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

Abstract

We introduce a new parameterization of $B\to D\pi \ell \nu$ 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.

Comments: 13 pages, 4 wonderful figures; Extended supplementary material, results and conclusions unchanged; Version accepted by PRD