Quasi-degenerate neutrinos and tri-bi-maximal mixing

Assuming high-energy tri-bi-maximal mixing we study the radiative running of leptonic mixing angles and obtain limits on the high-energy scale from requiring consistency with the observed mixing. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing.Comment: 7 pages, to appear in the proceedings of DISCRETE'0

Non-Abelian family symmetries in Pati-Salam unification

We present a framework of underlying SU(3) x SU(3) family symmetries consistent with Pati-Salam unification and discuss advantages that can justify introducing multiple non-Abelian factors. Advantages include improved vacuum alignment and increased predictivity. We explore in this framework deviations from tri-bi-maximal neutrinos, such as relatively large theta13.Comment: 11 pages, final version for publication in JHE

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

The Messenger Sector of SUSY Flavour Models and Radiative Breaking of Flavour Universality

The flavour messenger sectors and their impact on the soft SUSY breaking terms are investigated in SUSY flavour models. In the case when the flavour scale M is below the SUSY breaking mediation scale M_S, the universality of soft terms, even if assumed at M_S, is radiatively broken. We estimate this effect in a broad class of models. In the CKM basis that effect gives flavour off-diagonal soft masses comparable to the tree-level estimate based on the flavour symmetry.Comment: 24 pages, 3 figures. v3: minor changes in the text, typos corrected, version accepted for publication in JHE

Discrete family symmetry, Higgs mediators and theta_{13}

We present a new (supersymmetric) framework for obtaining an excellent description of quark, charged lepton and neutrino masses and mixings from a Delta(6n^2) family symmetry with multiplet assignments consistent with an underlying SO(10) Grand Unification. It employs a Higgs mediator sector in place of the usual Froggatt-Nielsen messengers, with quark and lepton messengers, and provides significant improvements over existing models of this type having unsuppressed Yukawa couplings to the third generation and a simplified vacuum alignment mechanism. The neutrino mass differences are naturally less hierarchical than those of the quarks and charged leptons. Similarly the lepton mixing angles are much larger than those in the quark sector and have an approximate tri-bi-maximal (TB) mixing form for theta_{12} and theta_{23}. However the mixing angle theta_{13} is naturally much larger than in pure TB mixing and can be consistent with the value found in recent experiments. The magnitude of theta_{13} is correlated with a the predicted deviation of theta_{23} from bi-maximal mixing. The model has light familon fields that can significantly modify the associated SUSY phenomenology.Comment: v3: accepted in JHE

Beyond MFV in family symmetry theories of fermion masses

Minimal Flavour Violation (MFV) postulates that the only source of flavour changing neutral currents and CP violation, as in the Standard Model, is the CKM matrix. However it does not address the origin of fermion masses and mixing and models that do usually have a structure that goes well beyond the MFV framework. In this paper we compare the MFV predictions with those obtained in models based on spontaneously broken (horizontal) family symmetries, both Abelian and non-Abelian. The generic suppression of flavour changing processes in these models turns out to be weaker than in the MFV hypothesis. Despite this, in the supersymmetric case, the suppression may still be consistent with a solution to the hierarchy problem, with masses of superpartners below 1 TeV. A comparison of FCNC and CP violation in processes involving a variety of different family quantum numbers should be able to distinguish between various family symmetry models and models satisfying the MFV hypothesis.Comment: 34 pages, no figure

The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.Comment: 62 pages, 4 figures; references added, version accepted for publication in JHE

Cascade Textures and SUSY SO(10) GUT

We give texture analyses of cascade hierarchical mass matrices in supersymmetric SO(10) grand unified theory. We embed cascade mass textures of the standard model fermion with right-handed neutrinos into the theory, which gives relations among the mass matrices of the fermions. The related phenomenologies, such as the lepton flavor violating processes and leptogenesis, are also investigated in addition to the PMNS mixing angles.Comment: 27 pages, 4 figures, comments and references added, final versio

A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing

We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of $\theta_{13}$ is within the sensitivity of the experiments which will take data in the near future. The light neutrino spectrum, typical of $A_4$ see-saw models, with its phenomenological implications, also including leptoproduction, is studied in detail.Comment: 20 pages, 2 figure