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, , to the physical scattering amplitude can be solved at and below threshold. We test our methods by reproducing known analytic results for the 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 lead to unphysical finite-volume energies, and give a preliminary analysis of these artifacts.
14 More- Received 4 April 2018
DOI:https://doi.org/10.1103/PhysRevD.98.014506
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.
Published by the American Physical Society