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arXiv · 1810.01429

Three-particle systems with resonant subprocesses in a finite volume

Raúl A. Briceño·Maxwell T. Hansen·Stephen R. Sharpe
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Abstract

In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. As in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as $a_2 \to \rho \pi \to \pi \pi \pi$, in which the $\rho$ is rigorously treated as a resonance state.

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Raúl A. Briceño, Maxwell T. Hansen, Stephen R. Sharpe. 2018-10-02. Three-particle systems with resonant subprocesses in a finite volume. https://doi.org/10.1103/physrevd.99.014516

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