Fermion Masses and Flavor Mixings in a Model with $S_4$ Flavor Symmetry

Gui-Jun Ding

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Fermion Masses and Flavor Mixings in a Model with $S_4$ Flavor Symmetry

Gui-Jun Ding

High Energy Physics - Phenomenology · Submitted 11 Sep 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Tri-Bimaximal mixing and the charged lepton mass hierarchies are reproduced simultaneously at leading order.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.66 · compares with prior results 0.09 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present a supersymmetric model of quark and lepton based on $S_4\times Z_3\times Z_4$ flavor symmetry. The $S_4$ symmetry is broken down to Klein four and $Z_3$ subgroups in the neutrino and the charged lepton sectors respectively. Tri-Bimaximal mixing and the charged lepton mass hierarchies are reproduced simultaneously at leading order. Moreover, a realistic pattern of quark masses and mixing angles is generated with the exception of the mixing angle between the first two generations, which requires a small accidental enhancement. It is remarkable that the mass hierarchies are controlled by the spontaneous breaking of flavor symmetry in our model. The next to leading order contributions are studied, all the fermion masses and mixing angles receive corrections of relative order $\lambda^2_c$ with respect to the leading order results. The phenomenological consequences of the model are analyzed, the neutrino mass spectrum can be normal hierarchy or inverted hierarchy, and the combined measurement of the $0\nu2\beta$ decay effective mass $m_{\beta\beta}$ and the lightest neutrino mass can distinguish the normal hierarchy from the inverted hierarchy.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a supersymmetric model of quark and lepton based on $S_4\times Z_3\times Z_4$ flavor symmetry.	contribution 0.91	0.90	0.06	asserted 1.00
s1	The $S_4$ symmetry is broken down to Klein four and $Z_3$ subgroups in the neutrino and the charged lepton sectors respectively.	method 0.83	0.70	0.05	asserted 1.00
s2	Tri-Bimaximal mixing and the charged lepton mass hierarchies are reproduced simultaneously at leading order.	result 1.00	0.89	0.30	asserted 1.00
s3	Moreover, a realistic pattern of quark masses and mixing angles is generated with the exception of the mixing angle between the first two generations, which requires a small accidental enhancement.	result 0.80	0.90	0.21	asserted 1.00
s4	It is remarkable that the mass hierarchies are controlled by the spontaneous breaking of flavor symmetry in our model.	interpretation 0.97	0.77	0.17	asserted 1.00
s5	The next to leading order contributions are studied, all the fermion masses and mixing angles receive corrections of relative order $\lambda^2_c$ with respect to the leading order results.	result 0.66	0.91	0.07	asserted 1.00
s6	The phenomenological consequences of the model are analyzed, the neutrino mass spectrum can be normal hierarchy or inverted hierarchy, and the combined measurement of the $0\nu2\beta$ decay effective mass $m_{\beta\beta}$ and the lightest neutrino mass can distinguish the normal hierarchy from the inverted hierarchy.	result 0.74	0.83	0.22	hedged possibility 0.54

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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The paper

Original abstract

We present a supersymmetric model of quark and lepton based on $S_4\times Z_3\times Z_4$ flavor symmetry. The $S_4$ symmetry is broken down to Klein four and $Z_3$ subgroups in the neutrino and the charged lepton sectors respectively. Tri-Bimaximal mixing and the charged lepton mass hierarchies are reproduced simultaneously at leading order. Moreover, a realistic pattern of quark masses and mixing angles is generated with the exception of the mixing angle between the first two generations, which requires a small accidental enhancement. It is remarkable that the mass hierarchies are controlled by the spontaneous breaking of flavor symmetry in our model. The next to leading order contributions are studied, all the fermion masses and mixing angles receive corrections of relative order $\lambda^2_c$ with respect to the leading order results. The phenomenological consequences of the model are analyzed, the neutrino mass spectrum can be normal hierarchy or inverted hierarchy, and the combined measurement of the $0\nu2\beta$ decay effective mass $m_{\beta\beta}$ and the lightest neutrino mass can distinguish the normal hierarchy from the inverted hierarchy.

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References

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Generalised CP and Trimaximal TM$_1$ Lepton Mixing in $S_4$ Family Symmetry
hep-ph 2013-12 conditional novelty 4.0 of 10

S4 family symmetry combined with generalized CP, broken to a Z2 subgroup in the neutrino sector, yields trimaximal TM1 lepton mixing with trivial Majorana phases and Dirac CP either conserved or maximal.
Discrete Flavour Groups, \theta_13 and Lepton Flavour Violation
hep-ph 2012-05 conditional novelty 4.0 of 10

Among discrete flavour models, Lin-type A4 best reproduces the measured mixing angles, and in the CMSSM the MEG muon-to-electron-gamma bound excludes the parameter region needed for the muon g-2 anomaly.
Non-Abelian Discrete Symmetries in Particle Physics
hep-th 2010-03 conditional novelty 2.0 of 10

A reference compilation of representations, tensor products, subgroup decompositions and anomaly-free conditions for the non-Abelian discrete groups most used in flavor model building, with three worked flavor models.
Discrete Flavor Symmetries and Models of Neutrino Mixing
hep-ph 2010-02 accept novelty 1.0 of 10

A review of how A4, S4, and related discrete flavor groups can produce tri-bimaximal neutrino mixing at leading order, with small calculable corrections and testable predictions for theta13 and lepton flavor violation.

How the literature uses it

23 arXiv papers cite this in 51 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 29 sentences without a confident label

Compares with it 1 paper

For the product of the singlet $1^'$ with a doublet or a triplet, we have [equation] The CG coefficients for the products involving the doublet representation $2$ are found to be [equation] Finally, for the products of the triplet representations $3$ and $3^'$, we find [equation] We note that the CG coefficients presented above are in accordance with the results of Refs. [ref] .

Generalised CP and Trimaximal TM$_1$ Lepton Mixing in $S_4$ Family Symmetry · Group Theory of $S_4$ · 0.86

Cites it as support 1 paper

Actually the exact TB mixing can be realized in the $S_4$ flavor model [ref] .

Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry · Introduction · 0.98

Cites it as background 15 papers

The total flavor symmetry of this model is $S_4×Z_3×Z_4$ [ref] , where the auxiliary symmetry $Z_3×Z_4$ is crucial to eliminate unwanted couplings and to insure the needed vacuum alignment.

Lepton Flavor Violation in Models with $A_4$ and $S_4$ Flavor Symmetries · $S_4$ model of Ding · 0.84
In this section, we recapitulate the main features of the $S_4$ flavor model of BMM [ref] and Ding [ref] .

Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry · Variants of the Two $S_4$ Models · 0.97
The technical details of the group are shown in [ref] .

A direct link between neutrinoless double beta decay and leptogenesis in a seesaw model with $S_4$ symmetry · Low energy observables · 0.99

What it cites · 28 sentences without a confident label

Uses data or values from 8 papers

The first one at $0.60$ eV corresponds to the combination of the Cosmic Microwave Background (CMB) anisotropy data (from WMAP 5y [ref] , Arcminute Cosmology Bolometer Array Receiver (ACBAR) [ref] , Very Small Array (VSA) [ref] , Cosmic Background Imager (CBI) [ref] and BOOMERANG [ref] experiments) plus the large-scale structure (LSS) information on galaxy clustering (from the Luminous Red Galaxies Sloan Digital Sky Survey (SDSS) [ref] ) plus the Hubble Space Telescope (HST) plus the luminosity distance SN-Ia data of [ref] and finally plus the BAO data from [ref] .

The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set · Sum of the neutrino masses · 0.92
The first one at $0.60$ eV corresponds to the combination of the Cosmic Microwave Background (CMB) anisotropy data (from WMAP 5y [ref] , Arcminute Cosmology Bolometer Array Receiver (ACBAR) [ref] , Very Small Array (VSA) [ref] , Cosmic Background Imager (CBI) [ref] and BOOMERANG [ref] experiments) plus the large-scale structure (LSS) information on galaxy clustering (from the Luminous Red Galaxies Sloan Digital Sky Survey (SDSS) [ref] ) plus the Hubble Space Telescope (HST) plus the luminosity distance SN-Ia data of [ref] and finally plus the BAO data from [ref] .

Cosmological Constraints from the SDSS Luminous Red Galaxies · Sum of the neutrino masses · 0.92
The first one at $0.60$ eV corresponds to the combination of the Cosmic Microwave Background (CMB) anisotropy data (from WMAP 5y [ref] , Arcminute Cosmology Bolometer Array Receiver (ACBAR) [ref] , Very Small Array (VSA) [ref] , Cosmic Background Imager (CBI) [ref] and BOOMERANG [ref] experiments) plus the large-scale structure (LSS) information on galaxy clustering (from the Luminous Red Galaxies Sloan Digital Sky Survey (SDSS) [ref] ) plus the Hubble Space Telescope (HST) plus the luminosity distance SN-Ia data of [ref] and finally plus the BAO data from [ref] .

High resolution CMB power spectrum from the complete ACBAR data set · Sum of the neutrino masses · 0.92

Compares with 1 paper

From these representation matrices, one can explicitly calculate the Clebsch-Gordan coefficients for the decomposition of the product representations, and the same results as those in Ref. [ref] are obtained.

Fermion Masses and Mixings in a S4 Based Model · The discrete group $S_4$ · 0.95

Cites as background 11 papers

The $A_4$ models are especially attractive, it has received considerable interest in the recent past [ref] .

Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses · Introduction · 0.91
The $A_4$ models are especially attractive, it has received considerable interest in the recent past [ref] .

Resonant leptogenesis and tribimaximal leptonic mixing with A4 symmetry · Introduction · 0.91
The $A_4$ models are especially attractive, it has received considerable interest in the recent past [ref] .

A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing · Introduction · 0.91

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