Three-parton contribution to the $B\to\pi$ form factors in $k_T$ factorization

TL;DR

This paper calculates the three-parton twist-3 contribution to the $B\to\pi$ form factors within the $k_T$ factorization framework, revealing it is a small correction at large pion recoil.

Contribution

It introduces a method to analyze three-parton contributions to $B$ meson decays using $k_T$ factorization, including the dominant diagrams and their quantitative impact.

Findings

Three-parton twist-3 contribution is a few percent of the form factors.

The dominant contribution comes from diagrams with an additional valence gluon attaching to the leading-order hard gluon.

The framework for analyzing three-parton contributions in $k_T$ factorization is established.

Abstract

We calculate the three-parton twist-3 contribution to the $B\to\pi$ transition form factors in the $k_T$ factorization theorem. Since different mesons are involved in the initial and final states, two(three)-parton-to-three(two)-parton amplitudes do not vanish. It is found that the dominant contribution arises from the diagrams with the additional valence gluon attaching to the leading-order hard gluon. Employing the three-parton meson distribution amplitudes from QCD sum rules, we show that this subleading piece amounts only up to few percents of the form factors at large recoil of the pion. The framework for analyzing three-parton contributions to $B$ meson decays in the $k_T$ factorization is established.