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

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 ${\bar{B}}_d^0\to J/\psi ({\pi }^0\eta ,K^{+}{K}^{-},K^0{\bar{K}}^0)$. 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 ${\bar{B}}_d^0\to J/\psi {\pi }^{+}{\pi }^{-}$ measured recently at LHCb, letting the corresponding measurement appear feasible.

Comments: 26 pages, 4 figures; v2: discussion extended, new sec. 3 and app. B, as published in JHEP