Analytic continuation of the finite-volume three-particle amplitudes
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.
Keywords
Cite
@article{arxiv.2312.16380,
title = {Analytic continuation of the finite-volume three-particle amplitudes},
author = {Sebastian M. Dawid},
journal= {arXiv preprint arXiv:2312.16380},
year = {2023}
}
Comments
12 pages, 2 figures. Proceedings for the 40th Lattice conference at Fermilab from July 31 to August 4, 2023