Momentum Transfer Dispersion Relations for Three-Particle Potential Scattering Amplitudes

Abstract

The analytic properties in momentum transfer of a class of three-particle scattering amplitudes are investigated in this paper. The amplitudes considered are those in which there is a two-particle bound state in both the initial and final state. The following results are obtained: (1) The amplitudes are analytic inside a Lehmann ellipse in the scattering angle for all real energies. (2) For real energies below the three-free-particle threshold, the amplitudes are analytic in the momentum transfer plane except for real left- and right-hand cuts.