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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 allowedby 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 andCP-violating phase in the $B_s$-$\bar{B}_s$ system. Using an effective fieldtheory approach, we show that a branching ratio as high as 15% may be allowedwhile being consistent with the above constraints. The model with a scalarleptoquark cannot increase the branching ratio to a per cent level. However, anenhancement up to 5% is possible in the model with an extremely light $Z'$ withflavor-dependent interactions, even after all the couplings are taken to beperturbative. This however cannot account for the dimuon anomaly completely byitself.

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