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

TL;DR

This paper measures the phase difference between short- and long-distance effects in the $B^{+} o K^{+}\mu^{+}\mu^{-}$ decay using LHCb data, providing insights into resonance interference and constraining Wilson coefficients.

Contribution

It introduces a model of the long-distance contribution as a sum of Breit--Wigner amplitudes and measures the phase difference and Wilson coefficients in this decay.

Findings

Small interference between resonances and short-distance component.

Constraints on Wilson coefficients $\\mathcal{C}_9$ and $\mathcal{C}_{10}$.

Branching fraction of the short-distance component measured.

Abstract

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.