Short- vs. long-distance physics in $B\to K^{(*)} \ell^+\ell^-$: a data-driven analysis

TL;DR

This paper performs a comprehensive data-driven analysis of $B o K^{(*)} o \, ext{dilepton}$ decays across all invariant mass ranges to distinguish short- and long-distance effects, revealing potential signs of new physics.

Contribution

It introduces a dispersive approach to account for long-distance resonances and independently determines the Wilson coefficient $C_9$ in each bin, testing the consistency with the Standard Model.

Findings

Long-distance contributions from $c\bar{c}$ resonances are effectively modeled.

The extracted $C_9$ values show systematic deviations from the Standard Model.

Results suggest possible non-standard short-distance $b\to s\mu^+^-$ amplitudes.

Abstract

We analyze data on $B\to K\mu^+\mu^-$ and $B\to K^*\mu^+\mu^-$ decays in the whole dilepton invariant mass spectrum with the aim of disentangling short- vs. long-distance contributions. The sizable long-distance amplitudes from $c \bar{c}$ narrow resonances are taken into account by employing a dispersive approach. For each available $q^2=m_{\mu\mu}^2$ bin and each helicity amplitude an independent determination of the Wilson coefficient $C_9$, describing $b\to s\ell^+\ell^-$ transitions at short distances, is obtained. The consistency of the $C_9$ values thus obtained provides an a posteriori check of the absence of additional, sizable, long-distance contributions. The systematic difference of these values from the Standard Model expectation supports the hypothesis of a non-standard $b\to s \mu^+\mu^-$ amplitude of short-distance origin.