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

Abstract

We reemphasize that the ratio Rsμ ≡ B(Bs → μμ̄)/∆Ms is a measure of the tension of the Standard Model (SM) with latest measurements of B(Bs → μμ̄) that does not suffer from the persistent puzzle on the |Vcb| determinations from inclusive versus exclusive b→ c`ν̄ decays and which affects the value of the CKM element |Vts| that is crucial for the SM predictions of both B(Bs → μμ̄) and ∆Ms, but cancels out in the ratio Rsμ. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about 2σ for Rsμ measurements with the SM independently of |Vts|. We also discuss the ratio Rdμ which could turn out, in particular in correlation with Rsμ, to be useful for the search for New Physics, when the data on both ratios improves. Also Rdμ is independent of |Vcb| or more precisely |Vtd|. ar X iv :2 10 4. 09 52 1v 1 [ he pph ] 1 9 A pr 2 02 1