Timelike-helicity $B\to \pi\pi$ form factor from light-cone sum rules with dipion distribution amplitudes

TL;DR

This paper derives new light-cone sum rules for $B o ho ho$ transition form factors using dipion distribution amplitudes, connecting them to the pion vector form factor and predicting all relevant form factors for small dipion masses.

Contribution

It introduces a novel sum rule for the timelike-helicity form factor $F_t$ and relates it to other $B o ho ho$ form factors, expanding the theoretical toolkit for these transitions.

Findings

Derived a sum rule for $F_t$ in terms of dipion DAs.

Connected $F_t$ to the pion vector form factor.

Predicted all four $B o ho ho$ form factors for small dipion masses.

Abstract

We complete the set of QCD light-cone sum rules for $B\to \pi\pi$ transition form factors, deriving a new sum rule for the timelike-helicity form factor $F_t$ in terms of dipion distribution amplitudes. This sum rule, in the leading twist-2 approximation, is directly related to the pion vector form factor. Employing a relation between $F_t$ and other $B\to \pi\pi$ form factors we obtain also the longitudinal-helicity form factor $F_0$. In this way, all four (axial-)vector $B\to \pi\pi$ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.