Measurement of the $B_c$ Lifetime Using the $B_c\rightarrow J/\psi + \mu^{\pm} + X$ Decay Channel

We report on a measurment of the lifetime of the $B_c$ meson in the semileptonic decay mode $B_c\rightarrow J/\psi + \mu^{\pm} + X$ with $J/\psi \rightarrow \mu^+ \mu^-$. The measurement utilizes 360 pb$^{-1}$ of data collected with the CDF II detector during Run II of the Fermilab Tevatron in pbarp collisions at $\sqrt{s} = 1.96$ TeV. We build a likelihood function, consisting of signal and background lifetime distribution functions, which is maximized when applied to the data sample of $J/\psi + \mu^{\pm}$ events to extract a measurement of the lifetime.