X₀ (2900) and ₂₀ (3930) in process B^+ D^+ D^- K^+

This study investigates the nature of the X₀ (2900) and ₂₀ (3930) based on experimental results of the process B^+D^+ D^- K^+. We focus on the S-wave D^*-K^*+ and Dₛ^+Dₛ^- molecular states, which can be related to the X₀ (2900) and ₂₀ (3930), respectively. Using effective Lagrangians, we construct the potential kernel of the D^*-K^*+-D^-K^+ and Dₛ^+Dₛ^--D^+D^- interactions with a one-boson-exchange model, and determine the scattering amplitudes and their poles through a quasipotential Bethe-Salpeter equation approach. By incorporating the potential kernel into the three-body decay process B^+D^+ D^- K^+, we evaluate the D^-K^+ and D^+D^- invariant mass spectra, as well as the Dalitz plot, with Monte Carlo simulation. A satisfactory fit to the D^-K^+ and D^+D^- invariant mass spectra is achieved after introducing additional Breit-Wigner resonances, the X₁ (2900), (3770), and ₂₂ (3930) states. Prominent signals of the X₀ (2900) and ₂₀ (3930) states appear as peaks in the D^-K^+ and D^+D^- invariant mass spectra near 2900 and 3930 MeV, respectively. Clear event concentration of the X₀ (2900) and ₀ (3930) states is evident as strips in the Dalitz plot. The results suggest that both X₀ (2900) and ₂₀ (3930) can be interpreted as molecular states, with the inclusion of X₁ (2900) and ₂ (3930) necessary to describe structures in the regions near 2900 and 3930 MeV.