Physical Review D
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.
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
0000-0002-3249-5410 (Jackura), 0000-0003-1109-1473 (Briceño)
Jackura, Andrew W.; Briceño, Raúl A.; Dawid, Sebastian M.; Islam, Md. Habib E.; and McCarty, Connor, "Solving Relativistic Three-Body Integral Equations in the Presence of Bound States" (2021). Physics Faculty Publications. 541.