Precision Top-Quark Mass Measurement in the $\mathrm{\text{Lepton}}\mathbf{+}\mathrm{\text{Jets}}$ Topology in $p\overline{p}$ Collisions at $\sqrt{s}\mathbf{=}1.96\mathrm{TeV}$

We report two measurements of the top-quark mass $M_{\mathrm{top}}$ using the CDF II detector at the Fermilab Tevatron in a $318{\mathrm{pb}}^{-1}$ data sample of $t\overline{t}$ events in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ final state. One method uses an event-based likelihood technique resulting in $M_{\mathrm{top}}={173.2}_{-2.4}^{+2.6}(\mathrm{stat})\pm 3.2(\mathrm{syst})\mathrm{GeV}/c^2$ or ${173.2}_{-4.0}^{+4.1}\mathrm{GeV}/c^2$. The second method reconstructs a top-quark mass in each event using the measured invariant mass of the hadronically decaying $W$ boson to constrain the jet energy scale to obtain a value for $M_{\mathrm{top}}$ of ${173.5}_{-3.6}^{+3.7}(\mathrm{stat})\pm 1.3(\mathrm{syst})\mathrm{GeV}/c^2$ or ${173.5}_{-3.8}^{+3.9}\mathrm{GeV}/c^2$. We take the latter, which is more precise, as our result.