Measurement of the branching fraction B(Bu+→J/ψπ+) and search for Bc+→J/ψπ+

We report on a measurement of the branching fraction of the Cabibbo-suppressed decay ${B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}$, where $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. The data were collected by the Collider Detector at Fermilab during 1992--1995 and correspond to an integrated luminosity of $110{\mathrm{pb}}^{\ensuremath{-}1}$ in $\overline{p}p$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\phantom{\rule{0ex}{0ex}}\mathrm{TeV}$. A signal of ${28}_{\ensuremath{-}9}^{+10}$ events is observed and we determine the ratio of branching fractions $B({B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+})/B({B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+})$ to be $[{5.0}_{\ensuremath{-}1.7}^{+1.9}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.1(\mathrm{syst})]%$. Using the world average value for $B({B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+})$, we calculate the branching fraction $B({B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+})$ to be $({5.0}_{\ensuremath{-}1.9}^{+2.1})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. We also search for the decay ${B}_{c}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}$ and report a $95%$ confidence level limit on $\ensuremath{\sigma}({B}_{c}^{+})B({B}_{c}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+})/\ensuremath{\sigma}({B}_{u}^{+})B({B}_{u}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+})$ as a function of the ${B}_{c}^{+}$ lifetime.