We present our recent results for long-distance QCD effects in the flavour-changing neutral current radiative leptonic decays B→γℓ+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, AFB, in a broad range of q2≥5 GeV2. Second, the shape of AFB in B→γℓ+ℓ− and in B→Vℓ+ℓ− (V the vector meson) {\it 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 AFB at q2=5−9 GeV2 where it has the sensitivity to physics beyond the SM.
