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

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.