Perturbative methods in non-perturbative Quantum Chromodynamics

The PhD will focus on the development of improved perturbative methods for Quantum Chromodynamics in the low-energy regime. The final aim of our research is to formulate a perturbation theory which remains consistent in the infrared, thus making it possible to extend the domain of validity of the ordinary analytical methods down to arbitrarily small scales. Of particular interest to our study is the phenomenon of dynamical mass generation for both the gluons and the quarks. The latter is likely triggered by the presence of non-vanishing condensates in the vacuum structure of QCD and cannot be described in the context of the standard perturbation theory, owing both to constraints imposed by gauge invariance and to the non-analiticity of the relation between the dynamical masses and the strong coupling constant. An improved version of perturbation theory could be able to incorporate dynamical mass generation in a nonperturbative fashion, thus bringing us closer to an exact description of the strong interactions at low energies.