# Hadronic uncertainties in $B\to K^*\mu^+\mu^-$: a state-of-the-art analysis

## TL;DR

This paper critically examines hadronic uncertainties in the $B o K^*\mu^+\mu^-$ decay, arguing that certain Standard Model explanations are unlikely, and emphasizes the potential of specific observables to reveal New Physics effects.

## Contribution

The paper provides a detailed, pedagogical analysis of hadronic uncertainties in $B o K^*\mu^+\mu^-$, demonstrating the limitations of factorisable power corrections and charm contributions in explaining anomalies.

## Key findings

- Factorisable power corrections cannot explain observed anomalies.
- Long-distance charm effects are disfavoured as explanations.
- Optimized observables at low dilepton mass are sensitive to New Physics.

## Abstract

In the absence of direct evidence for New Physics at present LHC energies, the focus is set on the anomalies and discrepancies recently observed in rare $b \to s\ell\ell$ transitions which can be interpreted as indirect hints. Global fits have shown that an economical New Physics solution can simultaneously alleviate the tensions in the various channels and can lead to a significant improvement in the description of the data. Alternative explanations within the Standard Model for part of the observed anomalies have been proposed in terms of (unexpectedly large) hadronic effects at low dilepton invariant mass and attributing tensions in protected observables to statistical fluctuations or experimental errors. We review the treatment of hadronic uncertainties in this kinematic regime for one of the most important channels, $B \to K^*\mu^+\mu^-$, in a pedagogical way. We provide detailed arguments showing that factorisable power corrections cannot account for the observed anomalies and that an explanation through long-distance charm contributions is disfavoured. Some optimized observables at very low dilepton invariant mass are shown to be protected against contributions from the semileptonic coefficient $C_9$ (including any associated long-distance charm effects), enhancing their sensitivity to New Physics contributions to other Wilson coefficients. Finally, we discuss how the recent measurement of $Q_5$ by Belle (and in the future by LHCb and Belle-II) may provide a robust cross-check of our arguments.