Rare FCNF radiative leptonic decays b → γℓ⁺ℓ^-

We present our recent results [1] for long-distance QCD effects in the flavour-changing neutral current radiative leptonic decays B → γ ℓ⁺ ℓ⁻, ℓ = {e, µ }. One encounters here two distinct types of long-distance effects: Those encoded in the B → γ transition form factors induced by the b → q quark currents, and those related to the charm-loop effects. We calculate the B → γ 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 ψ and ψ ^′, has impact on the differential distributions and on the forward-backward asymmetry, A_FB, in a broad range of q² ≥ 5 GeV². Second, the shape of A_FB in B → γ ℓ⁺ ℓ⁻ and in B → V ℓ⁺ ℓ− (V the vector meson) in the q²-region between ψ and ψ ^′ provides an unambiguous probe of the relative phases between ψ and ψ ^′. Fixing the latter will lead to a strong reduction of the theoretical uncertainties in A_FB at q² = 5 − 9 GeV² where it has the sensitivity to physics beyond the SM.