How large can the branching ratio of $B_s \to \tau^+ \tau^-$ be ?

TL;DR

This paper investigates the maximum possible branching ratio of the decay $B_s o au^+ au^-$ within current experimental constraints, finding it could be as high as 15% in some models, which may relate to recent anomalies.

Contribution

It provides a comprehensive analysis of the upper limits on $B_s o au^+ au^-$ branching ratio considering various constraints, highlighting potential new physics scenarios.

Findings

Branching ratio up to 15% is allowed in an effective field theory framework.

Scalar leptoquark models cannot enhance the decay to a percent level.

Light $Z'$ models can increase the branching ratio to about 5%, but not fully explain the dimuon anomaly.

Abstract

Motivated by the large like-sign dimuon charge asymmetry observed recently, whose explanation would require an enhanced decay rate of $B_s \to \tau^+ \tau^-$, we explore how large a branching ratio of this decay mode is allowed by the present constraints. We use bounds from the lifetimes of $B_d$ and $B_s$, constraints from the branching ratios of related $b \to s \tau^+ \tau^-$ modes, as well as measurements of the mass difference, width difference and CP-violating phase in the $B_s$-$\bar{B}_s$ system. Using an effective field theory approach, we show that a branching ratio as high as 15% may be allowed while being consistent with the above constraints. The model with a scalar leptoquark cannot increase the branching ratio to a per cent level. However, an enhancement up to 5% is possible in the model with an extremely light $Z'$ with flavor-dependent interactions, even after all the couplings are taken to be perturbative. This however cannot account for the dimuon anomaly completely by itself.