Analytic continuation of Pasquier inversion representation of Khuri-Treiman equation

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.