Measurement of the $B_s^0$ Lifetime in the Flavor-Specific Decay Channel $B_s^0\to D_s^{-}{\mu }^{+}\nu X$

We present an updated measurement of the $B_s^0$ lifetime using the semileptonic decays $B_s^0\to D_s^{-}{\mu }^{+}\nu X$, with $D_s^{-}\to \varphi {\pi }^{-}$ and $\varphi \to K^{+}{K}^{-}$ (and the charge conjugate process). This measurement uses the full Tevatron Run II sample of proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$, comprising an integrated luminosity of $10.4{\mathrm{fb}}^{-1}$. We find a flavor-specific lifetime ${\tau }_{\mathrm{fs}}(B_s^0)=1.479\pm 0.010(\text{stat})\pm 0.021(\text{syst})\mathrm{ps}$. This technique is also used to determine the $B^0$ lifetime using the analogous $B^0\to D^{-}{\mu }^{+}\nu X$ decay with $D^{-}\to \varphi {\pi }^{-}$ and $\varphi \to K^{+}{K}^{-}$, yielding $\tau (B^0)=1.534\pm 0.019(\text{stat})\pm 0.021(\text{syst})\mathrm{ps}$. Both measurements are consistent with the current world averages, and the $B_s^0$ lifetime measurement is one of the most precise to date. Taking advantage of the cancellation of systematic uncertainties, we determine the lifetime ratio ${\tau }_{\mathrm{fs}}(B_s^0)/\tau (B^0)=0.964\pm 0.013(\text{stat})\pm 0.007(\text{syst})$.