Construction of energy-independent potentials above inelastic thresholds in quantum field theories

TL;DR

This paper develops a method to construct energy-independent, non-local potentials for inelastic scattering processes in quantum field theories, applicable to systems like nucleon-nucleon and hyperon interactions, using wave functions and correlation functions.

Contribution

It introduces a framework for constructing energy-independent potentials above inelastic thresholds, including non-relativistic and relativistic cases, in quantum field theories such as QCD.

Findings

Constructed coupled channel potentials for NN scattering with inelastic channels.

Demonstrated potentials can be obtained without non-relativistic approximations for certain two-body scatterings.

Proposed a method to extract these potentials from correlation function time dependence.

Abstract

We construct energy independent but non-local potentials above inelastic thresholds, in terms of Nambu-Bethe-Salpeter wave functions defined in quantum field theories such as QCD. As an explicit example, we consider NN --> NN + n pi scattering processes for n=0,1,2,.... We show an existence of energy-independent coupled channel potentials with a non-relativistic approximation, where momenta of all particles are small compared with their own masses. In the case of two-body inelastic scatterings such as Lambda Lambda --> Lambda Lambda, N Xi, Sigma Sigma, on the other hand, we show that energy-independent potentials can be constructed without relying on non-relativistic approximations. We also propose a method to extract these potentials using time-dependence of general correlation functions.