X₀(2900) and χ c0(3930) in process B⁺→ D⁺ D⁻ K⁺

This study investigates the nature of the X₀(2900) X 0 ( 2900 ) and χ c0(3930) χ c 0 ( 3930 ) based on experimental results of the process B⁺ B + → → D⁺ D⁻ K⁺ D + D - K + . We focus on the S-wave D*-K*+ D ∗ - K ∗ + and Dₛ⁺Dₛ⁻ D s + D s - molecular states, which can be related to the X₀(2900) X 0 ( 2900 ) and χ c0(3930) χ c 0 ( 3930 ) , respectively. Using effective Lagrangians, we construct the potential kernel of the D*-K*+ D ∗ - K ∗ + – D⁻K⁺ D - K + and Dₛ⁺Dₛ⁻ D s + D s - – D⁺D⁻ 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⁺ B + → → D⁺ D⁻ K⁺ D + D - K + , we evaluate the D⁻K⁺ D - K + and D⁺D⁻ D + D - invariant mass spectra, as well as the Dalitz plot, using Monte Carlo simulation. A satisfactory fit to the D⁻K⁺ D - K + and D⁺D⁻ D + D - invariant mass spectra is achieved after introducing additional Breit–Wigner resonances, X₁(2900) X 1 ( 2900 ) , ψ (3770) ψ ( 3770 ) , and χ c2(3930) χ c 2 ( 3930 ) . Prominent signals of the X₀(2900) X 0 ( 2900 ) and χ c0(3930) χ c 0 ( 3930 ) states appear as peaks in the D⁻K⁺ D - K + and D⁺D⁻ D + D - invariant mass spectra near 2900 and 3930 MeV, respectively. Clear event concentration from the X₀(2900) X 0 ( 2900 ) and χ ₀(3930) χ 0 ( 3930 ) is evident as strips in the Dalitz plot. The results suggest that both X₀(2900) X 0 ( 2900 ) and χ c0(3930) χ c 0 ( 3930 ) can be interpreted as molecular states, with the inclusion of X₁(2900) X 1 ( 2900 ) and χ ₂(3930) χ 2 ( 3930 ) necessary to describe structures in the D⁻K⁺ D - K + and D⁺D⁻ D + D - invariant mass spectra, respectively.