# New Physics in $b \to s \mu^+ \mu^-$ after the Measurement of $R_{K^*}$

## TL;DR

Recent measurements of $R_{K^*}$ suggest new physics in $b o s \mu^+\mu^-$ decays, with specific scenarios involving $Z'$ or leptoquark models fitting the data and constraints.

## Contribution

The paper combines model-independent and model-dependent analyses to identify viable new physics scenarios explaining $b o s \mu^+\mu^-$ anomalies, especially after $R_{K^*}$ measurement.

## Key findings

- Two main NP scenarios: $C_9^{\mu\mu}({
m NP}) < 0$ or $C_9^{\mu\mu}({
m NP}) = - C_{10}^{\mu\mu}({
m NP}) < 0.
- Scenario involving $C_9^{\mu\mu}({
m NP}) = - C_{9}^{\prime \mu\mu}({
m NP})$ is rejected due to $R_K$ discrepancy.
- Light $Z'$ bosons are compatible with constraints, while leptoquarks are necessarily heavy.

## Abstract

The recent measurement of $R_{K^*}$ is yet another hint of new physics (NP), and supports the idea that it is present in $b\to s\mu^+\mu^-$ decays. We perform a combined model-independent and model-dependent analysis in order to deduce properties of this NP. Like others, we find that the NP must obey one of two scenarios: (I) $C_9^{\mu\mu}({\rm NP}) < 0$ or (II) $C_9^{\mu\mu}({\rm NP}) = - C_{10}^{\mu\mu}({\rm NP}) < 0$. A third scenario, (III) $C_9^{\mu\mu}({\rm NP}) = - C_{9}^{\prime \mu\mu}({\rm NP})$, is rejected largely because it predicts $R_K = 1$, in disagreement with experiment. The simplest NP models involve the tree-level exchange of a leptoquark (LQ) or a $Z'$ boson. We show that scenario (II) can arise in LQ or $Z'$ models, but scenario (I) is only possible with a $Z'$. Fits to $Z'$ models must take into account the additional constraints from $B^0_s$-${\bar B}^0_s$ mixing and neutrino trident production. Although the LQs must be heavy, O(TeV), we find that the $Z'$ can be light, e.g., $M_{Z'} = 10$ GeV or 200 MeV.