2019/04/26 by M. Mikhasenko, Y. Wunderlich, A. Jackura +5
Physics and Astronomy · #Algebraic number #Amplitude #Cold Atom Physics and Bose-Einstein Condensates #Factorization #Kernel (algebra) #Limit (mathematics) #Nuclear physics research studies #Quantum chaos and dynamical systems #Resonance (particle physics) #Unitarity #hep-ph
paper · pdf · doi:10.1007/jhep08(2019)080
15 pages, 1 figure
arxiv created 2019/04/26 · openalex publication_date 2019/08/01 · openalex created_date 2019/08/22 · arxiv updated 2019/09/04 · openalex updated_date 2026/08/06
A bstract 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.