Top quark mass measurement using the template method in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>lepton</mml:mi><mml:mo>+</mml:mo><mml:mi>jets</mml:mi></mml:math>channel at CDF II

This article presents a measurement of the top quark mass using the CDF II detector at Fermilab. Colliding beams of protons and antiprotons at Fermilab's Tevatron ($\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$) produce top/antitop pairs, which decay to ${W}^{+}{W}^{\ensuremath{-}}b\overline{b}$; events are selected where one $W$ decays to hadrons and the other $W$ decays to either $e$ or $\ensuremath{\mu}$ plus a neutrino. The data sample corresponds to an integrated luminosity of approximately $318\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. A total of 165 $t\overline{t}$ events are separated into four subsamples based on jet transverse energy thresholds and the number of $b$ jets identified by reconstructing a displaced vertex. In each event, the reconstructed top quark invariant mass is determined by minimizing a ${\ensuremath{\chi}}^{2}$ for the overconstrained kinematic system. At the same time, the mass of the hadronically decaying $W$ boson is measured in the same event sample. The observed $W$ boson mass provides an in situ improvement in the determination of the hadronic jet energy scale. A simultaneous likelihood fit of the reconstructed top quark masses and the $W$ boson invariant masses in the data sample to distributions from simulated signal and background events gives a top quark mass of ${173.5}_{\ensuremath{-}3.8}^{+3.9}\text{ }\text{ }\mathrm{GeV}/{c}^{2}$.