Dispersive approaches for three-particle final states interaction

TL;DR

This paper explores various dispersive methods for analyzing three-particle final state interactions, comparing their advantages and limitations through a toy model and discussing implications for Watson's theorem.

Contribution

It introduces different representations of the Khuri-Treiman equation and evaluates their effectiveness and sensitivity using a toy model, providing insights into three-particle interactions.

Findings

Different representations have distinct advantages and disadvantages.

Solution sensitivity depends on the left hand cut and approximation methods.

Discussion on the applicability of Watson's theorem to three-particle states.

Abstract

In this work, we present different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. Using a toy model for scattering amplitude, we study the sensitivity of solution of KT equation to the left hand cut of this toy model and to the different approximate methods. At last, we briefly discuss Watson's theorem when three particles in final states are involved.