The Nature of Massive Neutrinos and Unified Theories of Flavour

Abstract

The present Ph.D. thesis is devoted to two fundamental unsolved problems of neutrino physics, which are intimately connected: determining the nature - Dirac or Majorana - of massive neutrinos, which is related with the possibility of existence of New Physics beyond that predicted by the Standard Model (SM) of particle interactions, and, discovering the origin of the patterns of neutrino masses and of leptonic mixing, stemming from new underlying symmetries in the neutrino, charged lepton and quark sectors. The remarkable experimental efforts of the last 15 years or so have delivered an enormous amount of data that have to be explained in terms of possibly economic and simple theoretical models. Moreover, exciting times are ahead of us. Currently running and future upcoming experiments under construction aim at i) high precision measurement of the parameters characterizing the neutrino oscillations, ii) identifying the neutrino mass hierarchy, and iii) establishing the status of the CP symmetry in the leptonic sector by searching for CP violation effects in neutrino oscillations. In addition, significant experimental efforts are been made to unveil the possible Majorana nature of massive neutrinos by searching for neutrinoless double beta (\betabeta-) decay with increasing sensitivity. Unique data on the absolute scale of neutrino masses, which is unknown at present, is expected to be provided by $\beta$-decay experiments under preparation. The first part of the Ph.D. thesis is devoted to the problem of extracting information about the New Physics if it will be experimentally established via the observation of the \betabeta-decay that the massive neutrinos are Majorana particles. In this case new couplings, changing the total lepton charge $L=L_e + L_\mu + L_\tau$ by two units, must be admitted in the Lagrangian of particle interactions and there is the possibility that more than one such coupling is operative in \betabeta-decay. We discuss four such couplings (arising in seesaw and ight-Left (L-R) symmetric models and in supersymmetric extensions of the SM with $R$-parity nonconservation) and analyze in detail the possibility to determine which couplings, if any, might be involved in \betabeta-decay from data on the \betabeta-decay half-lives of several different isotopes. In the second part of the Ph.D thesis we analyze the neutrino flavour problem in connection with new underlying symmetries in the leptonic sector. The existence of an organizing principle which could explain the pattern of masses and mixing of the neutrinos is explored in two different approaches based on the use of finite discrete non-Abelian groups. A unified model of flavour based on the symmetry group $SU(5)\times T^\prime$, incorporating the seesaw mechanism of neutrino mass generation is constructed and the predictions of this model for the neutrino mixing angles, the Dirac and Majorana CP violation phases in the neutrino mixing matrix, the sum of neutrino masses and for the \betabeta-decay effective Majorana mass are derived. The model can be tested in the future planned neutrino physics experiments