Measurement of the Charge Asymmetry in Semileptonic $B_s^0$ Decays

We have performed the first direct measurement of the time-integrated flavor untagged charge asymmetry in semileptonic $B_s^0$ decays $A_{\mathrm{SL}}^{s,\mathrm{unt}}$ by comparing the decay rate of $B_s^0\to {\mu }^{+}{D}_s^{-}\nu X$, where $D_s^{-}\to \varphi {\pi }^{-}$ and $\varphi \to K^{+}{K}^{-}$, with the charge-conjugate ${\overline{B}}_s^0$ decay rate. This sample was selected from $1.3{\mathrm{fb}}^{-1}$ of data collected by the D0 experiment in run II of the Fermilab Tevatron collider. We obtain $A_{\mathrm{SL}}^{s,\mathrm{unt}}=[1.23\pm 0.97(\mathrm{stat})\pm 0.17(\mathrm{syst})]\times {10}^{-2}$. Assuming that $\Delta m_s/{\overline{\Gamma }}_s\gg 1$, this result can be translated into a measurement of the $CP$-violating phase in $B_s^0$ mixing: $\Delta {\Gamma }_s/\Delta m_s\tan {\varphi }_s=[2.45\pm 1.93(\mathrm{stat})\pm 0.35(\mathrm{syst})]\times {10}^{-2}$.

Figure 1

The invariant mass distribution $M(\varphi \pi )$ for the selected $B_s^0$ candidates. The curve shows the result of fit by a function described in the text.