47 research outputs found
Towards Minimal S4 Lepton Flavor Model
We study lepton flavor models with the flavor symmetry. We construct
simple models with smaller numbers of flavon fields and free parameters, such
that we have predictions among lepton masses and mixing angles. The model with
a triplet flavon is not realistic, but we can construct realistic models
with two triplet flavons, or one triplet and one doublet flavons.Comment: 18 pages, 4 figures, references are adde
Discrete symmetries and models of flavor mixing
Evidences of a discrete symmetry behind the pattern of lepton mixing are
analyzed. The program of "symmetry building" is outlined. Generic features and
problems of realization of this program in consistent gauge models are
formulated. The key issues include the flavor symmetry breaking, connection of
mixing and masses, {\it ad hoc} prescription of flavor charges, "missing"
representations, existence of new particles, possible accidental character of
the TBM mixing. Various ways are considered to extend the leptonic symmetries
to the quark sector and to reconcile them with Grand Unification. In this
connection the quark-lepton complementarity could be a viable alternative to
TBM. Observational consequences of the symmetries and future experimental tests
of their existence are discussed.Comment: 14 pages, 5 figures. Talk given at the Symposium "DISCRETE 2010", 6 -
11 December 2010, La Sapienza, Rome, Ital
The Golden Ratio Prediction for the Solar Angle from a Natural Model with A5 Flavour Symmetry
We formulate a consistent model predicting, in the leading order
approximation, maximal atmospheric mixing angle, vanishing reactor angle and
tan {\theta}_12 = 1/{\phi} where {\phi} is the Golden Ratio. The model is based
on the flavour symmetry A5 \times Z5 \times Z3, spontaneously broken by a set
of flavon fields. By minimizing the scalar potential of the theory up to the
next-to-leading order in the symmetry breaking parameter, we demonstrate that
this mixing pattern is naturally achieved in a finite portion of the parameter
space, through the vacuum alignment of the flavon fields. The leading order
approximation is stable against higher-order corrections. We also compare our
construction to other models based on discrete symmetry groups.Comment: 28 pages, 2 figures. Minor changes, references added. Corrected typos
in Appendix A. Version appeared on JHE
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 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 and , with .
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
Trimaximal neutrino mixing from modular A 4 invariance with residual symmetries
We construct phenomenologically viable models of lepton masses and mixing based on modular A 4 invariance broken to residual symmetries Z 3T or Z 3ST and Z 2S respectively in the charged lepton and neutrino sectors. In these models the neutrino mixing matrix is of trimaximal mixing form. In addition to successfully describing the charged lepton masses, neutrino mass-squared differences and the atmospheric and reactor neutrino mixing angles \u3b8 23 and \u3b8 13 , these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as the existence of specific correlations between i) the values of the solar neutrino mixing angle \u3b8 12 and the angle \u3b8 13 (which determines \u3b8 12 ), ii) the values of the Dirac CPV phase \u3b4 and of the angles \u3b8 23 and \u3b8 13 , iii) the sum of the neutrino masses and \u3b8 23 , iv) the neutrinoless double beta decay effective Majorana mass and \u3b8 23 , and v) between the two Majorana phases
Repressing Anarchy in Neutrino Mass Textures
The recent results that is relatively large, of the order of
the previous upper bound, and the indications of a sizable deviation of
from the maximal value are in agreement with the predictions of
Anarchy in the lepton sector. The quark and charged lepton hierarchies can then
be reproduced in a SU(5) GUT context by attributing non-vanishing
charges, different for each family, only to the SU(5) tenplet states. The fact
that the observed mass hierarchies are stronger for up quarks than for down
quarks and charged leptons supports this idea. As discussed in the past, in the
flexible context of , different patterns of charges can
be adopted going from Anarchy to various types of hierarchy. We revisit this
approach by also considering new models and we compare all versions to the
present data. As a result we confirm that, by relaxing the extreme ansatz of
equal charges for all SU(5) pentaplets and singlets, better
agreement with the data than for Anarchy is obtained without increasing the
model complexity. We also present the distributions obtained in the different
models for the Dirac CP-violating phase. Finally we discuss the relative merits
of these simple models.Comment: v1: 12 pages, 3 figures; v2: 13 pages, 3 figures, text improved,
matches version accepted for publication; v3: submitted to add an
acknowledgment to a networ
Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with Flavor Symmetry
We study the renormalization group running of the tri-bimaximal mixing
predicted by the two typical flavor models at leading order. Although the
textures of the mass matrices are completely different, the evolution of
neutrino mass and mixing parameters is found to display approximately the same
pattern. For both normal hierarchy and inverted hierarchy spectrum, the quantum
corrections to both atmospheric and reactor neutrino mixing angles are so small
that they can be neglected. The evolution of the solar mixing angle
depends on and neutrino mass spectrum, the deviation
from its tri-bimaximal value could be large. Taking into account the
renormalization group running effect, the neutrino spectrum is constrained by
experimental data on in addition to the self-consistency
conditions of the models, and the inverted hierarchy spectrum is disfavored for
large . The evolution of light-neutrino masses is approximately
described by a common scaling factor.Comment: 23 pages, 6figure
Leptons in Holographic Composite Higgs Models with Non-Abelian Discrete Symmetries
We study leptons in holographic composite Higgs models, namely in models
possibly admitting a weakly coupled description in terms of five-dimensional
(5D) theories. We introduce two scenarios leading to Majorana or Dirac
neutrinos, based on the non-abelian discrete group which is
responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino
masses is naturally explained and normal/inverted mass ordering can be
accommodated. We analyze two specific 5D gauge-Higgs unification models in
warped space as concrete examples of our framework. Both models pass the
current bounds on Lepton Flavour Violation (LFV) processes. We pay special
attention to the effect of so called boundary kinetic terms that are the
dominant source of LFV. The model with Majorana neutrinos is compatible with a
Kaluza-Klein vector mass scale TeV, which is roughly the
lowest scale allowed by electroweak considerations. The model with Dirac
neutrinos, although not considerably constrained by LFV processes and data on
lepton mixing, suffers from a too large deviation of the neutrino coupling to
the boson from its Standard Model value, pushing TeV.Comment: 37 pages, 4 figures; v2: Note added in light of recent T2K and MINOS
results, figures updated with new limit from MEG, references added, various
minor improvements, matches JHEP published versio
Natural Vacuum Alignment from Group Theory: The Minimal Case
Discrete flavour symmetries have been proven successful in explaining the
leptonic flavour structure. To account for the observed mixing pattern, the
flavour symmetry has to be broken to different subgroups in the charged and
neutral lepton sector. However, cross-couplings via non-trivial contractions in
the scalar potential force the group to break to the same subgroup. We present
a solution to this problem by extending the flavour group in such a way that it
preserves the flavour structure, but leads to an 'accidental' symmetry in the
flavon potential. We have searched for symmetry groups up to order 1000, which
forbid all dangerous cross-couplings and extend one of the interesting groups
A4, T7, S4, T' or \Delta(27). We have found a number of candidate groups and
present a model based on one of the smallest extension of A4, namely Q8 \rtimes
A4. We show that the most general non-supersymmetric potential allows for the
correct vacuum alignment. We investigate the effects of higher dimensional
operators on the vacuum configuration and mixing angles, and give a
see-saw-like UV completion. Finally, we discuss the supersymmetrization of the
model. Additionally, we release the Mathematica package "Discrete" providing
various useful tools for model building such as easily calculating invariants
of discrete groups and flavon potentials.Comment: 33 pages, 7 figures; references added, minor changes, matches version
published in JHE