Measurement of the phase difference between short- and long-distance amplitudes in the $B^{+}to K^{+}mu^{+}mu^{-}$ decay

A measurement of the phase difference between the short- and long-distance contributions to the $B^{+}to K^{+}mu^{+}mu^{-}$ decay is performed by analysing the dimuon mass distribution. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 3 $rm fb^{-1}$ collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the $B^{+}to K^{+}mu^{+}mu^{-}$ decay is modelled as a sum of relativistic Breit--Wigner amplitudes representing different vector meson resonances decaying to muon pairs, each with their own magnitude and phase. The measured phases of the $J/psi$ and $psi(2S)$ resonances are such that the interference with the short-distance component in dimuon mass regions far from their pole masses is small. In addition, constraints are placed on the Wilson coefficients, $mathcal{C}_{9}$ and $mathcal{C}_{10}$, and the branching fraction of the short-distance component is measured.