QCD light-cone sum rules for B to dipion transition form factors

Abstract

The form factors of the semileptonic $B\to \pi\pi\ell\bar\nu$ decay are calculated from QCD light-cone sum rules, employing as a nonperturbative input the distribution amplitudes of dipion states. In the leading twist-2 approximation, we predict all $\bar{B}^0\to \pi^+\pi^0$ form factors in the kinematic region, where the hadronic dipion state has a small invariant mass and simultaneously a large recoil. The sum rule results reveal a suppression of the higher partial waves in the form factors and indicate that the lowest $P$-wave contribution is not saturated by the $\rho$-meson term.