Impact on the decay rate of Bs→μ+μ− from the dispersive two-photon transition

Abstract

We study the long-distance contribution to ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay, which is generated by the two-photon intermediate state via the ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ transition. It is found that the dispersive two-photon amplitude can interfere with the dominant short-distance amplitude, which gives rise to new theoretical uncertainty in the branching ratio of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Our analysis shows that, by taking into account present experimental constraints, this uncertainty could be up to the same order of magnitude as some theoretical uncertainties of $\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ given in the past literature. Future precise studies of the double radiative ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decay, both experimentally and theoretically, may help to reduce the uncertainty. This novel effect has never been examined in ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay.