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

TL;DR

This paper demonstrates that the gauge-invariant non-perturbative gluon distribution function in QCD, consistent with the operator product expansion at high energies, is incompatible with the quantum field theory definition, highlighting a fundamental inconsistency.

Contribution

It reveals an inconsistency between the gauge-invariant definitions of gluon distribution functions in QCD and quantum field theory, questioning the applicability of OPE at long distances.

Findings

Gauge-invariant gluon distribution functions are inconsistent between QCD and quantum field theory.

Operator product expansion does not resolve the confinement problem in QCD.

Non-perturbative definitions of gluon distributions are incompatible with QFT principles.

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 non-perturbative 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.