ETD

• axion
• chiral symmetry
• chiral transition
• effective lagrangian models
• quantum chromodynamics
• topological susceptibility

The aim of this thesis is to study some properties of the QCD axion at finite temperature, using Effective Lagrangian Models. First of all, we have focused on a relation between the axion mass and the "Topological Susceptibility of QCD", a topic already partially explored in previous works. We have directly derived an expression for the topological susceptibility, and using the known formula for the axion mass obtained through the study of the mass spectrum of the theory, we have verified the validity of the above-mentioned relation.
Furthermore, under appropriate working hypotheses, an effort has been made to relate the topological susceptibility to other data available from lattice QCD studies (specifically, meson masses and the chiral condensate), also highlighting potential challenges and limitations of the approach.
In the remaining part of the thesis we have performed a detailed study of the interactions of the axion with scalar and pseudoscalar mesons (in the form of three-field and four-field vertices), using the so-called "Extended Linear Sigma-Model".
Then, the corresponding Feynman rules for these vertices have been employed for the study of physical processes, including, for example, pion-axion scattering, which is particularly relevant in Cosmology and which was previously examined in the literature through a different approach.
Moreover, we have estimated the contribution to three-field vertices from the "anomalous" part of the Lagrangian, comparing it to the "anomaly-independent" term and also trying to find which one is dominant at different ranges of temperature.