  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 $|V_{td}|$.
