How to employ $\bar{B}^0_d \to J/\psi(\pi\eta,\bar{K}K)$ decays to extract information on $\pi\eta$ scattering

TL;DR

This paper shows how dispersion theory can extract $oldsymbol{ extit{ ext{pi}} ext{eta}}$ scattering information from $ar{B}^0_d$ decay data, emphasizing the importance of precise measurements of decay spectral distributions.

Contribution

It introduces a method to determine $ ext{pi eta}$ scattering from $ar{B}^0_d$ decay final-state interactions using dispersion theory, linking decay observables to scattering data.

Findings

Predicted decay rates are comparable to recent LHCb measurements.

High-quality spectral data can reveal $ ext{pi eta}$ scattering details.

Method enables indirect scattering analysis via decay processes.

Abstract

We demonstrate that dispersion theory allows one to deduce crucial information on $\pi\eta$ scattering from the final-state interactions of the light mesons visible in the spectral distributions of the decays $\bar{B}^0_d \to J/\psi(\pi^0\eta,K^+K^-,K^0\bar{K}^0)$. Thus high-quality measurements of these differential observables are highly desired. The corresponding rates are predicted to be of the same order of magnitude as those for $\bar{B}^0_d \to J/\psi\pi^+\pi^-$ measured recently at LHCb, letting the corresponding measurement appear feasible.