Document Type


Publication Date




Publication Title

Physical Review D






034016 (1-38)


We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the nonrelativistic three-body scattering theory, we provide a detailed and general prescription for solving and analytically continuing integral equations describing the three-body reactions. We use these techniques to study a system with zero angular momenta described by a single scattering length leading to a bound state in a two-body subchannel. We obtain bound-state-particle and three-particle amplitudes in the previously unexplored kinematical regime; in particular, for real energies below elastic thresholds and complex energies in the physical and unphysical Riemann sheets. We extract positions of three-particle bound-states that agree with previous finite-volume studies, providing further evidence for the consistency of the relativistic finite-volume three-body quantization conditions. We also determine previously unobserved virtual bound states in this theory. Finally, we find numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of the left-hand cuts and argue for the generalization of the existing formalism.


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Original Publication Citation

Dawid, S. M., Islam, M. H. E., & Briceño, R. A. (2023). Analytic continuation of the relativistic three-particle scattering amplitudes. Physical Review D, 108(3), 1-38, Article 034016.


0000-0003-2163-2026 (Islam)