The complex relation between production and scattering amplitudes

TL;DR

This paper derives a unitarity relation for three-body production amplitudes expressed as a complex combination of two-body scattering amplitudes, revealing that unitarity does not restrict the coefficients to be real.

Contribution

It provides a new derivation of the unitarity relation for three-body production amplitudes and clarifies the nature of the coefficients involved.

Findings

Unitarity relation for three-body amplitudes derived

Coefficients in the amplitude expansion are not constrained to be real

The relation connects production and scattering amplitudes without additional restrictions

Abstract

The unitarity relation, Im(A)=T* A, is derived for a three-body production amplitude, A, that consists of a complex linear combination of elements of the two-body scattering amplitude, T. We conclude that the unitarity relation does not impose a realness condition on the coefficients in the expansion of, A, in terms of, T.