Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems

Abstract

We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include ${\pi }^{+}{\pi }^{+}{K}^{+}$ and $K^{+}{K}^{+}{\pi }^{+}$. We derive the formalism necessary to extract two- and three-particle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume. We use a relativistic formalism based on an all-orders diagrammatic analysis in generic effective field theory, adopting the methodology used recently to study the case of three nondegenerate particles. We present both a direct derivation, and also a cross-check based on an appropriate limit and projection of the fully nondegenerate formalism. We also work out the threshold expansions for the three-particle K matrix that will be needed in practical applications, both for systems with two identical particles plus a third, and also for the fully nondegenerate theory.

Comments: 24 pages, no figures; v2 updated to match published version (discussion improved, typos fixed, references updated--results unchanged)