Modified initial state for perturbative QCD

TL;DR

This paper proposes a modified initial state for perturbative QCD, constructed as a superposition of zero-momentum gluon pairs, which preserves symmetries and leads to finite gluon condensation in perturbation theory.

Contribution

It introduces a new initial state in perturbative QCD that maintains symmetries and aligns with an alternative perturbation approach, enabling finite gluon condensation at early orders.

Findings

Gluon and ghost propagators match alternative perturbation theory.

State satisfies BRST physicality condition.

Predicts finite gluon condensation in first-order perturbation.

Abstract

A particular initial state for the construction of the perturbative expansion of QCD is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global SU(3) symmetries. It follows that the gluon and ghost propagators determined by it, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. The BRST quantization is done for the value alpha=1 of the gauge parameter where the procedure is greatly simplified. Therefore, after assuming that the adiabatic connection of the interaction does not take out the state from the interacting physical space, the predictions of the perturbation expansion, at the value alpha=1, for the physical quantities should have meaning. The validity of this conclusion solves the gauge dependence indeterminacy remained in the proposed perturbation expansion.