Two-particle resonances and singularities of the $(2\to 3)$ scattering amplitude

A study is made of the analytic properties of the scattering amplitude for reactions with the formation of three particles in the final state under the assumption that the two-particle subsystems have resonance states. It is shown that on the unphysical sheet with respect to the energies of the relative motions of the pairs, the amplitude has pole and logarithmic singularities.