Three-particle formalism for multiple channels: the ηππ + $ K\overline{K}\pi $ system in isosymmetric QCD

We generalize previous three-particle finite-volume formalisms to allow for multiple three-particle channels. For definiteness, we focus on the two-channel ηππ and $ K\overline{K}\pi $ system in isosymmetric QCD, considering the positive G parity sector of the latter channel, and neglecting the coupling to modes with four or more particles. The formalism we obtain is thus appropriate to study the b₁(1235) and η(1295) resonances. The derivation is made in the generic relativistic field theory approach using the time-ordered perturbation theory method. We study how the resulting quantization condition reduces to that for a single three-particle channel when one drops below the upper ($ K\overline{K}\pi $) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.. Authors: Draper, Zachary T. [University of Washington, Seattle, WA (United States); University of Washington] (ORCID:0000000337137871); Sharpe, Stephen R. [University of Washington, Seattle, WA (United States)] (ORCID:0000000305162597). DOE Contract: SC0011637; SC0023598. Subjects: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Hadronic Spectroscopy; Lattice QCD; Structure and Interactions