Non-perturbative study of QCD correlators

TL;DR

This dissertation uses lattice QCD to non-perturbatively analyze QCD correlators, determine the $ ext{L}_ ext{QCD}$ parameter with improved accuracy, and investigate the infrared behavior of Green functions related to confinement.

Contribution

It introduces a new method to remove power corrections, enabling a more precise estimate of $ ext{L}_ ext{QCD}$ and provides insights into the infrared behavior of gluon and ghost propagators.

Findings

The $ ext{L}_ ext{QCD}$ parameter is estimated as 269(5)^{+12}_{-9} MeV.

The gluon propagator is finite and non-zero at zero momentum.

The ghost propagator exhibits a power-law behavior similar to a free particle.

Abstract

This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $\Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new method of removing these power corrections allows a better estimate of $\Lqcd$. Our result is $\Lambda^{n_f=0}_{\ms} = 269(5)^{+12}_{-9}$ MeV. Another question that we address is the infrared behaviour of Green functions, at momenta of order and below $\Lqcd$. At low energy the momentum dependence of the propagators changes considerably, and this is probably related to confinement. The lattice approach allows to check the predictions of analytical methods because it gives access to non-perturbative correlators. According to our analysis the gluon propagator is finite and non-zero at vanishing momentum, and the power-law behaviour of the ghost propagator is the same as in the free case.