Measurements of the S-wave fraction in $B^{0}\rightarrow K^{+}π^{-}μ^{+}μ^{-}$ decays and the $B^{0}\rightarrow K^{\ast}(892)^{0}μ^{+}μ^{-}$ differential branching fraction
A measurement of the differential branching fraction of the decay ${B^{0}\rightarrow K^{\ast}(892)^{0}μ^{+}μ^{-}}$ is presented together with a determination of the S-wave fraction of the $K^+π^-$ system in the decay $B^{0}\rightarrow K^{+}π^{-}μ^{+}μ^{-}$. 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 $B^{0}\rightarrow K^{\ast}(892)^{0}μ^{+}μ^{-}$ 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 $K^+π^-$ invariant mass range $796 < m_{Kπ} < 996\,{\rm MeV}/c^2$, the S-wave fraction of the $K^+π^-$ system in $B^{0}\rightarrow K^{+}π^{-}μ^{+}μ^{-}$ decays is found to be \begin{equation*} F_{\rm S} = 0.101\pm0.017({\rm stat})\pm0.009 ({\rm syst}), \end{equation*} and the differential branching fraction of $B^{0}\rightarrow K^{\ast}(892)^{0}μ^{+}μ^{-}$ 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.