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

Abstract

We construct energy-independent but nonlocal 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+nπ scattering processes for n=0,1,2,.... We show the existence of energy-independent coupled channel potentials with a nonrelativistic approximation, where momenta of all particles are small compared with their own masses. In the case of two-body inelastic scatterings such as ΛΛ→ΛΛ, NΞ, ΣΣ, on the other hand, we show that energy-independent potentials can be constructed without relying on nonrelativistic approximations. We also propose a method to extract these potentials using time dependence of general correlation functions. © 2013 American Physical Society.