One-loop fermion mass corrections and flavour symmetries

The fermion mass spectrum and the form of the two mixing matrices is a long-standing mystery in particle physics that comprises the strong hierarchy in all three mass spectra of the charged fermions, the mild hierarchy in in the neutrino mass spectrum, the smallness of the neutrino masses, the CKM matrix with small mixing angles but large CP-violating phase and the lepton mixing matrix with two large and one small mixing angle. The most popular approach in this context is the application of flavour symmetries which act on the Yukawa couplings and the scalar potential in the Lagrangian. Although such symmetries entail an enlarged scalar sector, they allow to construct models where some features of the mixing matrices are reproduced or mixing angles and phases are related to mass ratios at tree level. The question arises whether such relations are stable under radiative corrections. It is the purpose of the proposed project to systematically compute one-loop corrections to the fermion mass matrices in a class of models which then allows, within this class, to answer this question. As a renormalizable class of models we want to consider the multi-Higgs doublet Standard Model, enlarged in the lepton sector by right-handed neutrino singlets and the seesaw mechanism. We additionally allow for Yukawa couplings of the right-handed neutrino singlets to scalar gauge singlets. One of the main issues of the project is to devise a renormalization scheme which allows to incorporate the effect of flavour symmetries. Another main issue is the application of the thus obtained radiative corrections to models existing in the literature and to compute the numerical corrections to their tree level relations. Another topic in this context is the generation of the light fermion masses by radiative corrections.