Neutrino Mass Models: From Type III See-saw to Non-Commutative Geometry

Today we know that neutrinos are massive, but we ignore both the origin of their masses and the reason why those masses are so tiny. A natural mechanism that can explain the smallness of neutrino masses is the See-saw Mechanism, that in this work is studied in its Type III variant. However, even in the scope of the See-saw Mechanism, the origin of the huge neutrino Majorana mass (which is a fundamental prerequisite for any see-saw model) remains to be explained. A possible explanation can be found in Twisted Non-Commutative Geometry (NCG): for particular twists of the so-called Connes Model (which is the NCG formulation of the Standard Model) a new scalar field appears naturally, whose vacuum expectation value generates a Majorana mass for the neutrinos, and the order of magnitude of said v.e.v. is precisely the natural scale of the Majorana mass of See-saw Mechanisms (10^15 GeV). In this work, three different twists of the Connes Model are studied, paying particular attention to the new boson field content, their gauge transformations, as well as the fermionic actions of each model.