Discovering the $D_0^\ast(2100)$ in $B$ semileptonic decays

The mass and width of the lightest scalar open-charm state listed in the Review of Particle Physics, the $D_0^\ast(2300)$, are in puzzling tension with predictions from unitarized chiral perturbation theory (UChPT) and lattice QCD, which favor a lighter state at around $2100$ MeV. However, to date, no direct experimental evidence for this lighter state exists. In an effort to facilitate a direct observation, we introduce angular asymmetries of $B\rightarrow D \pi \ell \nu$ decays that allow for a direct extraction of the $D\pi$ S-wave phase shift and discuss a novel measurement strategy for the Belle II experiment. We conduct a sensitivity study, finding that the Belle II experiment can determine the pole location with sufficient precision to firmly establish the $D_0^\ast(2100)$ using the currently available data set. We also investigate the possibility and necessary statistics of measuring the $D\pi$ isospin 1/2 scattering length with an accuracy sufficient to distinguish between the predictions from both UChPT and lattice QCD and the measurement by ALICE using femtoscopy.