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

TL;DR

The paper addresses the tension between the established $D_0^*(2300)$ and lighter predictions near $2100$ MeV from UChPT and lattice QCD, proposing a direct extraction of the $D\pi$ S-wave phase via semileptonic $B$ decays. It develops a three-channel S-wave plus narrow P-wave formalism, incorporating the Adler zero, and constructs angular observables whose ratios yield $\tan(\delta_0-\delta_1)$ for a model-independent phase determination. A Belle II–focused measurement strategy using hadronic tagging is described, with pseudo-data studies showing that the $D_0^*(2100)$ pole can be established and the isospin-1/2 scattering length measured with sufficient precision to distinguish UChPT, lattice QCD, and ALICE femtoscopy. The work provides projections across luminosities up to $10~\mathrm{ab}^{-1}$ and highlights experimental and theoretical avenues for future refinement.

Abstract

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 $B\rightarrow D π\ell ν$ decays that allow for a direct extraction of the $Dπ$ 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 $Dπ$ 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.

Figures (5)

• Figure 1: Diagram for the semileptonic decay $B\to D\pi/D\eta/D_s\bar{K}$ at the quark level.
• Figure 2: Illustrative schematic of the equivalence between the two-dimensional asymmetry categories and the simplified one-dimensional categories. The asymmetry variables are defined as differences between yields of $+$ (blue) and $-$ (yellow) regions of their respective angular variable(s). The upper observable is proportional to $\mathrm{Im}(f_+f_1^\ast)$ and the lower one to $\mathrm{Re}(f_+ f_1^\ast)$.
• Figure 3: Illustrative schematic of the equivalence between the one-dimensional asymmetry categories and the simplified one-dimensional categories. The asymmetry variables are defined as differences between yields of $+$ (blue) and $-$ (yellow) regions of their respective angular variable(s). The upper observable is proportional to $\mathrm{Im}(f_+g_1^\ast)$ and the lower one to $\mathrm{Re}(f_+ g_1^\ast)$.
• Figure 4: The pole location $M + i\Gamma/2$ extracted from the pseudo-data generated from the amplitude of Ref. Liu:2012zya in the mass versus width plane. For the five different scenarios we show the $68\%$ confidence contours. In addition, we show the pole location from Ref. Du:2017zvv, as well as the average from the RPP ParticleDataGroup:2024cfk.
• Figure 5: Example scattering phase fit for the $5~\text{ab}^{-1}$ scenario. The pseudo-data is shown together with the result of the fit to the parameterization in Eq. \ref{['eq:eff2']} and a curve obtained from ALICE' measurement of $a_0^{(1/2)}$, but neglecting the higher orders in the effective range expansion ($r_i^{(1/2)} = 0$ in Eq. \ref{['eq::ere']}).