On the Standard Model prediction for BR(B{s,d} to mu+ mu-)

TL;DR

This paper reevaluates the Standard Model prediction for the rare decay B_s to mu+ mu-, emphasizing the importance of higher-order electroweak corrections and soft radiation effects, resulting in refined branching ratio estimates.

Contribution

It provides a comprehensive analysis of electroweak corrections and soft radiation effects, leading to more accurate Standard Model predictions for B_s and B_d to mu+ mu- decays.

Findings

Non-radiative BR(B_s to mu+ mu-) = (3.23 +/- 0.27) x 10^{-9}

Non-radiative BR(B_d to mu+ mu-) = (1.07 +/- 0.10) x 10^{-10}

Electroweak corrections can be negligible in a specific scheme.

Abstract

The decay Bs to mu+ mu- is one of the milestones of the flavor program at the LHC. We reappraise its Standard Model prediction. First, by analyzing the theoretical rate in the light of its main parametric dependence, we highlight the importance of a complete evaluation of higher-order electroweak corrections, at present known only in the large-mt limit, and leaving sizable dependence on the definition of electroweak parameters. Using insights from a complete calculation of such corrections for K to pi bar{nu} nu decays, we find a scheme in which NLO electroweak corrections are likely to be negligible. Second, we address the issue of the correspondence between the initial and the final state detected by the experiments, and those used in the theoretical prediction. Particular attention is devoted to the effect of the soft radiation, that has not been discussed for this mode in the previous literature, and that can lead to O(10%) corrections to the decay rate. The "non-radiative" branching ratio (that is equivalent to the branching ratio fully inclusive of bremsstrahlung radiation) is estimated to be (3.23 +/- 0.27) x 10^{-9} for the flavor eigenstate, with the main uncertainty resulting from the value of f_{Bs}, followed by the uncertainty due to higher order electroweak corrections. Applying the same strategy to Bd to mu+ mu-, we find for its non-radiative branching ratio (1.07 +/- 0.10) x 10^{-10}.