Timelike-helicity y B → ππ form factor from light-cone sum rules with dipion distribution amplitudes

Abstract

We complete the set of QCD light-cone sum rules for B→ππ transition form factors, deriving a new sum rule for the timelike-helicity form factor F[subscript t] in terms of dipion distribution amplitudes. This sum rule, in the leading twist-two approximation, is directly related to the pion vector form factor. Employing a relation between F[subscript t] and other B→ππ form factors, we obtain also the longitudinal-helicity form factor F[subscript 0]. In this way, all four (axial-)vector B→ππ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.