A model independent description of $B\rightarrow D \pi \ell \nu$ decays

TL;DR

This paper develops a model-independent framework for describing $B ightarrow D ext{pi} ext{l} u$ decays, enabling robust data-driven form factor analysis with systematic uncertainty control.

Contribution

It generalizes the Boyd-Grinstein-Lebed formalism to multi-hadron final states, allowing for systematic, model-independent form factor extraction in semileptonic decays.

Findings

Extracted $B o D_2^* o D ext{pi} ext{l} u$ form factors from Belle data.

Studied the two-pole structure in the $D ext{pi}$ S-wave using unitarized chiral perturbation theory.

Provided bounds on series coefficients using analyticity and unitarity.

Abstract

We introduce a new parameterization of $B\rightarrow D \pi \ell \nu$ form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the model-independent formalism developed by Boyd, Grinstein, and Lebed for $B \to D \ell \nu$ to semileptonic decays with multi-hadron final states, and enables data-driven form factor determinations with robust, systematically-improvable uncertainties. Using this formalism, we extract the form-factor parameters for $B \to D_2^\ast(\to D\pi) \ell \nu$ decays in a model-independent way from fits of data from the Belle Experiment, and, for the first time, study the two-pole structure in the $D\pi$ S-wave in semileptonic decays employing lineshapes from unitarized chiral perturbation theory.