31 research outputs found
Lepton mixing from the hidden sector
Experimental results indicate a possible relation between the lepton and
quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X
is a matrix with special structure related to the mechanism of neutrino mass
generation. We propose a framework which can realize such a relation. The main
ingredients of the framework are the double seesaw mechanism, SO(10) Grand
Unification and a hidden sector of theory. The latter is composed of singlets
(fermions and bosons) of the GUT symmetry with masses between the GUT and
Planck scale. The interactions in this sector obey certain symmetries G_hidden.
We explore the conditions under which symmetries G_hidden can produce flavour
structures in the visible sector. Here the key elements are the basis-fixing
symmetry and mediators which communicate information about properties of the
hidden sector to the visible one. The interplay of SO(10) symmetry,
basis-fixing symmetry identified as Z2 x Z2 and G_hidden can lead to the
required form of U_X. A different kind of new physics is responsible for
generation of the CKM mixing. We present the simplest realizations of the
framework which differ by nature of the mediators and by symmetries of the
hidden sector.Comment: 30 pages, 6 figures; typo corrected, one reference added, version for
publication in Phys. Rev.
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
Five models for lepton mixing
We produce five flavour models for the lepton sector. All five models fit perfectly well - at the 1 sigma level - the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type I seesaw mechanism, on a Z(2) symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange - or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for the phase delta in lepton mixing; the fifth model also predicts a correlation between the lepton mixing angles theta(12) and theta(23)
On a possible relationship between lepton mixing and the stability of dark matter
I comment on the proposal that the stability of dark matter may be due to an
unbroken Z_2 symmetry contained in the partially broken lepton flavour symmetry
group. I remark that (1) there is no Z_2 symmetry apparent in the lepton mass
spectrum and in lepton mixing, (2) predictive models of this type may be
constructed by using a lepton flavour symmetry group with three inequivalent
singlets, to which the three left-handed-lepton gauge-SU(2) doublets are
assigned, and (3) some predictions for the lepton masses and mixings are likely
to be altered by radiative contributions to the neutrino mass matrix. I
construct two models of this type in which the conserved Z_2 originates in a
lepton flavour symmetry group D_4.Comment: 13 page
Finite flavour groups of fermions
We present an overview of the theory of finite groups, with regard to their
application as flavour symmetries in particle physics. In a general part, we
discuss useful theorems concerning group structure, conjugacy classes,
representations and character tables. In a specialized part, we attempt to give
a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which
we apply and illustrate the general theory. Moreover, we also provide a concise
description of the symmetric and alternating groups and comment on the
relationship between finite subgroups of U(3) and finite subgroups of SU(3).
Though in this review we give a detailed description of a wide range of finite
groups, the main focus is on the methods which allow the exploration of their
different aspects.Comment: 89 pages, 6 figures, some references added, rearrangement of part of
the material, section on SU(3) subgroups substantially extended, some minor
revisions. Version for publication in J. Phys. A. Table 12 corrected to match
eq.(256), table 14 and eq.(314) corrected to match the 2-dimensional irreps
defined on p.6
Principal series of finite subgroups of SU(3)
We attempt to give a complete description of the "exceptional" finite
subgroups Sigma(36x3), Sigma(72x3) and Sigma(216x3) of SU(3), with the aim to
make them amenable to model building for fermion masses and mixing. The
information on these groups which we derive contains conjugacy classes, proper
normal subgroups, irreducible representations, character tables and tensor
products of their three-dimensional irreducible representations. We show that,
for these three exceptional groups, usage of their principal series, i.e.
ascending chains of normal subgroups, greatly facilitates the computations and
illuminates the relationship between the groups. As a preparation and testing
ground for the usage of principal series, we study first the dihedral-like
groups Delta(27) and Delta(54) because both are members of the principal series
of the three groups discussed in the paper.Comment: 43 pages, no figures; typos corrected, clarifications and references
added, version matches publication in J. Phys.
Two-parameter neutrino mass matrices with two texture zeros
We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by
searching for viable hybrid textures in which the non-zero matrix elements of
M_nu have simple ratios. Referring to the classification scheme of Frampton,
Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the
ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu
tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid
textures, one obtains, for instance, good agreement with the data if one
computes the three mixing angles in terms of the experimentally determined
mass-squared differences Delta m^2_21 and Delta m^2_31. We could not find
viable hybrid textures based on mass matrices different from those of cases A1
and A2.Comment: 10 pages, no figures, minor changes, some references adde