2,131 research outputs found
Lepton Family Symmetry and Possible Application to the Koide Mass Formula
A finite group generated by four Z_3 transformations is applied to lepton
families in a supersymmetric model, resulting in the charged-lepton masses m_i
being proportional to v_i^2, where v_i are three vacuum expectation values.
This may be relevant in obtaining the Koide formula m_e + m_mu + m_tau =
(2/3)(sqrt{m_e} + sqrt{m_mu} + sqrt(m_tau})^2.Comment: 10 pages, no figur
Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry
The discrete subgroup Delta(27) of SU(3) has the interesting multiplication
rule 3 X 3 = bar{3} + bar{3} + bar{3}, which is used to obtain near
tribimaximal neutrino mixing. Using present neutrino oscillation data as input,
this model predicts that the effective mass m_{ee} measured in neutrinoless
double beta decay will be 0.14 eV.Comment: 6 pages, no figur
Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group
We discuss various "minimalist'' schemes to derive the neutrino mixing matrix
using the tetrahedral group $A_{4}.
Tri-bimaximal Neutrino Mixing from A(4) and \theta_{13} \sim \theta_C
It is a common believe that, if the Tri-bimaximal mixing (TBM) pattern is
explained by vacuum alignment in an A(4) model, only a very small reactor
angle, say \theta_{13} \sim \lambda^2_C being \lambda_C \equiv \theta_C the
Cabibbo angle, can be accommodated. This statement is based on the assumption
that all the flavon fields acquire VEVs at a very similar scale and the
departures from exact TBM arise at the same perturbation level. From the
experimental point of view, however, a relatively large value \theta_{13} \sim
\lambda_C is not yet excluded by present data. In this paper, we propose a
Seesaw A(4) model in which the previous assumption can naturally be evaded. The
aim is to describe a \theta_{13} \sim \lambda_C without conflicting with the
TBM prediction for \theta_{12} which is rather close to the observed value (at
\lambda^2_C level). In our model the deviation of the atmospherical angle from
maximal is subject to the sum-rule: \sin ^2 \theta_{23} \approx 1/2 +
\sqrt{2}/2 \sin \delta \cos \theta_{13} which is a next-to-leading order
prediction of our model.Comment: 16 pages, revised, typos corrected, references adde
CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model
We propose a model based on SU(5) x {}^{(d)}T which successfully gives rise
to near tri-bimaximal leptonic mixing as well as realistic CKM matrix elements
for the quarks. The Georgi-Jarlskog relations for three generations are also
obtained. Due to the {}^{(d)}T transformation property of the matter fields,
the b-quark mass can be generated only when the {}^{(d)}T symmetry is broken,
giving a dynamical origin for the hierarchy between m_{b} and m_{t}. There are
only nine operators allowed in the Yukawa sector up to at least mass dimension
seven due to an additional Z_{12} x Z'_{12} symmetry, which also forbids, up to
some high orders, operators that lead to proton decay. The resulting model has
a total of nine parameters in the charged fermion and neutrino sectors, and
hence is very predictive. In addition to the prediction for \theta_{13} \simeq
\theta_{c}/3 \sqrt{2}, the model gives rise to a sum rule,
\tan^{2}\theta_{\odot} \simeq \tan^{2} \theta_{\odot, \mathrm{TBM}} - {1/2}
\theta_{c} \cos\beta, which is a consequence of the Georgi-Jarlskog relations
in the quark sector. This deviation could account for the difference between
the experimental best fit value for the solar mixing angle and the value
predicted by the tri-bimaximal mixing matrix.Comment: 11 pages; v2: additional references added; minor modifications made;
conclusion unchanged; v3: version to appear in Phys. Lett.
Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
We formulate and discuss a 4-dimensional SUSY version of an A4 model for
tri-bimaximal neutrino mixing which is completely natural. We also study the
next-to-the-leading corrections and show that they are small, once the ratios
of A4 breaking VEVs to the cutoff are fixed in a specified interval. We also
point out an interesting way of presenting the A4 group starting from the
modular group. In this approach, which could be interesting in itself as an
indication on a possible origin of A4, the lagrangian basis where the symmetry
is formulated coincides with the basis where the charged leptons are diagonal.
If the same classification structure in A4 is extended from leptons to quarks,
the CKM matrix coincides with the unit matrix in leading order and a study of
non leading corrections shows that the departures from unity of the CKM matrix
are far too small to accomodate the observed mixing angles.Comment: 21 pages, 1 figure; added section on a see-saw realization; version
to appear on Nucl. Phys.
Tri-Bimaximal Lepton Mixing and Leptogenesis
In models with flavour symmetries added to the gauge group of the Standard
Model the CP-violating asymmetry necessary for leptogenesis may be related with
low-energy parameters. A particular case of interest is when the flavour
symmetry produces exact Tri-Bimaximal lepton mixing leading to a vanishing
CP-violating asymmetry. In this paper we present a model-independent discussion
that confirms this always occurs for unflavoured leptogenesis in type I see-saw
scenarios, noting however that Tri-Bimaximal mixing does not imply a vanishing
asymmetry in general scenarios where there is interplay between type I and
other see-saws. We also consider a specific model where the exact Tri-Bimaximal
mixing is lifted by corrections that can be parametrised by a small number of
degrees of freedom and analyse in detail the existing link between low and
high-energy parameters - focusing on how the deviations from Tri-Bimaximal are
connected to the parameters governing leptogenesis.Comment: 29 pages, 6 figures; version 2: references added, minor correction
Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
The Non-Abelian finite group PSL_2(7) is the only simple subgroup of SU(3)
with a complex three-dimensional irreducible representation. It has two maximal
subgroups, S_4 which, along with its own A_4 subgroup, has been successfully
applied in numerous models of flavor, as well as the 21 element Frobenius group
Z_7 x Z_3, which has gained much less attention. We show that it can also be
used to generate tri-bimaximal mixing in the neutrino sector, while allowing
for quark and charged lepton hierarchies.Comment: 15 pages, matches published version, updated reference
Tri-bimaximal Neutrino Mixing and Quark Masses from a Discrete Flavour Symmetry
We build a supersymmetric model of quark and lepton masses based on the
discrete flavour symmetry group T', the double covering of A_4. In the lepton
sector our model is practically indistinguishable from recent models based on
A_4 and, in particular, it predicts a nearly tri-bimaximal mixing, in good
agreement with present data. In the quark sector a realistic pattern of masses
and mixing angles is obtained by exploiting the doublet representations of T',
not available in A_4. To this purpose, the flavour symmetry T' should be broken
spontaneously along appropriate directions in flavour space. In this paper we
fully discuss the related vacuum alignment problem, both at the leading order
and by accounting for small effects coming from higher-order corrections. As a
result we get the relations: \sqrt{m_d/m_s}\approx |V_{us}| and
\sqrt{m_d/m_s}\approx |V_{td}/V_{ts}|.Comment: 27 pages, 1 figure; minor correction
Lepton Flavour Violation in a Supersymmetric Model with A4 Flavour Symmetry
We compute the branching ratios for mu-> e gamma, tau-> mu gamma and tau -> e
gamma in a supersymmetric model invariant under the flavour symmetry group A4 X
Z3 X U(1)_{FN}, in which near tri-bimaximal lepton mixing is naturally
predicted. At leading order in the small symmetry breaking parameter u, which
is of the same order as the reactor mixing angle theta_{13}, we find that the
branching ratios generically scale as u^2. Applying the current bound on the
branching ratio of mu -> e gamma shows that small values of u or tan(beta) are
preferred in the model for mass parameters m_{SUSY} and m_{1/2} smaller than
1000 GeV. The bound expected from the on-going MEG experiment will provide a
severe constraint on the parameter space of the model either enforcing u approx
0.01 and small tan(beta) or m_{SUSY} and m_{1/2} above 1000 GeV. In the special
case of universal soft supersymmetry breaking terms in the flavon sector a
cancellation takes place in the amplitudes and the branching ratios scale as
u^4, allowing for smaller slepton masses. The branching ratios for tau -> mu
gamma and tau -> e gamma are predicted to be of the same order as the one for
mu -> e gamma, which precludes the possibility of observing these tau decays in
the near future.Comment: 44 page
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