$B_c\rightarrow J/\psi+\mu^{\pm}$ decays at CDF

We report on a study of the $B_c$ meson in the semileptonic decay mode $B_c\rightarrow J/\psi+\mu^{\pm}X$ with $J/\psi\rightarrow \mu^+\mu^-$ using 360 pb$^{-1}$ of data collected at the CDF detector during Run II of the Fermilab Tevatron. We examine the sources of background and report on the status of establishing a $B_c$ signal over the predicted background. The possible uses of the data to determine the $B_c$ lifetime, mass, and the ratio $\frac{\sigma BR(B_c\rightarrow J/\psi \mu^{\pm} X)}{\sigma BR(B^{\pm}\rightarrow J/\psi K^{\pm})}$ are discussed and some preliminary results presented.