Three-body scattering: ladders and resonances

• Main Authors: M. Mikhasenko, Y. Wunderlich, A. Jackura, V. Mathieu, A. Pilloni, B. Ketzer, A.P. Szczepaniak
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of High Energy Physics
• Subjects: Phenomenological Models; QCD Phenomenology
• Online Access: http://link.springer.com/article/10.1007/JHEP08(2019)080

Abstract We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular the one-pion-exchange process. It is demonstrated that unitarity demands a specific functional form of the amplitude with a clear interpretation: the bare three-particle resonances are dressed by the initial- and final-state interaction, in a way that is consistent with the considered long-range forces. We postulate that the resonance kernel admits a factorization in the energy variables of the initial- and the final-state particles. The factorization assumption leads to an algebraic form for the unitarity equations, which is reminiscent of the well-known two-body-unitarity condition and approaches it in the limit of the narrow-resonance approximation.