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

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 $Z^{\prime }$ 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.

Typos corrected, some discussions added, accepted for publication in Phys.Rev.D

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