Study of the $B_c$ lifetime via the decay $B_c \rightarrow J/\psi \mu \nu X$

The $B_c$ meson is unique as a meson in that it contains two different, yet heavy quarks, resulting in a lifetime that is expected to be shorter than the other $b$ hadrons. Using approximately 1 fb$^{-1}$ of data collected with the D$\O$ detector at the Fermilab Tevatron during Run \textrm{II}, the $B_c$ meson in the semileptonic mode $B_c^\pm \rightarrow J/\psi \mu^\pm \nu X$ is studied. Preliminary results on the measured lifetime of this particle are presented.