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arXiv · 2312.16380

Analytic continuation of the finite-volume three-particle amplitudes

Sebastian M. Dawid
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Abstract

One has to study multivariable scattering amplitudes to extract properties of the three-body states from the generalizations of the L\"uscher finite-volume formalism. In particular, a three-body amplitude obtained from a Lattice QCD calculation must be analytically continued to unphysical Riemann sheets of the complex energy plane, where resonances of interest appear as poles. In this article, we provide a pedagogical overview of a method for solving and analytically continuing the on-shell integral equations describing a three-body elastic scattering process. We illustrate the procedure by applying it to a relativistic system of three identical bosons characterized by pair-wise interactions. We describe the analytic structure of the reaction amplitude, show how to access its physical and unphysical Riemann sheets, and analyze the behavior of the three-body spectrum under variations of the interaction parameters.

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Sebastian M. Dawid. 2023-12-27. Analytic continuation of the finite-volume three-particle amplitudes. https://arxiv.org/abs/2312.16380

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