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

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 $|V_{td}|$.

Comments: 14 pages, 2 figures; v2: updated experimental input and added discussion on top-quark-mass dependence, added references, conclusions unchanged; v3: matches published version, updated LHCb references