Short- vs Long-Distance Dynamics in $b \rightarrow s\bar{\ell} \ell$ Decays

Abstract

The tension of $B\to K^{(*)}\bar\ell\ell$ decays with the Standard Model (SM) can be attributed to a short-distance (SD) $b s\bar\ell\ell$ interaction. We show two methods to disentangle this effect from long-distance (LD) dynamics. Firstly, we perform a comparison of the inclusive $b\to s\bar\ell\ell$ rate at high $q^2=m^2_{\ell\ell}\geq 15~\rm GeV^2$ with a determination based on data on the leading exclusive modes, finding a $\sim 2\sigma$ discrepancy. Secondly, we analyze the exclusive $B\to K^{(*)}\bar\ell\ell$ spectrum in the entire $q^2$ region. With a dispersive parametrization of the charmonia resonances, we extract the non-SM contribution to the Wilson coefficient $C_9$ for every bin in $q^2$. The result is compatible with the SD hypothesis and the inclusive determination. Finally, with the aim of having better control over LD effects that mimic the $C_9$ contribution, we estimate the size of a few charm-rescattering processes in $B\to K\bar\ell\ell$.