An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization

Abstract

A particular choice of renormalization, within the simplifications provided by the nonperturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no 'self-energy' to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion's chain graphs, and yields a set of contributions which can be summed and provide a finite colorcharge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway. *

Comparison of QCD curves with elastic pp scattering data

“…In a set of recent papers [1][2][3][4] that we will call for all along this article, the present authors have shown how it is possible to proceed from any relativistic, gauge dependent generating functional of QCD, to new explicit solutions for its quark and/or antiquark correlation functions, in a gauge invariant and non-perturbative manner. All those computations rely strongly on a given function, ϕ( b), partly phenomenological, which depicts the transverse fluctuations of quark position inside a hadron [1,5].…”

A new approach to analytic, non-perturbative, gauge-invariant QCD renormalization is described, with applications to high energy elastic pp-scattering.

“…Low and behold, we have a diffraction dip as seen in experiments. It comes from quark-GB-quark and quark-GB-virtualquarkloop-GB-quark, figure 8, [10]. Figure 8.…”

Casimir operator dependences of nonperturbative fermionic QCD amplitudes

“…Then the consequences of effective locality, even when examined 'at tree level', should exhibit admissible as well as new aspects of the confined phase of QCD; and so far, it seems to be so [2][3][4][5].…”

“…In some recent articles [1][2][3][4][5], a property, which bears on the non-perturbative fermionic Green's functions of QCD, has been put forth under the name of effective locality. This property can be phrased as follows.…”