31 research outputs found
Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models
Recent T2K results indicate a sizeable reactor angle theta_13 which would
rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of
the Altarelli-Feruglio A4 family symmetry model including additional flavons in
the 1' and 1" representations and show that it leads to trimaximal mixing in
which the second column of the lepton mixing matrix consists of the column
vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to
limit the reactor angle and control the higher order corrections, we propose a
renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a
doublet of S4 which is spontaneously broken to A4 by a flavon which enters the
neutrino sector at higher order. We study the vacuum alignment in the S4 model
and show that it predicts accurate trimaximal mixing with approximate
tri-bimaximal mixing, leading to a new mixing sum rule testable in future
neutrino experiments. Both A4 and S4 models preserve form dominance and hence
predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE
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
An SO(10) Grand Unified Theory of Flavor
We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based
on an family symmetry. It makes use of our recent proposal to use SO(10)
with type II seesaw mechanism for neutrino masses combined with a simple ansatz
that the dominant Yukawa matrix (the {\bf 10}-Higgs coupling to matter) has
rank one. In this paper, we show how the rank one model can arise within some
plausible assumptions as an effective field theory from vectorlike {\bf 16}
dimensional matter fields with masses above the GUT scale. In order to obtain
the desired fermion flavor texture we use flavon multiplets which acquire
vevs in the ground state of the theory. By supplementing the theory with
an additional discrete symmetry, we find that the flavon vacuum field
alignments take a discrete set of values provided some of the higher
dimensional couplings are small. Choosing a particular set of these vacuum
alignments appears to lead to an unified understanding of observed quark-lepton
flavor:
(i) the lepton mixing matrix that is dominantly tri-bi-maximal with small
corrections related to quark mixings; (ii) quark lepton mass relations at GUT
scale: and and (iii) the solar to
atmospheric neutrino mass ratio in agreement with observations. The model predicts the neutrino
mixing parameter, ,
which should be observable in planned long baseline experiments.Comment: Final version of the paper as it will appear in JHEP
Strong coupling, discrete symmetry and flavour
We show how two principles - strong coupling and discrete symmetry - can work
together to generate the flavour structure of the Standard Model. We propose
that in the UV the full theory has a discrete flavour symmetry, typically only
associated with tribimaximal mixing in the neutrino sector. Hierarchies in the
particle masses and mixing matrices then emerge from multiple strongly coupled
sectors that break this symmetry. This allows for a realistic flavour
structure, even in models built around an underlying grand unified theory. We
use two different techniques to understand the strongly coupled physics:
confinement in N=1 supersymmetry and the AdS/CFT correspondence. Both
approaches yield equivalent results and can be represented in a clear,
graphical way where the flavour symmetry is realised geometrically.Comment: 31 pages, 5 figures, updated references and figure
Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis
We derive predictions for the Dirac phase present
in the unitary neutrino mixing
matrix , where and are
unitary matrices which arise from the diagonalisation
respectively of the charged lepton and the neutrino mass matrices.
We consider forms of and allowing us to express
as a function of three
neutrino mixing angles,
present in ,
and the angles contained in .
We consider several forms of
determined by, or associated with, symmetries,
tri-bimaximal, bimaximal, etc.,
for which the angles in are
fixed. For each of these forms and forms of
allowing to reproduce the measured values of the neutrino
mixing angles,
we construct the likelihood function
for , using i) the latest results of the global
fit analysis of neutrino oscillation data,
and ii) the prospective sensitivities
on the neutrino mixing angles.
Our results, in particular, confirm the conclusion
reached in earlier similar studies
that the measurement of the Dirac phase
in the neutrino mixing matrix, together with an improvement
of the precision on the mixing angles,
can provide unique information about the
possible existence of symmetry
in the lepton sector
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