Analytic continuation of Pasquier inversion representation of Khuri-Treiman equation

TL;DR

This paper develops a method for the analytic continuation of the Pasquier inversion representation of the Khuri-Treiman equation, enabling its application across the entire energy spectrum for three-body decay processes.

Contribution

It introduces a well-defined analytic continuation of the Pasquier inversion form of the KT equation applicable to all energy regions, extending its utility beyond the decay region.

Findings

Successfully derived a continuous representation valid for all energies.

Facilitated improved modeling of three-body decay interactions.

Enhanced the theoretical framework for final state interaction analysis.

Abstract

The single integral form of Pasquier inversion representation of Khuri-Treiman (KT) equation presents great advantages for describing final state interaction of three-body decay or production processes. However, the original form of Pasquier inversion representation is only given in decay region and regions below. For the regions above, analytic continuation of original form is required. Because of non-trivial nature of analytic continuation procedure, it is the purpose of this work to obtain a well-defined Pasquier inversion representation of KT equation for all the energy range.