Measurements of the S-wave fraction in B⁰ → K⁺π⁻μ⁺μ⁻ decays and the B⁰ → K^∗(892)⁰μ⁺μ⁻ differential branching fraction

A measurement of the differential branching fraction of the decay B⁰ → K^∗(892)⁰μ⁺μ⁻ is presented together with a determination of the S-wave fraction of the K⁺π⁻ system in the decay B⁰ → 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, q². Precise theoretical predictions for the differential branching fraction of B⁰ → K^∗(892)⁰μ⁺μ⁻ decays are available for the q² region 1.1 < q²< 6.0 GeV²/c⁴. In this q² region, for the K⁺π⁻ invariant mass range 796 < m_Kπ< 996 MeV/c², the S-wave fraction of the K⁺π⁻ system in B⁰ → K⁺π⁻μ⁺μ⁻ decays is found to be FS=0.101±0.017(stat)±0.009(syst), and the differential branching fraction of B⁰ → K^∗(892)⁰μ⁺μ⁻ decays is determined to be dB/dq2=(0.392+0.020−0.019(stat)±0.010(syst)±0.027(norm))×10−7c4/GeV2.The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.