  In a Quantum Field Theory, the analytic structure of the 2-points correlation
functions, ie the propagators, encloses information about the properties of the
corresponding quanta, particularly if they are or not confined. However, in
Quantum Chromodynamics (QCD), we can only have an analytic solution in a
perturbative picture of the theory. For the non-perturbative propagators, one
resorts on numerical solutions of QCD that accesses specific regions of the
Euclidean momentum space, as, for example, those computed via Monte Carlo
simulations on the lattice. In the present work, we rely on Pad\'e Approximants
(PA) to approximate the numerical data for the gluon and ghost propagators, and
investigate their analytic structures. In a first stage, the advantages of
using PAs are explored when reproducing the properties of a function, focusing
on its analytic structure. The use of PA sequences is tested for the
perturbative solutions of the propagators, and a residue analysis is performed
to help in the identification of the analytic structure. A technique used to
approximate a PA to a discrete set of points is proposed and tested for some
test data sets. Finally, the methodology is applied to the Landau gauge gluon
and ghost propagators, obtained via lattice simulations. The results identify a
conjugate pair of complex poles for the gluon propagator, that is associated
with the infrared structure of the theory. This is in line with the presence of
singularities for complex momenta in theories where confinement is observed.
Regarding the ghost propagator, a pole at $p^2=0$ is identified. For both
propagators, a branch cut is found on the real negative $p^2$-axis, which
recovers the perturbative analysis at high momenta.

High Energy Physics - Lattice;High Energy Physics - Phenomenology;High Energy Physics - Theory