Search for the charged Higgs boson in the decays of top quark pairs in the $e\tau$ and $\mu \tau$ channels at $\sqrt{s}=1.8\mathrm{}$ TeV

Top quark production offers the unique opportunity to search for a charged Higgs boson ${(H}^{\pm }),$ as the contribution from $\overrightarrow{t}{H}^{+}\overrightarrow{b}{\tau }^{+}\nu b$ can be large in extensions of the standard model. We use results from a search for top quark pair production by the Collider Detector at Fermilab (CDF) in the $e\tau +E_T+\mathrm{jets}$ and $\mu \tau +E_T+\mathrm{jets}$ signatures to set an upper limit on the branching ratio of $\mathcal{B}\left(\overrightarrow{t}{H}^{+}b\right)$ in 106 ${\mathrm{pb}}^{-1}$ of data. The upper limit is in the range 0.5 to 0.6 at 95% C.L. for $H^{+}$ masses in the range 60 to 160 GeV, assuming the branching ratio for $H^{+}\to \tau \nu$ is 100%. The $\tau$ lepton is detected through its 1-prong and 3-prong hadronic decays.