# “Neutrino Mass Models” by Steve King

Let’s continue with theoretical talk summaries… Here I’m going to post on the talk by Steve King on the impact of flavour symmetries to explain neutrino mixings (and more in general, fermion masses and mixings).

Just to remind you: assuming 3 active oscillating neutrinos, we have two oscillation frequencies, a large Δm^2∼2×10^-3 eV^2 and a small δm^2∼8×10^-5 eV^2, and three mixing angles, the solar θ_12 (about 34.4°), the atmospheric θ_23 (about 42.8°) and the reactor θ_13 (about 5.6°).

When constructing Flavour Models, usually one takes approximate values that well describes the experimental data (something similar in taking the Wolfenstein parametrization to approximate the experimental CKM matrix). At this point, however, we find many different possibilities:

the Tri-Bimaximal Mixing (TB)

the Golden Ratio Pattern

The main difference between the first two patterns and the last one is that the first two are compatible with the data at the 1σ and 3σ level, respectively, while the BM predicts a maximal solar angle, that is completely out of the 3σ error range. However, if corrections enter in the model, also the BM could be corrected and brought in agreement with the data: in particular these corrections should be of the order of the Cabibbo angle and as a result one can think at this scenario as a realization of the Quark-Lepton Complementarity relation.

In the rest of the talk, Steve concentrated only on the TB mixing discussing a plethora of scenarios where it has been implemented. He put large attention to Discrete non-Abelian Flavour symmetries:

To make it simple for all the non-model builders, in general all these discrete symmetries are subgroups of SU(3). It should remember the permutation of the three families, that happens in the particular limit in which the Yukawa terms are switched off in the SM Lagrangian (as in the Minimal Flavour Violation [by the way a paper on this subject has appeared today on ArXiv:http://arxiv.org/abs/1103.2915%5D). In the figure, you can also see a table from a paper by Altarelli and Feruglio, in which almost all the discrete symmetries used to construct flavour models are listed. What you cannot see is the long list of papers published in literature dealing with these discrete symmetries…

Why these Discrete symmetries have been studied so much? Here is the answer: it is extremely simple to reproduce the Tri-Bimaximal mixing and therefore it is easy to construct models in which the neutrino mixing matrix is described very close to the experimental one, WITHOUT introducing fine-tunings on the parameters. Unfortunately, in my opinion, this is possible using many different symmetries and therefore we cannot discriminate among the different realizations, looking only at the predicted masses and mixings.

All these models need some new ingredients to find these nice results and these new ingredients are new fields, usually (very) heavy scalar fields, in the context of either SM or SUSY or Extra D’s. Models in which these new fields are simply replicants of the SM SU(2) doublet have also been proposed, but all of them (but feel free to supply to my ignorance) suffer from large fine-tunings on the parameters and/or strong FCNC processes.

A further interesting subject that Steve has addressed for is the combination of GUT’s and Flavour Symmetries. Indeed the See-Saw mechanism naturally suggests a high scale and therefore points to GUT’s.

In the context of Flavour GUT’s, the construction of modes is further more constrained, but there could be interesting predictions among the observables and/or sum rules. A relevant observation is that the Tri-Bimaximal mixing can never exactly arise in these flavor GUT’s. Steve then presented a detailed analysis in which he has parametrized the deviations from TB mixing, discussing the different scenarios that could arise, depending on the measurement of one or an other of these deviations.

The final message of the talk is that all the deviations from TB are important, not just that one on the reactor angle.

I add a couple of personal comments on the subject, both concerning the global coherence of flavour models.

First, when discussing Flavour GUT’s, many authors are satisfied in finding realistic descriptions of masses and mixing (I’m not considering the prize that they must pay to get them), but they completely “forget” to discuss the Higgs sector: I mean all that part of the model dealing with the breaking of the GUT gauge group down to the SM one. This is indeed a highly non-trivial aspect, because usually the large Higgs GUT representations transform under the flavour symmetry and therefore the usual discussion of pure GUT symmetry breaking cannot apply.

Second, there is a jungle of flavour models present in the literature, but only few studies on their phenomenological consequences can be found. It is, in my view, extremely relevant to know if a model, apart from predicting masses and mixings, is able to survive to LFV and/or FCNC processes. Furthermore, only through these kind of analysis, it is possible, hopefully, to distinguish one model from the others.

My final message is to study a flavour model in all its directions and implications!!!

Stay tuned!

(posted by Luca Merlo)

Well, in an emergent non local approach, where classical symmetries are secondary to quantum information transformations, the fairy field mechanism becomes a commutativization (like a diagonalization) process for the noncommutative geometry of mixing. Since this looks nothing like the particle spectrum, fairy fields are just that: non existent.