Operator Product Expansion in QCD Is Not Consistent With Quantum Field Theory For Gluon Distribution Function

Abstract

Since the operator product expansion (OPE) is applicable at short distance the OPE in QCD does not solve the long distance confinement problem involving hadron in QCD where the nonperturbative QCD is applicable. In this paper we show that the gauge invariant definition of the non-perturbative gluon distribution function inside the hadron consistent with the operator product expansion (OPE) in QCD at high energy colliders is not consistent with the gauge invariant definition of the non-perturbative gluon distribution function in the quantum field theory.