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

Abstract

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.

All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-012.html ; corrected numerical results