use any calorimeter information and thus avoids any jet energy scale uncertainty.
Lepton+Jetstop quark candidate events are selected by requiring an isolated high E_{T} lepton (e or mu) accompanied by significant missing energy and three or more high E_{T} jets. One or more of these jets must be
taggedby the reconstruction of a displaced secondary vertex. The 2D distance bewteen the primary vertex and the secondary vertex is the transverse decay length, which we denote L_{2D}:
This quantity is histogrammed for all tags in selected events and the mean of this distribution is computed. The measured mean L_{2D} is converted to a most-probable top mass (and corresponding 1 sigma confidence interval) using correlation functions derived from Monte Carlo simiulations of signal (tt events with varied top mass) and background. Details of the analysis are described in the conference note linked below.
Measurement of the Top Quark Mass in ppbar Collisions at sqrt(s) = 1.96 TeV using the Decay Length Technique
Transverse Decay Length Simulaton vs. Data L_{2D} for jets with positive secondary vertex tags obtained from CDF data and CDF Monte Carlo simulation are overlaid. The CDF data sample is b-enriched dijet data recorded on an 8 GeV lepton trigger. The simulation is Herwig dijet MC. Events are required to have two jets in opposite hemispheres, both of which are secondary vertex tagged and one of which contains an identified lepton. This selection prodresults in samples which are nearly 100% bb. |
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Tranverse Decay Length - Control Sample Points are the L_{xy} distribution of positive tags in selected W plus 1 or 2 jet data, for which little top contribution is expected. Expected contributions from background Monte Carlo are overlaid in the solid stacked histogram. N.B. to facilitate the shape comparison, the MC is normalized to the observed data. A Kolmogorov-Smirnov test is performed on these distributions, with a resultant probability of 30.6%. |
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Tranverse Decay Length - Signal Sample Points are the L_{2D} distribution of positive tags in selected W plus 3 or more jet data, from which the mean transverse deacy length used to measure the top mass is extracted. Expected contributions from signal background Monte Carlo are overlaid in the solid stacked histogram. N.B. to facilitate the shape comparison, the MC is normalized to the observed data. A Kolmogorov-Smirnov test is performed on these distributions, with a resultant probability of 16.7%. |
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Top Mass Result Most probable top mass and 1 sigma Neyman confidence intervals as a function of mean transverse decay length. The mean decay length measured in 695 pb^{-1} of CDF data is overlaid as the dashed line, from which the measured top mass and its uncertainty can be read off. N.B. the uncertainty represented in the plot is statistical only. |
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Systematic Uncertainties Summary of sources of systematic error and their estimated uncertainties. Note the small systematic error arising from the jet-energy scale. |
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Backgrounds Background sources and their estimated contributions to the tagged lepton+jets sample used in this analysis with 3 or more jets. |
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