Dispersive approaches for three-particle final state interaction

In this work, we present different representations of the Khuri-Treiman equation and discuss advantages and disadvantages of each representation. In particular we focus on the inversion technique proposed by Pasquier, which, even though developed a long time ago, has not been used in modern analyses of data on three particle decays. We apply the method to a toy model and compare the sensitivity of this and alternative solution methods to the left-hand cut contribution. We also discuss the meaning and applicability of Watson's theorem when three particles in final states are involved.