Measurement of the phase difference between short- and long-distance amplitudes in the [Formula: see text] decay

A measurement of the phase difference between the short- and long-distance contributions to the [Formula: see text] decay is performed by analysing the dimuon mass distribution. The analysis is based on pp collision data corresponding to an integrated luminosity of 3[Formula: see text] collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the [Formula: see text] 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 [Formula: see text] and [Formula: see text] 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, [Formula: see text] and [Formula: see text], and the branching fraction of the short-distance component is measured.