Perturbative methods in non-perturbative Quantum Chromodynamics

TL;DR

This thesis introduces two novel perturbative frameworks, the Screened Massive Expansion and the Dynamical Model, to study low-energy QCD, successfully matching lattice data and offering new insights into gluon mass generation.

Contribution

The paper presents two new perturbative approaches for low-energy QCD that align with non-perturbative results and extend to finite temperatures and full QCD.

Findings

Gluon and ghost propagators agree with lattice data within one-loop approximation.

Both frameworks eliminate Landau poles in the strong coupling constant.

Extensions to finite temperature and full QCD are proposed.

Abstract

The objective of this thesis is to present two new perturbative frameworks for the study of low-energy Quantum Chromodynamics (QCD), termed the Screened Massive Expansion and the Dynamical Model. Both the frameworks paint a picture of the infrared regime of QCD which is consistent with the current knowledge provided by the lattice calculations and by other non-perturbative methods, displaying dynamical mass generation in the gluon sector and a massless ghost propagator. The Screened Massive Expansion achieves this by operating a shift of the QCD perturbative series, performed by adding a mass term for the transverse gluons in the kinetic part of the Faddeev-Popov Lagrangian and subtracting it back from its interaction part so that the total action remains unchanged. The Dynamical Model, on the other hand, interprets the generation of a dynamical mass for the gluons as being triggered by a non-vanishing condensate of the form $\langle (A^{h})^{2}\rangle$, where $A^{h}$ is a gauge- and BRST-invariant non-local version of the gluon field, and explores the consequences of the inclusion of the former in the partition function of the theory. Since the main focus of this thesis is on the gauge sector of QCD, most of our calculations will be carried out in the context of pure Yang-Mills theory. There we will show that the gluon and the ghost propagator derived by making use of the two frameworks are in good agreement with the Euclidean Landau-gauge lattice data, within the limits of a one-loop approximation. During the course of the thesis we will address topics such as the first-principles status of the two methods, the absence of Landau poles from the strong running coupling constant and the extension of the Screened Massive Expansion to finite temperatures and to full QCD. Future research prospects are discussed in the Conclusions.