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.
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Mikhasenko, M., Wunderlich, Y., Jackura, A. et al. Three-body scattering: ladders and resonances. J. High Energ. Phys. 2019, 80 (2019). https://doi.org/10.1007/JHEP08(2019)080
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DOI: https://doi.org/10.1007/JHEP08(2019)080