Non-perturbative QCD amplitudes in quenched and eikonal approximations

•We discuss the physical insight of effective locality to QCD fermionic amplitudes.•We show that an unavoidable delta function goes along with the effective locality property.•The generic structure of QCD fermion amplitudes is obtained through Random Matrix calculus.

Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.