Roles of D^*K^* and D^*D molecular states in decay B^+ D^*+ D^- K^+

This study investigates the three-body decay process B^+ D^*+ D^- K^+, aiming to explore the possible origins of T^*₂ₒ₀ (2870) ⁰ and χ₂₁ (3872) as intermediate states. Within the molecular state framework, T^*₂ₒ₀ (2870) ⁰ and χ₂₁ (3872) are considered as possible D^*K^ and D^*D molecular states, respectively. Using effective Lagrangians, the interaction kernels of the D^*K^* and D^*D systems are constructed within the one-boson-exchange model. The corresponding rescattering amplitudes and pole positions are obtained by solving the quasipotential Bethe-Salpeter equation. These amplitudes are incorporated into the decay amplitude of the three-body process, and the D^-K^+ and D^*+D^- invariant mass spectra are simulated via Monte Carlo methods. To better reproduce the experimental data, additional Breit-Wigner contributions from T^*₂ₒ₁ (2900) ⁰, χ₂₁ (4010), and hc (4300) are included. The results show a pronounced enhancement near 2900 MeV in the D^-K^+ invariant mass spectrum, strongly supporting the interpretation of T^*₂ₒ₀ (2870) ⁰ as a D^*K^* molecular state. While the D^*K^* molecular state provides a reasonable contribution to the D^-K^+ spectrum, the D^*D molecular state yields no significant effect on either the D^-K^+ or D^*+D^- distributions. This suggests that the observed χ₂₁ (3872) structure around 3872 MeV may not be interpreted as a D^*D molecular state.