Measurement of the Charge Asymmetry in Semileptonic $B^0_s$ Decays

We have performed the first direct measurement of the time integrated, flavor untagged, charge asymmetry in semileptonic $B^0_s$ decays, $A_{SL}^{s,unt} $, by comparing the decay rate of $B^0_s\rightarrow \mu^+D^-_s\nu X$, where $D^- _s\rightarrow \phi\pi^-$ and $\phi\rightarrow K^+K^-$, with the charge-conjugate ${\bar B} ^0_s$ decay rate. This sample was selected from $1.3$ fb$^{-1}$ of data collected by the D0 experiment in Run II of the Fremilab Tevatron collider. We obtain $A_{SL}^{s,unt} = (1.23 \pm 0.97 \pm 0.17)\%$ which can be translated to a measurement of the CP-violating phase in $B^0_s$ mixing: $(\Delta \Gamma_s/\Delta m_s)\tan \phi_s = (2.45\pm 1.93\pm 0.35)\%$.