$B_{d,s}\to\gamma\ell\bar{\ell}$ decay with an energetic photon

Understand

We calculate the differential branching fraction, lepton forward-backward asymmetry and direct CP asymmetry for $B_{d,s}\to\gamma\ell\bar{\ell}$ decays with an energetic photon.

• We employ factorization methods, which result in rigorous next-to-leading order predictions in the strong coupling at leading power in the large-energy/heavy-quark expansion, together with estimates of power corrections and a resonance parameterization of sub-leading power form factors in the region of small lepton invariant mass $q^2$.
• The $B_{d,s}\to\gamma\ell\bar{\ell}$ decay shares features of the charged-current decay $B_u \to \gamma\ell\bar\nu_\ell$, and the FCNC decays $B\to K^{(*)}\ell\bar\ell$.
• As in the former, the leading-power decay rates can be expressed in terms of the $B$-meson light-cone distribution amplitude and short-distance factors.