Gauge Invariant Summation of All QCD Virtual Gluon Exchanges

TL;DR

This paper develops a gauge-invariant, Lorentz covariant formulation of QCD virtual gluon exchanges, enabling finite, numerical evaluation of quark scattering amplitudes with physically consistent behavior at high energies.

Contribution

It introduces a novel gauge-invariant approach to summing all virtual gluon exchanges in QCD, applicable at all coupling strengths, and demonstrates its effectiveness in a high-energy quark scattering model.

Findings

Finite, local integrals for quark scattering can be numerically evaluated.

Results depend only on momentum transfer and show damping at high energies.

The approach aligns with previous field-strength analyses.

Abstract

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. A similar but more complicated integral will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al.