33 research outputs found
Comments on the classification of the finite subgroups of SU(3)
Many finite subgroups of SU(3) are commonly used in particle physics. The
classification of the finite subgroups of SU(3) began with the work of H.F.
Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two
series (C) and (D) of finite subgroups of SU(3) are defined. While the group
series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D),
respectively) have been intensively studied, there is not much knowledge about
the group series (C) and (D). In this work we will show that (C) and (D) have
the structures (C) \cong (Z_m x Z_m') \rtimes Z_3 and (D) \cong (Z_n x Z_n')
\rtimes S_3, respectively. Furthermore we will show that, while the (C)-groups
can be interpreted as irreducible representations of Delta(3n^2), the
(D)-groups can in general not be interpreted as irreducible representations of
Delta(6n^2).Comment: 15 pages, no figures, typos corrected, clarifications and references
added, proofs revise
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
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
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
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
Discrete Flavour Groups, \theta_13 and Lepton Flavour Violation
Discrete flavour groups have been studied in connection with special patterns
of neutrino mixing suggested by the data, such as Tri-Bimaximal mixing (groups
A4, S4...) or Bi-Maximal mixing (group S4...) etc. We review the predictions
for sin(\theta_13) in a number of these models and confront them with the
experimental measurements. We compare the performances of the different classes
of models in this respect. We then consider, in a supersymmetric framework, the
important implications of these flavour symmetries on lepton flavour violating
processes, like \mu -> e gamma and similar processes. We discuss how the
existing limits constrain these models, once their parameters are adjusted so
as to optimize the agreement with the measured values of the mixing angles. In
the simplified CMSSM context, adopted here just for indicative purposes, the
small tan(beta) range and heavy SUSY mass scales are favoured by lepton flavour
violating processes, which makes it even more difficult to reproduce the
reported muon g-2 discrepancy.Comment: 45 pages, 16 figures, 3 tables; V3 submitted to add an acknowledgment
to a Networ