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

The mass and width of the lightest scalar open-charm state listed in the Review of Particle Physics, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo></mml:msubsup> <mml:mrow><mml:mo>(</mml:mo> <mml:mn>2300</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>D</mml:mi> <mml:mi>π</mml:mi> <mml:mi>ℓ</mml:mi> <mml:mi>ν</mml:mi></mml:mrow> </mml:math> decays that allow for a direct extraction of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi> <mml:mi>π</mml:mi></mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>D</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo></mml:msubsup> <mml:mrow><mml:mo>(</mml:mo> <mml:mn>2100</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> </mml:math> using the currently available data set. We also investigate the possibility and necessary statistics of measuring the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi> <mml:mi>π</mml:mi></mml:mrow> </mml:math> 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.