Physical Review D
014506 (25 pp.)
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.
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
Briceño, Raúl A.; Hansen, Maxwell T.; and Sharpe, Stephen R., "Numerical Study of the Relativistic Three-Body Quantization Condition in the Isotropic Approximation" (2018). Physics Faculty Publications. 219.