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

TL;DR

This paper develops a new parametrization for $B o ho ho$ form factors at large dipion masses, combining QCD factorization and analyticity constraints, to improve decay rate predictions relevant for Belle II.

Contribution

It introduces a novel form factor parametrization that unifies QCDF results with analytic constraints, enabling more accurate predictions of $B o ho ho \, \ell\nu$ decay rates.

Findings

Predicted a $B\to \pi\pi\ell\nu$ branching ratio up to $10^{-6}$.

Demonstrated the potential for Belle II to measure non-resonant semileptonic decays.

Provided a new framework for form factor analysis 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 $B^*$ 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.