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

A measurement of the differential branching fraction of the decay B ⁰ → K ^∗(892) ⁰μ ⁺μ ⁻ is presented together with a determination of the S-wave fraction of the K ⁺π ⁻ system in the decay B ⁰ → 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 → K ^∗(892) ⁰μ ⁺μ ⁻ 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 ⁺π ⁻ invariant mass range 796 < m _Kπ< 996 MeV/c ², the S-wave fraction of the K ⁺π ⁻ system in B ⁰ → K ⁺π ⁻μ ⁺μ ⁻ decays is found to be F _S=0.101±0.017(stat)±0.009(syst), and the differential branching fraction of B ⁰ → K ^∗(892) ⁰μ ⁺μ ⁻ decays is determined to be dℬ/dq ²=(0.392 _−0.019 ^+0.020(stat)±0.010(syst)±0.027(norm))×10 ⁻⁷c 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.