B →ππ form factors from light-cone sum rules with B-meson distribution amplitudes

Abstract

We study B → ππ form factors using QCD light-cone sum rules with B-meson distribution amplitudes. These form factors describe the semileptonic decay B → ππ ν , and constitute an essential input in B → ππ + − and B → πππ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the P -waveB 0 → π + π 0 form factors with the timelike pion vector form factor are related to universal B-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for B → ρ form factors in the limit of ρ-dominance and zero width, thus providing a systematics for so far unaccounted corrections to B → ρ transitions. Using data for the pion vector form factor, we estimate finite-width effects and the contribution of excited ρ-resonances to the B → ππ form factors. We find that these contributions amount up to ∼ 20% in the small dipion mass region where they can be effectively regarded as a nonresonant (P -wave) background to the B → ρ transition.

Light-cone sum rules for B → K π form factors and applications to rare decays

“…This generalizes the results of Ref. [18] to the case where the two mesons have different masses. We also include the tensor form factors that were not considered in that reference.…”

“…As discussed originally in Ref. [18], the LCSRs with B-meson LCDAs provide a natural framework to perform this generalization, making also the relationship with the narrow-width limit completely transparent. This method was used in Ref.…”

“…This method was used in Ref. [18] to study the B → ππ form factors and their relation to B → ρ transitions. The purpose of the present article is to derive the corresponding LCSRs for B → Kπ form factors, and to study some of the phenomenological implications, with a focus on the semileptonic decay B → Kπ both on and off resonance.…”

CP violation in multibody B decays from QCD factorization

“…The isovector form factor F I=1 t has been studied using QCD light-cone sum rules in [23,24], (see also [25] for a similar study of the other P -wave form factors). Analogous studies of the isoscalar form factor F I=0 t have not been performed.…”

“…In addition, these models can be fitted separately to the light-cone sum rules with B distribution amplitudes, as done in ref. [23].…”