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

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