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Non-perturbative study of QCD correlators

Abstract : This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool
that we use is lattice QCD. Lattice QCD has been successfully used in phenomenology, but it can
also be used to study the fundamental parameters (like the coupling constant) and properties of
the theory itself. This is the main goal of the present dissertation. 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
-the fundamental scale of the pure Yang-Mills theory. 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. We shall see that these corrections are quite important up to energies of the order of 10
GeV. A new method of removing these power corrections allows a better estimate of LQCD. Our
result is Lambda_nf_MSbar = 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. We
try to clarify the laws that govern the infrared gluodynamics in order to understand the radical
nature of the changes in the infrared behaviour. Many questions arise: the Gribov ambiguity,
the impact of different non-perturbative relations at low momenta, self-consistency of the lattice
approach in this domain. 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.
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Submitted on : Wednesday, November 15, 2006 - 5:09:57 PM
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Alexey Lokhov. Non-perturbative study of QCD correlators. Mathematical Physics [math-ph]. Ecole Polytechnique X, 2006. English. ⟨tel-00114163⟩

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