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 $K\overline{K}\pi$ \( K\overline{K}\pi \) 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 ( $K\overline{K}\pi$ \( K\overline{K}\pi \) ) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.