Flavour symmetry and its implications in Yukawa couplings

Abstract

We study the flavour symmetry as a hidden structure of the Yukawa interaction sector. The flavour symmetry is explicitly broken in the Standard Model lagrangian by the Yukawa interaction terms. The smallness of the Yukawa couplings is the evidence of the approximate flavour symmetry of the theory. By a model independent study, we show that the approximate flavour symmetry may suppress the flavour-changing neutral currents within the experimental bounds, which appear when more Higgs bosons are introduced. Thus, we need no more discrete symmetries usually introduced when we extend the Higgs sector by inclusion of multi-Higgs bosons. On the lepton sector, the situation is more complex. Due to ignorance of the lepton mixing angles and neutrino masses, it is impossible to estimate the flavour symmetry breaking in the lepton sector. We should assume a specific mechanism for the neutrino masses. By assuming the seesaw mechanism, we can give some predictions for the neutrino masses and mixings, it could reduce the number of parameters for the lepton sector. We also study its phenomenological implications in MSW solution for solar neutrino deficit, the possibilities for the neutrinoless double-beta decays and the direct search of the neutrino oscillations. In the near future, we will obtain much experimental results from various experiment for the neutrino and our predictions are expected to be tested.