Abstract
We study the rare radiative leptonic decays ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}\ensuremath{\gamma}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$) within the Standard Model, considering both the structure-dependent amplitude and bremsstrahlung. In the framework of the covariant confined quark model developed by us, we calculate the form factors characterizing the ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}$ transition in the full kinematical region of the dilepton momentum squared and discuss their behavior. We provide the analytic formula for the differential decay distribution and give predictions for the branching fractions in both cases: with and without long-distance contributions. Finally, we compare our results with those obtained in other approaches.
Highlights
The rare radiative decays Bq → lþl−γ with l 1⁄4 e, μ, τ and q 1⁄4 d, s are of great interest for several reasons
They are complementary to the well-known decays B → KðÃÞlþl− and provide us with extra tests of the Standard Model (SM) predictions for processes which proceed at loop level
Using various techniques described in our previous papers, a form factor F can be written in the form of a threefold integral dtt dα1 dα2δð1 − α1 − α2Þfðtα1; tα2Þ; ð7Þ
Summary
The rare radiative decays Bq → lþl−γ with l 1⁄4 e, μ, τ and q 1⁄4 d, s are of great interest for several reasons. In this paper we calculate the matrix elements and the differential decay rates of the decays Bs → lþl−γ in the framework of the covariant confined quark model previously developed by us The interaction with the electromagnetic field is introduced by gauging the interaction Lagrangian in such a way as to keep the gauge invariance of the matrix elements at all calculation steps This model has been successfully applied for the description of the matrix elements and form factors in the full kinematical region in semileptonic and rare decays of heavy mesons as well as baryons
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