• field-strength-correlators
• latticeqcd
• quantum-chromodynamics

Strong interactions, described by Quantum Chromodynamics (QCD), play a fundamental role in understanding the behaviour of subatomic particles. They become non-perturbative at low energies, posing significant challenges for theoretical calculations. However, numerical methods, such as lattice QCD (LQCD), provide a powerful approach to study and simulate these non-perturbative phenomena, allowing us to explore the intricate dynamics of quarks and gluons within hadrons and uncover the rich structure of the strong force.

The gauge invariant two-point correlation functions of the gauge field strengths are fundamental quantities used to describe many interesting aspects of gluodynamics and QCD.
uch
correlators regulate the influence of the gluon condensate on the energy levels of heavy ̄qq systems
and play a basic role in understanding colour confinement, in particular, they are frequently used
to parametrize the non-perturbative properties of the QCD vacuum within the framework of the
Stochastic Vacuum Model (SVM). In particular, in the so-called Gaussian approximation to
the SVM, they represent the leading (Gaussian) term and quantities of physical interests, such as
the string tension σ, can be expressed in terms of these functions. Some years ago, these correlators have been measured on the lattice in the SU (3) theory with no dynamical quarks, for full
QCD with two flavours at zero and non-zero temperature, and in the presence of a magnetic
background field .
In this thesis work, the two-point correlators have been computed for the first time in full QCD
with 2+1 flavours and quark masses tuned to their phenomenological values, using three different
lattices in order to perform a continuum extrapolation of the physical quantities. The measure
function has been implemented on a LQCD code running on GPUs utilizing the OpenAcc and
OpenMPI libraries for parallel computations. To properly treat the effects of short-range fluctu-
ations due to the ultraviolet cutoff various smoothing techniques have been developed. Following
previous works, the approach used in this work is a local smoothing technique, called cooling, in
order to remove the effects of short–range fluctuations on large-distance correlators.
Generally, there are various prescriptions to define the correlators, depending on the amount of smoothing carried out. This leads to an ambiguity in the definition, which has been re-evaluated in this work. For this reason, three different methods were adopted to define the correlators, one follows the same prescription of previous work and two others are new. These methods have been discussed based on a preliminary analysis of the continuum scaling and of the best fits to the predicted functional dependence of the correlators. Moreover, the obtained results have been compared with analytic predictions obtained within perturbation theory, or used, within the Stochastic Vacuum Model, to predict physical quantities of phenomenological relevance, such as the gluon condensate, the correlation length of the gluon field strengths and the string tension.
From the preliminary analysis, we obtained reasonable good fits in all cases, while the first two prescriptions seem to be preferable when one considers the impact of discretization effects. As well as the continuum scaling the gluonic condensate and the correlation length were found to be slightly sensitive to the prescription adopted. However, the comparison with perturbative theory at short distances and the derivation of quantities such as the string tension within the SVM has given substantial further insight to solve the prescription ambiguity. In particular, the analysis suggests that, contrary to previous studies, perhaps the most correct prescription seems to be the second one, as the results are more in agreement with the perturbative predictions and the phenomenological ones concerning the string tension.