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

Abstract

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 K ¯ π 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 K ¯ π ) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.