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arXiv · 2105.12094

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

Tyler D. Blanton·Stephen R. Sharpe
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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.

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Tyler D. Blanton, Stephen R. Sharpe. 2021-05-25. Three-particle finite-volume formalism for $\pi^+\pi^+ K^+$ and related systems. https://doi.org/10.1103/physrevd.104.034509

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