Discovering the $$D_0^*(2100)$$ in B semileptonic decays Article Swipe
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· 2025
· Open Access
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· DOI: https://doi.org/10.1140/epjc/s10052-025-15035-7
· OA: W4416146492
The mass and width of the lightest scalar open-charm state listed in the Review of Particle Physics, the $$D_0^*(2300)$$ <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 $$B\rightarrow D \pi \ell \nu $$ <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 $$D\pi $$ <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 $$D_0^*(2100)$$ <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 $$D\pi $$ <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.
