Measurement of the Forward-Backward Asymmetry in the $B\to K^{(*)}{\mu }^{+}{\mu }^{-}$ Decay and First Observation of the $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ Decay

We reconstruct the rare decays $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$, $B^0\to K^{*}(892{)}^0{\mu }^{+}{\mu }^{-}$, and $B_s^0\to \varphi (1020){\mu }^{+}{\mu }^{-}$ in a data sample corresponding to $4.4{\mathrm{fb}}^{-1}$ collected in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ by the CDF II detector at the Tevatron Collider. Using $121\pm 16$ $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ and $101\pm 12$ $B^0\to K^{*0}{\mu }^{+}{\mu }^{-}$ decays we report the branching ratios. In addition, we report the differential branching ratio and the muon forward-backward asymmetry in the $B^{+}$ and $B^0$ decay modes, and the $K^{*0}$ longitudinal polarization fraction in the $B^0$ decay mode with respect to the squared dimuon mass. These are consistent with the predictions, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ decay and measure its branching ratio $\mathrm{BR}(B_s^0\to \varphi {\mu }^{+}{\mu }^{-})=[1.44\pm 0.33\pm 0.46]\times {10}^{-6}$ using $27\pm 6$ signal events. This is currently the most rare $B_s^0$ decay observed.

Figure 1

Mass of $B^0\to K^{*0}{\mu }^{+}{\mu }^{-}$ and $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ candidates with fit results overlaid. The vertical lines show the signal region.

Figure 2

Differential BR of $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ (a) and differential BR (b), longitudinal $K^{*0}$ polarization fraction (c), and forward-backward asymmetry (d) of $B^0\to K^{*0}{\mu }^{+}{\mu }^{-}$, as a function of squared dimuon mass. Points are the fit result. The solid curves are the SM expectation [1]. Two solid curves in (a),(b) use maximum- and minimum- allowed form factors on differential BR plots. The dotted curves are the $C_7=-C_7^{\mathrm{SM}}$ expectation. The dashed line is the averaged expectation in each squared dimuon mass bin and hatched regions are charmonium veto regions.