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

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## Abstract

A measurement of the phase difference between the short- and long-distance contributions to the ${{B} ^+} \!\rightarrow {{{K}} ^+} {\mu ^+\mu ^-}$ decay is performed by analysing the dimuon mass distribution. The analysis is based on pp collision data corresponding to an integrated luminosity of 3 $\mathrm{\,fb}^{-1}$ collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the ${{B} ^+} \!\rightarrow {{{K}} ^+} {\mu ^+\mu ^-}$ 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 ${{J}/\psi }$ 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.
Original language English Aaij:2016cbx 161 European Physical Journal C C77 3 https://doi.org/10.1140/epjc/s10052-017-4703-2 Published - 16 Mar 2017

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