Measurement of $B_{c}^{+} \rightarrow J/\psi \mu^{+} \nu$ Cross Section Times Branching Ratio Relative to $B^+ \rightarrow J/\psi K^+$with the CDF\,II Detector

The production cross section times branching ratio for $B_{c}^{\pm} \rightarrow J/\psi \mu^{\pm} \nu$ relative to $B^{\pm} \rightarrow J/\psi K^{\pm}$ is measured using an inclusive $J/\psi$ trigger stream with an integrated luminosity of 1~fb$^{-1}$. The results are an update of earlier work by the CDF Collaboration that used an integrated luminosity of 360~pb$^{-1}$. The measurement is made in the kinematic region $-1.0 < \eta < 1.0$ for both $p_T(B_c) >$ 4 and 6~GeV/$c$. The new results along with a comparison with earlier results will be presented.