Roles of D̄*K* and D^*D̄ 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^*c̄s̄0(2870)⁰ and χc1(3872) as intermediate states. Within the molecular state framework, T^*c̄s̄0(2870)⁰ and χc1(3872) are considered as possible D̄*K^ and D^*D̄ molecular states, respectively. Using effective Lagrangians, the interaction kernels of the D̄*K* and D^*D̄ 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^*c̄s̄1(2900)⁰, χc1(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^*c̄s̄0(2870)⁰ as a D̄*K* molecular state. While the D̄*K* molecular state provides a reasonable contribution to the D⁻K⁺ spectrum, the D^*D̄ molecular state yields no significant effect on either the D⁻K⁺ or D*+D⁻ distributions. This suggests that the observed χc1(3872) structure around 3872 MeV may not be interpreted as a D^*D̄ molecular state.