Rare FCNC radiative leptonic decays $B\to \gamma {\ell }^{+}{\ell }^{-}$

Abstract

We present our recent results for long-distance QCD effects in the FCNC radiative leptonic decays $B\to \gamma {\ell }^{+}{\ell }^{-}$, $\ell =\{e,\mu \}$. One encounters here two distinct types of long-distance effects: those encoded in the $B\to \gamma$ transition form factors induced by the $b\to q$ quark currents, and those related to the charm-loop effects. We calculate the $B\to \gamma$ form factors in a broad range of the momentum transfers making use of the relativisitc dispersion approach based on the constituent quark picture which has proven to provide reliable predictions for many weak-transition form factors. Concerning the description of the charm-loop contributions, we point out two observations: First, the precise description of the charmonium resonances, in particular, the relative phases between $\psi$ and ${\psi }^{\prime }$, has impact on the differential distributions and on the forward-backward asymmetry, $A_{\mathrm{FB}}$, in a broad range of $q^2\ge 5$ GeV${}^2$. Second, the shape of $A_{\mathrm{FB}}$ in $B\to \gamma {\ell }^{+}{\ell }^{-}$ and in $B\to V{\ell }^{+}{\ell }^{-}$ ($V$ the vector meson) {\it in the $q^2$-region between $\psi$ and ${\psi }^{\prime }$} provides an unambiguous probe of the relative phases between $\psi$ and ${\psi }^{\prime }$. Fixing the latter will lead to a strong reduction of the theoretical uncertainties in $A_{\mathrm{FB}}$ at $q^2=5-9$ GeV${}^2$ where it has the sensitivity to physics beyond the SM.

Comments: 6 pages, talk given at "The European Physical Society Conference on High Energy Physics - EPS-HEP 2017" (5 - 12 July 2017, Venice, Italy)