X₀(2900) and χc0(3930) in process B⁺→ D⁺ D⁻ K⁺

This study investigates the nature of the X₀(2900) and χc0(3930) based on experimental results of the process B⁺⁺ D⁻ K⁺. We focus on the S-wave D*-K*+ and Dₛ⁺Dₛ⁻ molecular states, which can be related to the X₀(2900) and χc0(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⁻ 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), ψ(3770), and χc2(3930) states. Prominent signals of the X₀(2900) and χc0(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 χ₀(3930) states is evident as strips in the Dalitz plot. The results suggest that both X₀(2900) and χc0(3930) can be interpreted as molecular states, with the inclusion of X₁(2900) and χ₂(3930) necessary to describe structures in the regions near 2900 and 3930 MeV.