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.
Categories: hep-ex