Combination of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mover accent="true"><mml:mi>t</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>cross section measurements and constraints on the mass of the top quark and its decays into charged Higgs bosons

We combine measurements of the top quark pair production cross section in $p\overline{p}$ collisions in the $\ensuremath{\ell}+\mathrm{\text{jets}}$, $\ensuremath{\ell}\ensuremath{\ell}$, and $\ensuremath{\tau}\ensuremath{\ell}$ final states (where $\ensuremath{\ell}$ is an electron or muon) at a center of mass energy of $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ in $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected with the D0 detector. For a top quark mass of $170\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, we obtain ${\ensuremath{\sigma}}_{t\overline{t}}={8.18}_{\ensuremath{-}0.87}^{+0.98}\text{ }\text{ }\mathrm{pb}$ in agreement with the theoretical prediction. Based on predictions from higher order quantum chromodynamics, we extract a mass for the top quark from the combined $t\overline{t}$ cross section, consistent with the world average of the top quark mass. In addition, the ratios of $t\overline{t}$ cross sections in different final states are used to set upper limits on the branching fractions $B(t\ensuremath{\rightarrow}{H}^{+}b\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu}b)$ and $B(t\ensuremath{\rightarrow}{H}^{+}b\ensuremath{\rightarrow}c\overline{s}b)$ as a function of the charged Higgs boson mass.

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