Strange quark mass effect in Bs→γγ, γℓℓ¯ decays

Abstract

In this paper we investigate the next-to-leading power contribution to the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decays from the strange quark mass effect with the dispersion approach which is QCD inspired and more predictive. We present the analytic expression of the quark mass contribution in the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decays, together with a new term that is missed in the previous study. We also evaluate the resolved photon contribution from the A-type amplitude in ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decay. The numerical results of the strange quark mass contribution to the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decay is about 6% relative to the total branching ratio, while it is relatively small in the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\overline{\ensuremath{\ell}}$ decay due to the large resonance contribution.