# Correlating Lepton Flavour (Universality) Violation in $B$ Decays with $\mu\to e\gamma$ using Leptoquarks

## TL;DR

This paper investigates how leptoquark models can explain lepton flavor violation observed in B decays and its connection to muon-to-electron gamma decay, providing a comprehensive analysis of possible new physics signals.

## Contribution

It offers a detailed correlation analysis of B decay anomalies and lepton flavor violation within all scalar and vector leptoquark representations, including loop effects and phenomenological implications.

## Key findings

- New physics in muons is necessary to fit data.
- Couplings to electrons can be large without violating bounds.
- Predicted effects in $b\to s\mu e$ transitions are within experimental reach.

## Abstract

Motivated by the measurements of $b\to s\ell^+\ell^-$ transitions, including $R(K)$ and $R(K^*)$, we examine lepton flavour (universality) violation in $B$ decays and its connections to $\mu\to e\gamma$ in generic leptoquark models. Considering all 10 representations of scalar and vector leptoquarks under the Standard Model gauge group we compute the tree-level matching for semileptonic $b$-quark operators as well as their loop effects in $\ell\to\ell^\prime\gamma$. In our phenomenological analysis we correlate $R(K)$, $R(K^*)$ and the other $b\to s\mu^+\mu^-$ data to $\mu\to e\gamma$ and $b\to s\mu e$ transitions for the three leptoquark representations that generate left-handed currents in $b\to s\ell^+\ell^-$ transitions and, therefore, provide a good fit to data. We find that while new physics contributions to muons are required by the global fit, also couplings to electrons can be sizeable without violating the stringent bounds from $\mu\to e\gamma$. In fact, if the effect in electrons in $b\to s\ell^+\ell^-$ has opposite sign than the effect in muons the bound from $\mu\to e\gamma$ can always be avoided. However, unavoidable effects in $b\to s\mu e$ transitions (i.e. $B_s\to\mu e$, $B\to K\mu e$, etc.) appear which are within the reach of LHCb and BELLE II.