A model independent description of $B\rightarrow D π\ell ν$ decays

Abstract

We introduce a new parameterization of $B\rightarrow D π\ell ν$ 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 $B \to D \ell ν$ 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 $B \to D_2^\ast(\to Dπ) \ell ν$ 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 $Dπ$ S-wave in semileptonic decays employing lineshapes from unitarized chiral perturbation theory.