Coupled-channel analysis of $D^+\to K^- π^+π^+$ decay

Abstract: We perform a coupled-channel analysis of pseudodata for the D+-> K-pi+pi+ Dalitz plot. The pseudodata are generated from the isobar model of the E791 Collaboration, and are reasonably realistic. We demonstrate that it is feasible to analyze the high-quality data within a coupled-channel framework that describes the final state interaction of D+-> K-pi+pi+ as multiple rescatterings of three pseudoscalar mesons through two-pseudoscalar-meson interactions in accordance with the two-body and three-body unitarity. The two-pseudoscalar-meson interactions are designed to reproduce empirical pi pi and pi bar K scattering amplitudes. Furthermore, we also include mechanisms that are beyond simple iterations of the two-body interactions, i.e., a three-meson force, derived from the hidden local symmetry model. A picture of hadronic dynamics in D+-> K-pi+pi+ described by our coupled-channel model is found to be quite different from those of the previous isobar-type analyses. For example, we find that the D+-> K-pi+pi+ decay width can get almost triplicated when the rescattering mechanisms are turned on. Among the rescattering mechanisms, those associated with the rho(770) bar K0 channel, which contribute to D+-> K-pi+pi+ only through a channel coupling, give a large contribution, and significantly improve the quality of the fits. The K-pi+ s-wave amplitude from our analysis is reasonably consistent with those extracted from the E791 model independent partial-wave analysis; the hadronic rescattering and the coupling to the rho(770) bar K0 channel play a major role here. We also find that the dressed D+ decay vertices have phases, induced by the strong rescatterings, that strongly depend on the momenta of the final pseudoscalar mesons. Although the conventional isobar-type analyses have assumed the phases to be constant, this common assumption is not supported by our more microscopic viewpoint.