Lawrence Berkeley National Laboratory

A measurement of the phase difference between the short- and long-distance contributions to the B+→K+μ+μ-$${{B} ^+} \!\rightarrow {{{K}} ^+} {\mu ^+\mu ^-} $$ decay is performed by analysing the dimuon mass distribution. The analysis is based on pp collision data corresponding to an integrated luminosity of 3fb-1$$\mathrm{\,fb}^{-1}$$ collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the B+→K+μ+μ-$${{B} ^+} \!\rightarrow {{{K}} ^+} {\mu ^+\mu ^-} $$ 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/ψ$${{J}/\psi }$$ and ψ(2S)$$\psi {(2S)}$$ 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, C9$$\mathcal {C}_{9}$$ and C10$$\mathcal {C}_{10}$$, and the branching fraction of the short-distance component is measured.