Casimir operator dependences of non-perturbative fermionic QCD amplitudes

TL;DR

This paper investigates how non-perturbative fermionic QCD amplitudes depend on higher-order Casimir operators, revealing an additional cubic Casimir dependence that signifies non-perturbative effects beyond traditional quadratic Casimir dependence.

Contribution

It demonstrates the emergence of cubic Casimir operator dependence in non-perturbative fermionic QCD amplitudes, extending the understanding of gauge algebra effects beyond perturbation theory.

Findings

Dependence on cubic Casimir operator observed in non-perturbative QCD amplitudes.

Cubic Casimir effects are numerically sub-leading but algebraically significant.

Signature of non-perturbative fermionic sector in QCD through Casimir operator dependence.

Abstract

In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes depart from a sole dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the fundamental gauge group representation. Noticed in non-relativistic Quark Models and in a non-perturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other non-perturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of SUc(3). Though numerically sub-leading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the non-perturbative fermonic sector of QCD.