Mixing Patterns from the Groups Sigma (n phi)

We survey the mixing patterns which can be derived from the discrete groups Sigma (36 x 3), Sigma (72 x 3), Sigma (216 x 3) and Sigma (360 x 3), if these are broken to abelian subgroups Ge and Gnu in the charged lepton and neutrino sector, respectively. Since only Sigma (360 x 3) possesses Klein subgroups, only this group allows neutrinos to be Majorana particles. We find a few patterns that can agree well with the experimental data on lepton mixing in scenarios with small corrections and that predict the reactor mixing angle theta_{13} to be 0.1 <= theta_{13} <= 0.2. All these patterns lead to a trivial Dirac phase. Patterns which instead reveal CP violation tend to accommodate the data not well. We also comment on the outer automorphisms of the discussed groups, since they can be useful for relating inequivalent representations of these groups.Comment: 1+28 pages, 6 tables, no figures; v2: matches version published in J. Phys. A: Math. Theo

The Nature of Massive Neutrinos and Unified Theories of Flavour

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

Neutrino mass generation and leptogenesis via pseudo-Nambu-Goldstone Higgs portal

We consider an extension of the Standard Model with the global symmetry-breaking pattern SO(5)/SO(4), where the Higgs boson arises as a pseudo-Nambu-Goldstone boson. The scalar content of the theory consists of a Standard-Model-like Higgs field and an extra real scalar field. The flavor sector of the model is extended by two right-handed neutrinos compatible with the observed light-neutrino phenomenology, and we find that the correct vacuum alignment determines the mass of the heavier neutrino eigenstate to be around 80 TeV. The new singlet-scalar state generates dynamically a Majorana mass term for the heavy-neutrino states. We show how the model leads to the correct baryon asymmetry of the Universe via leptogenesis in the case of two degenerate or hierarchical heavy neutrinos.Peer reviewe

A SUSY SU(5)xT' Unified Model of Flavour with large \theta_{13}

We present a SUSY SU(5)xT' unified flavour model with type I see-saw mechanism of neutrino mass generation, which predicts the reactor neutrino angle to be \theta_{13} = 0.14 close to the recent results from the Daya Bay and RENO experiments. The model predicts also values of the solar and atmospheric neutrino mixing angles, which are compatible with the existing data. The T' breaking leads to tri-bimaximal mixing in the neutrino sector, which is perturbed by sizeable corrections from the charged lepton sector. The model exhibits geometrical CP violation, where all complex phases have their origin from the complex Clebsch-Gordan coefficients of T'. The values of the Dirac and Majorana CP violating phases are predicted. For the Dirac phase in the standard parametrisation of the neutrino mixing matrix we get a value close to 90 degrees \delta = \pi/2 - 0.45 \theta^c = 84.3 degrees, \theta^c being the Cabibbo angle. The neutrino mass spectrum can be with normal ordering (2 cases) or inverted ordering. In each case the values of the three light neutrino masses are predicted with relatively small uncertainties, which allows to get also unambiguous predictions for the neutrino-less double beta decay effective Majorana mass.Comment: 31 pages, 7 figures; typos corrected, a few clarifying comments added; version to be published in Phys. Rev.

Radiatively induced Fermi scale and unification

We consider extensions of the Standard Model in which the hierarchy between the unification and the Fermi scale emerges radiatively. Within the Pati-Salam framework, we show that it is possible to construct a viable model where the Higgs is an elementary pseudo-Goldstone boson, and the correct hierarchy is generated.Peer reviewe

Leptogenesis in SO(10)

We consider $SO(10)$ Grand Unified Theories (GUTs) with vacuum expectation values (vevs) for fermion masses in the $\mathbf{10} + \mathbf{\overline{126}}$ representation. We show that the baryon asymmetry generated via leptogenesis is completely determined in terms of measured low energy observables and of one single high energy parameter related to the ratio of the $\mathbf{10}$ and $\mathbf{\overline{126}}$ $SU(2)$ doublet vevs. We identify new decay channels for the heavy Majorana neutrinos into $SU(2)$ singlet leptons $e^c$ which can sizeably affect the size of the resulting baryon asymmetry. We describe how to equip $SO(10)$ fits to low energy data with the additional constraint of successful leptogenesis, and we apply this procedure to the fits carried out in ref.~\cite{Dueck:2013gca}. We show that a baryon asymmetry in perfect agreement with observations is obtained.Comment: 19 pages, 2 figures; references added and typos corrected to match the published versio

Generalised Geometrical CP Violation in a T\u27 Lepton Flavour Model

We analyse the interplay of generalised CP transformations and the non-Abelian discrete group T &#8242; and use the semi-direct product G f = T &#8242; &#8906; H CP , as family symmetry acting in the lepton sector. The family symmetry is shown to be spontaneously broken in a geometrical manner. In the resulting flavour model, naturally small Majorana neutrino masses for the light active neutrinos are obtained through the type I see-saw mechanism. The known masses of the charged leptons, lepton mixing angles and the two neutrino mass squared differences are reproduced by the model with a good accuracy. The model allows for two neutrino mass spectra with normal ordering (NO) and one with inverted ordering (IO). For each of the three spectra the absolute scale of neutrino masses is predicted with relatively small uncertainty. The value of the Dirac CP violation (CPV) phase &#948; in the lepton mixing matrix is predicted to be &#948; = &#960;/ 2 or 3 &#960;/ 2. Thus, the CP violating effects in neutrino oscillations are predicted to be maximal (given the values of the neutrino mixing angles) and experimentally observable. We present also predictions for the sum of the neutrino masses, for the Majorana CPV phases and for the effective Majorana mass in neutrinoless double beta decay. The predictions of the model can be tested in a variety of ongoing and future planned neutrino experiments