Revisiting $B\to \pi \pi \ell \nu$ at Large Dipion Masses

Abstract

We revisit QCD factorization of $B\to \pi \pi$ form factors at large dipion masses, by deriving new constraints based on the analyticity properties of these objects. We then propose a parametrization of the form factors, inspired by the leading-twist QCD factorization formula, that incorporates all known analytic properties. This parameterization is used to interpolate between the QCDF results and the constraints from the $B^{\ast }$ pole. Based on this interpolation, we predict the $B\to \pi \pi \ell \nu$ decay rate in a larger phase space region than previous studies could. We obtain a partially-integrated branching ratio up to $\mathcal{B}\simeq \mathcal{O}(10^{-6})$, which implies that a measurement of the non-resonant semileptonic decay is potentially within reach of the Belle II experiment.

Comments: 15 pages, 1 figure, 2 tables