Document Type

Article

Publication Date

2021

DOI

10.1103/PhysRevD.104.014507

Publication Title

Physical Review D

Volume

104

Issue

1

Pages

014507 (1-21)

Abstract

We present a simple scheme for solving relativistic integral equations for the partial-wave projected three-body amplitudes. Our techniques are used to solve a problem of three scalar particles with a formation of a S-wave two-body bound state. We rewrite the problem in a form suitable for numerical solution and then explore three solving strategies. In particular, we discuss different ways of incorporating the bound-state pole contribution in the integral equations. All of them lead to agreement with previous results obtained using finite-volume spectra of the same theory, providing further evidence of the validity of the existing finite- and infinite-volume formalism for studying three-particle systems. We discuss an analytic and numerical estimate of the systematic errors and provide numerical evidence that the methods presented allow for determination of amplitude above the three-body threshold as well. In conjunction with the previously derived finite-volume formalism, this work furthers the objective for extracting three-hadron scattering amplitudes directly from lattice QCD.

Comments

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (CC BY 4.0). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3

Original Publication Citation

Jackura, A. W., Briceño, R. A., Dawid, S. M., Islam, M. H. E., & McCarty, C. (2021). Solving relativistic three-body integral equations in the presence of bound states. Physical Review D, 104(1), 1-21, Article 014507. https://doi.org/10.1103/PhysRevD.104.014507

ORCID

0000-0002-3249-5410 (Jackura), 0000-0003-1109-1473 (Briceño)

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