## Abstract

A measurement of the differential branching fraction of the decay $K^∗(892)^0\mu^+\mu^−$ is presented together with a determination of the S-wave fraction of the $K^+\pi^−$ system in the decay $B^0 \to K^+\pi^−\mu^+\mu^−$. 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 $B^0 \to K^∗(892)^0\mu^+\mu^−$ decays are available for the $q^2$ region $1.1 < q 2 < 6.0 GeV^2 /c^4$. In this $q^2$ region, for the $K^+\pi^−$ invariant mass range $796 < m_{K_{\pi}} < 996 MeV/c^2$, the S-wave fraction of the $K^+\pi^−$ system in $B^0 \to K^+\pi^−\mu^+\mu^−$ decays is found to be

$F_S = 0.101 \pm 0.017(stat) \pm 0.009(syst)$,

and the differential branching fraction of $B^0 \to K^∗(892)^0\mu^+\mu^−$ decays is determined to be

$d\mathcal{B}/dq^2 = (0.392^{+0.020}_{−0.019}(stat) \pm 0.010(syst) \pm 0.027(norm)) \times 10^{−7}c^4/GeV^2$.

The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.