$$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) in process $$B^+\rightarrow D^+ D^- K^+$$ B + → D + D - K +

Abstract

Abstract This study investigates the nature of the $$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) based on experimental results of the process $$B^+$$ B + $$\rightarrow $$ → $$D^+ D^- K^+$$ D + D - K + . We focus on the S-wave $$D^{*-}K^{*+}$$ D ∗ - K ∗ + and $$D_s^+D_s^-$$ D s + D s - molecular states, which can be related to the $$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) , respectively. Using effective Lagrangians, we construct the potential kernel of the $$D^{*-}K^{*+}$$ D ∗ - K ∗ + – $$D^{-}K^{+}$$ D - K + and $$D_s^+D_s^-$$ 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 + $$\rightarrow $$ → $$D^+ D^- K^+$$ 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, $$X_1(2900)$$ X 1 ( 2900 ) , $$\psi (3770)$$ ψ ( 3770 ) , and $$\chi _{c2}(3930)$$ χ c 2 ( 3930 ) . Prominent signals of the $$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _{c0}(3930)$$ 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 $$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _0(3930)$$ χ 0 ( 3930 ) is evident as strips in the Dalitz plot. The results suggest that both $$X_0(2900)$$ X 0 ( 2900 ) and $$\chi _{c0}(3930)$$ χ c 0 ( 3930 ) can be interpreted as molecular states, with the inclusion of $$X_1(2900)$$ X 1 ( 2900 ) and $$\chi _2(3930)$$ χ 2 ( 3930 ) necessary to describe structures in the $$D^-K^+$$ D - K + and $$D^+D^-$$ D + D - invariant mass spectra, respectively.