A cascade mechanism of three-particle resonance production

We study the mechanism of the three-particle resonance production in a system consisting of a two-particle resonance and of one particle, the resonance and the particle permanently exchanging the decay product particle. The N/D method is used to show that the solution of the unitarity for the resonance-particle amplitude reduces to solving a one-dimensional nonsingular integral equation for the denominator of the amplitude D(y). The contribution from the right-hand cut of the exchange decay diagram is considered explicitly and the final equation contains only the integral over an arbitrary left-hand cut as in the case of the interaction amplitude of stable particles. It is as well shown that if only the right-hand cut is present, than the denominator D(y) for L=0 has no singularities, whereas the amplitude may have virtual or real poles at L=1