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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.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summa
Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on
We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-$x$ dependence of a mo
In this talk we present a numerical lattice study of an SU(3) gauge model where an SU(2) doublet of non-Abelian strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. The model enjoys an exact
We present a fully non-perturbative determination of the $O(a)$ improvement coefficient $c_{rm SW}$ in three-flavor dynamical QCD for the RG improved as well as the plaquette gauge actions, using the Schrodinger functional scheme. Results are compared with one-loop estimates at weak gauge coupling.