New tests of short-distance dynamics in $b \rightarrow s\bar{\ell} \ell$ decays

Abstract

The rare $B \to K^{(*)} \bar{\ell} \ell$ decays exhibit a long-standing tension with Standard Model (SM) predictions, which can be attributed to a lepton-universal short-distance $b \to s \bar{\ell} \ell$ interaction. We present two novel methods to disentangle this effect from long-distance dynamics: one based on the determination of the inclusive $b \to s \bar{\ell} \ell$ rate at high dilepton invariant mass ($q^2\geq 15~{\rm GeV}^2$), the other based on the analysis of the $q^2$ spectrum of the exclusive modes $B \to K^{(*)} \bar{\ell} \ell$ (in the entire $q^2$ range). Using the first method, we show that the SM prediction for the inclusive $b \to s \bar{\ell} \ell$ rate at high dilepton invariant mass is in good agreement with the result obtained summing the SM predictions for one- and two-body modes ($K$, $K^*$, $K\pi$). This observation allows us to perform a direct comparison of the inclusive $b \to s \bar{\ell} \ell$ rate with data. This comparison shows a significant deficit ($\sim 2\sigma$) in the data, fully compatible with the deficit observed at low-$q^2$ on the exclusive modes. This provides independent evidence of an anomalous $b \to s \bar{\ell} \ell$ short-distance interaction, free from uncertainties on the hadronic form factors. To test the short-distance nature of this effect we use a second method, where we analyze the exclusive $B \to K^{(*)} \bar{\ell} \ell$ data in the entire $q^2$ region. Here, after using a dispersive parametrization of the charmonia resonances, we extract the non-SM contribution to the universal Wilson coefficient $C_9$ for every bin in $q^2$ and for every polarization. The $q^2$- and polarization-independence of the result, and its compatibility with the inclusive determination, provide a consistency check of the short-distance nature of this effect.