Three-particle formalism for multiple channels: the $\eta \pi \pi +K\overline{K}\pi$ 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 $\eta \pi \pi$ 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 $b_1(1235)$ and $\eta (1295)$ 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.

49 pages, no figures. v2: Fixed typos, added additional comments to the conclusion, made other minor changes

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Cited by in corpus (1)

• $D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD