How large can the branching ratio of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\mathbf{+}}{\ensuremath{\tau}}^{\mathbf{\ensuremath{-}}}$ be?

How large can the branching ratio of $B_{s} \to τ^{+} τ^{-}$ be?

Amol Dighe and Diptimoy Ghosh

Phys. Rev. D 86, 054023 – Published 25 September 2012

Abstract

Motivated by the large like-sign dimuon charge asymmetry observed recently, whose explanation would require an enhanced decay rate of $B_{s} \to τ^{+} τ^{-}$ , 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 $b \to s τ^{+} τ^{-}$ modes, as well as measurements of the mass difference, width difference and $C P$ -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 measurement of this decay, therefore, may be within the reach of current experiments and can point toward a specific class of new physics models. We also explore the possible enhancement of this decay in models with leptoquarks and $Z^{'}$ and find that, in the latter case, the branching ratio may be as much as 5%, which can alleviate the dimuon anomaly to some extent.