Document Type

Article

Publication Date

2018

DOI

10.1103/PhysRevD.98.014506

Publication Title

Physical Review D

Volume

98

Issue

1

Pages

014506 (25 pp.)

Abstract

We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized s-wave) approximation, and keeping only the leading terms in the effective range expansion, we show how the quantization condition can be solved numerically in a straightforward manner. In addition, we show how the integral equations that relate the intermediate three-particle infinite-volume scattering quantity, Kdf,3, to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 1/L expansion of the threshold state, the volume dependence of three-particle bound-state energies, and the Bethe-Salpeter wave functions for these bound states. We also find that certain values of Kdf;3 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.

Comments

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. 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

Briceño, R. A., Hansen, M. T., & Sharpe, S. R. (2018). Numerical study of the relativistic three-body quantization condition in the isotropic approximation. Physical Review D, 98(1), 014506. doi:10.1103/PhysRevD.98.014506

ORCID

0000-0003-1109-1473 (Briceño)

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