Searching for New Physics with $\overline{\mathcal{B}}(B_{s,d}\to\mu\bar\mu)/\Delta M_{s,d}$

TL;DR

This paper investigates the ratio of branching fractions to mass differences in B mesons as a clean probe for new physics, finding a 2-sigma tension with Standard Model predictions that is independent of CKM element uncertainties.

Contribution

The study introduces a refined analysis of the ratio $R_{s ext{mu}}$ as a robust test for new physics, incorporating higher order corrections and latest hadronic inputs, highlighting its independence from certain CKM uncertainties.

Findings

Identifies a 2-sigma tension between $R_{s ext{mu}}$ measurements and SM predictions.

Shows $R_{s ext{mu}}$ is unaffected by $|V_{cb}|$ uncertainties.

Discusses the potential of $R_{d ext{mu}}$ in future new physics searches.

Abstract

We reemphasize that the ratio $R_{s\mu} \equiv \overline{\mathcal{B}}(B_s\to\mu\bar\mu)/\Delta M_s$ is a measure of the tension of the Standard Model (SM) with latest measurements of $\overline{\mathcal{B}}(B_s\to\mu\bar\mu)$ that does not suffer from the persistent puzzle on the $|V_{cb}|$ determinations from inclusive versus exclusive $b\to c\ell\bar\nu$ decays and which affects the value of the CKM element $|V_{ts}|$ that is crucial for the SM predictions of both $\overline{\mathcal{B}}(B_s\to\mu\bar\mu)$ and $\Delta M_s$, but cancels out in the ratio $R_{s\mu}$. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about $2\sigma$ for $R_{s\mu}$ measurements with the SM independently of $|V_{ts}|$. We also discuss the ratio $R_{d\mu}$ which could turn out, in particular in correlation with $R_{s\mu}$, to be useful for the search for New Physics, when the data on both ratios improves. Also $R_{d\mu}$ is independent of $|V_{cb}|$ or more precisely $|V_{td}|$.