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

Abstract This study investigates the nature of the X₀ (2900) X 0 (2900) and ₂₀ (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 ₂₀ (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), (3770) ψ (3770), and ₂₂ (3930) χ c 2 (3930). Prominent signals of the X₀ (2900) X 0 (2900) and ₂₀ (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 ₀ (3930) χ 0 (3930) is evident as strips in the Dalitz plot. The results suggest that both X₀ (2900) X 0 (2900) and ₂₀ (3930) χ c 0 (3930) can be interpreted as molecular states, with the inclusion of X₁ (2900) X 1 (2900) and ₂ (3930) χ 2 (3930) necessary to describe structures in the D^-K^+ D - K + and D^+D^- D + D - invariant mass spectra, respectively.