Measurements of the S-wave fraction in $B^{0}rightarrow K^{+}pi^{-}mu^{+}mu^{-}$ decays and the $B^{0}rightarrow K^{ast}(892)^{0}mu^{+}mu^{-}$ differential branching fraction

A measurement of the differential branching fraction of the decay ${B^{0}rightarrow K^{ast}(892)^{0}mu^{+}mu^{-}}$ is presented together with a determination of the S-wave fraction of the $K^+pi^-$ system in the decay $B^{0}rightarrow K^{+}pi^{-}mu^{+}mu^{-}$. The analysis is based on $pp$-collision data corresponding to an integrated luminosity of 3,fb$^{-1}$ collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, $q^2$. Precise theoretical predictions for the differential branching fraction of $B^{0}rightarrow K^{ast}(892)^{0}mu^{+}mu^{-}$ decays are available for the $q^2$ region $1.1<q^2<6.0,{rm GeV}^2/c^4$. In this $q^2$ region, for the $K^+pi^-$ invariant mass range $796 < m_{Kpi} < 996,{rm MeV}/c^2$, the S-wave fraction of the $K^+pi^-$ system in $B^{0}rightarrow K^{+}pi^{-}mu^{+}mu^{-}$ decays is found to be begin{equation*} F_{rm S} = 0.101pm0.017({rm stat})pm0.009 ({rm syst}), end{equation*} and the differential branching fraction of $B^{0}rightarrow K^{ast}(892)^{0}mu^{+}mu^{-}$ decays is determined to be begin{equation*} {rm d}mathcal{B}/{rm d} q^2 = (0.342_{,-0.017}^{,+0.017}({rm stat})pm{0.009}({rm syst})pm0.023({rm norm}))times 10^{-7}c^{4}/{rm GeV}^{2}. end{equation*} The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.