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Equivalence of three-particle scattering formalisms

A.W. Jackura, S.M. Dawid, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, A. Pilloni, S.R. Sharpe, A.P. Szczepaniak
In recent years, different on-shell 3->3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite-volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in [Phys. Rev. D 92, 114509 (2015)] and subsequently Briceño et al. in [Phys. Rev. D 95, 074510 (2017)] can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai et al. in [Eur. Phys. J. A 53, 177 (2017)] and Jackura et al. in [Eur. Phys. J. C 79, 56 (2019)]. Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the nonrelativistic limit of both representations.
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Phys.Rev. D100 (2019) no.3, 034508