Baryon Asymmetry in the Early Universe -- Baryogenesis via Leptogenesis -- Effective Field Theories -- Thermal Field Theory in a Nutshell -- EFT Approach for Right-handed Neutrinos in a Thermal Bath -- CP Asymmetries at Finite Temperature: the Nearly Degenerate Case -- CP Asymmetries at Finite Temperature: the Hierarchical Case -- Flavoured CP Asymmetries.

This thesis discusses the construction of an effective field theory (EFT) for non-relativistic Majorana fermions, shows how to use it to calculate observables in a thermal medium, and derives the effects of these thermal particles on the CP asymmetry.  The methods described in this thesis are the only ones to date that allow a systematic and effective description of the non-relativistic dynamics of a heavy Majorana fermion at finite temperature. The CP asymmetry is studied for hierarchical and nearly degenerate heavy-neutrino masses and the analysis includes the treatment of lepton-flavor effects.  Heavy Majorana neutrinos are involved in many scenarios of physics beyond the standard model and, in the leptogenesis framework, they are at the root of the baryon asymmetry in the Universe. Besides simplifying existing results, the EFT approach provides useful tools for addressing even more involved observables. Indeed, taken together, the approach and the material pres ented here represent an important step toward a systematic improvement of our knowledge of the CP asymmetry in heavy-neutrino decays at finite temperature.

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