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

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Journal of High Energy Physics

, Volume 2017, Issue 5, pp 1–25

First Online: 30 May 2017Received: 24 January 2017Revised: 30 April 2017Accepted: 19 May 2017DOI: 10.1007-JHEP052017157

Cite this article as: Cheng, S., Khodjamirian, A. & Virto, J. J. High Energ. Phys. 2017 2017: 1. doi:10.1007-JHEP052017157 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\to \pi \pi \ell {\overline{ u}} {\ell } \, and constitute an essential input in B → ππℓℓ 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 -wave \ {\overline{B}}^0\to {\pi}^{+}{\pi}^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.

KeywordsHeavy Quark Physics Quark Masses and SM Parameters ArXiv ePrint: 1701.01633

Autor: Shan Cheng - Alexander Khodjamirian - Javier Virto