Measurement of the $B^0_s$~Meson Lifetime with the CDF~II Detector

We present a measurement of the $B^0_s$ meson lifetime using fully and partially reconstructed hadronic decays $B^0_s\rightarrow D_s^- \pi^+(X)$ followed by $D_s^- \rightarrow \phi\pi^-$. The data sample was recorded with the CDF~II detector at the Fermilab Tevatron and corresponds to an integrated luminosity of 1.3 fb$^{-1}$ from $p\bar{p}$ collisions at $\sqrt{s} = 1.96$~TeV.