Measurement of the Branching Fraction $\mathit{B}(B_{\mathit{u}}^{+}\to \mathit{J}/{\mathit{\psi }\mathit{\pi }}^{+})$ and Search for $B_{\mathit{c}}^{+}\to \mathit{J}/{\mathit{\psi }\mathit{\pi }}^{+}$

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