Comprehensive analysis of local and nonlocal amplitudes in the $B^0\rightarrow K^{*0}\mu^+\mu^-$ decay

TL;DR

This paper performs a detailed analysis of local and nonlocal amplitudes in the decay $B^0 ightarrow K^{*0} o K^+\pi^-\, \mu^+\,\mu^-$, utilizing LHCb data to measure interference effects and deviations from the Standard Model.

Contribution

It introduces a novel model for both one-particle and two-particle nonlocal amplitudes, analyzing the full dimuon mass spectrum without vetoes, and provides the first direct measurement of the $b s au au$ vector coupling.

Findings

Interference with nonlocal contributions is larger than predicted but has minor impact on Wilson coefficients.

The Wilson coefficient $C_9$ shows a 2.1$\sigma$ deviation from the Standard Model.

Other Wilson coefficients are in better agreement with the Standard Model, with a global significance of 1.5$\sigma$.

Abstract

A comprehensive study of the local and nonlocal amplitudes contributing to the decay $B^0\rightarrow K^{*0}(\to K^+\pi^-) \mu^+\mu^-$ is performed by analysing the phase-space distribution of the decay products. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 8.4fb$^{-1}$ collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient $C_9$, responsible for vector dimuon currents, exhibits a $2.1\sigma$ deviation from the Standard Model expectation. The Wilson Coefficients $C_{10}$, $C_{9}'$ and $C_{10}'$ are all in better agreement than $C_{9}$ with the Standard Model and the global significance is at the level of $1.5\sigma$. The model used also accounts for nonlocal contributions from $B^{0}\to K^{*0}\left[\tau^+\tau^-\to \mu^+\mu^-\right]$ rescattering, resulting in the first direct measurement of the $b s\tau\tau$ vector effective-coupling $C_{9\tau}$.