Three-body final state interactions in B⁺→ DD̄K⁺ decays

This paper presents a detailed analysis of the three-body final state interactions in the B⁺→ DD̄K⁺ process, whose phase space is sufficient small. To precisely extract the resonance parameters, for instance the χc0/2(3930) in the DD̄ invariant mass distributions, in this process, one has to take into account final state interaction, especially the three-body final state interaction. We employ the dispersive Khuri-Treiman formalism, combined with a parameterization of the DD̄ interaction based on Heavy Quark Spin Symmetry. By performing a simultaneous fit to the experimental data from LHCb, BaBar, and Belle collaborations, the scheme with three-body interaction successfully describes the invariant mass distributions of the three two-body subsystems. We precisely extract the pole structures of χc0(3930) and $ψ(3770)$ as 3.913-0.018i~GeV and 3.764-0.002i~GeV in B⁺ decay. By performing the pole trajectory analysis on a uniformized complex plane, we find that both of them stem from the input bare state.