Three-body final state interactions in B + → D D ¯ K + decays

This paper presents a detailed analysis of the three-body final state interactions in the B + → D D ¯ K + process, whose phase space is sufficient small. To precisely extract the resonance parameters, for instance the χ c 0 / 2 ( 3930 ) in the D D ¯ 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 parametrization of the D D ¯ interaction based on heavy quark spin symmetry. By performing a simultaneous fit to the experimental data from LHCb, , 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 χ c 0 ( 3930 ) and ψ ( 3770 ) as 3.913 − 0.016 i GeV and 3.761 − 0.006 i 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.