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.

The masses of the elementary fermions (quarks and leptons) and the values of the elements of the mixing matrices in the quark and lepton sector constitute one of the biggest mysteries of particle physics. In a simplified manner, one can list the following unexplained issues: The strong hierarchy in all three mass spectra of the charged fermions (quarks with charge 2/3 and -1/3 and charged leptons), the smallness of the three mixing angles in the quark mixing matrix, while two of the mixing angles in the lepton mixing matrix are large, the smallness of the neutrino masses, which are at least six orders of magnitude smaller than the electron mass. An often quoted mechanism for the smallness of the neutrino masses is the so-called seesaw mechanism. It is hoped that the first two issues find an explanation in the framework of ex- tensions of the Standard Model with flavour symmetries. It is true that none of the numerous models has gained wider acceptance, nevertheless it is interesting to investigate the stability of the predictions of such models under quantum corrections. For this purpose it is expedient to work out a renormalization prescription of extensions of the Standard Model in which these models are embedded. In the project we have considered the lepton sector of the Standard Model, extended by an arbitrary number of Higgs doublets and an arbitrary number of right-handed neutrino singlets. The prescription we have worked out to treat an arbitrary number of Yukawa couplings consists in quantizing the theory in the R gauge and MS renormalization of the parameters of the unbroken theory. However, for consistency reasons, this prescription has to be supplemented for = 0 by a renormalization of the vacuum expectation values. We have performed a complete computation of the one-loop counterterms and the fermion masses. Moreover, in this approximation we demonstrated explicitly the -independence of these fermion masses and we have computed the finite shift of the vacuum expectation values. It turns out that for large seesaw scales our renormalization scheme becomes inconsistent because then these finite shifts become much larger than the tree-level vacuum expectation values.