Fermion Mass Hierarchies and Flavour Mixing from a Minimal Discrete Symmetry

Ferruccio Feruglio; Yin Lin

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Fermion Mass Hierarchies and Flavour Mixing from a Minimal Discrete Symmetry

Ferruccio Feruglio, Yin Lin

High Energy Physics - Phenomenology · Submitted 10 Dec 2007

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

The authors' main claim A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2), \lambda_c denoting the Cabibbo angle.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.92 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is broken down to a \nu_\mu-\nu_\tau parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing \theta_{13}. In the charged lepton sector the \nu_\mu-\nu_\tau parity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2), \lambda_c denoting the Cabibbo angle. A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.

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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 construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group.	contribution 0.94	0.95	0.08	asserted 1.00
s1	At the leading order, in the neutrino sector S3 is broken down to a \nu_\mu-\nu_\tau parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing \theta_{13}.	result 0.91	0.77	0.21	asserted 1.00
s2	In the charged lepton sector the \nu_\mu-\nu_\tau parity is maximally broken and the resulting mass matrix is nearly diagonal.	result 0.97	0.81	0.08	asserted 1.00
s3	The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone.	result 0.98	0.84	0.13	asserted 1.00
s4	A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2), \lambda_c denoting the Cabibbo angle.	result 1.00	0.93	0.46	asserted 1.00
s5	A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.	limitation 0.48	0.86	0.13	asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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The paper

Original abstract

We construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is broken down to a \nu_\mu-\nu_\tau parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing \theta_{13}. In the charged lepton sector the \nu_\mu-\nu_\tau parity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2), \lambda_c denoting the Cabibbo angle. A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.

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References

Forward citations

Cited by 3 Pith papers

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

Quark sector of S3 models: classification and comparison with experimental data
hep-ph 2013-04 conditional novelty 4.0 of 10

S3 family-symmetry models of quarks, with one to four Higgs doublets, yield mixing matrices that fit current CKM data well, though the fit uses several adjustable parameters and measured masses as inputs.
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

22 arXiv papers cite this in 32 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 · 20 sentences without a confident label

Contests it 1 paper

In [ref] it has been suggested to introduce a further symmetry under which $x_1 = -x_2$ and $v_ϕ= v_χ$; however, as pointed out in [ref] , this additional symmetry does not commute with $S_3$ and the whole symmetry group is larger than the latter.

S3 as a flavour symmetry for quarks and leptons after the Daya Bay result on \theta 13 · Charged leptons · contest 0.74

Compares with it 2 papers

This way of aligning the vacuum is similar to the one found in [ref] .

D14 - A Common Origin of the Cabibbo Angle and the Lepton Mixing Angle theta^l_13 · Lepton sector · 0.99
Note that a similar suppression of the reactor angle has been found for the model in Ref. [ref] .

Group space scan of flavor symmetries for nearly tribimaximal lepton mixing · Results of the Group Space Scan · 0.99

Cites it as background 9 papers

singlet under $S_3$ [ref] .

Quark sector of S3 models: classification and comparison with experimental data · Introduction · 0.81
Several models have been constructed that account for the structure of leptonic mixings, e.g. [ref] , while other models extend the underlying family symmetry to provide a description of the complete fermionic structure [ref] .[See [ref] for review papers with more extensive references.] If the neutrino flavour symmetry arises directly from the family symmetry [ref] then this implies that the family symmetry should contain the generators $S$ and $U$ so that they can be preserved in the neutrino sector at LO.

A SUSY GUT of Flavour with S4 x SU(5) to NLO · Introduction · 0.95
There has been much recent work based on this idea that the postulated TB symmetry can arise from a family symmetry [ref] .

SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry · Introduction · 0.80

What it cites · 20 sentences without a confident label

Uses data or values from 2 papers

The present data [ref] : θ_12=(34.5±1.4)^0 , θ_23=(42.3^+5.1_-3.3)^0 , θ_13=(0.0^+7.9_-0.0)^0 ,

Neutrino masses and mixings and... · Introduction · 0.98
The upper bound on $θ_13$ is dominated by the CHOOZ data [ref] , though the preference for a small $θ_13$ is also present in the solar and the atmospheric data samples.

Search for neutrino oscillations on a long base-line at the CHOOZ nuclear power station · Introduction · 0.80

Cites as background 5 papers

Several theoretical mechanisms leading to a nearly TB mixing have been suggested in the last years [ref] .

Tri-bimaximal Neutrino Mixing and Quark Masses from a Discrete Flavour Symmetry · Introduction · 0.96
Several theoretical mechanisms leading to a nearly TB mixing have been suggested in the last years [ref] .

Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters · Introduction · 0.96
Several theoretical mechanisms leading to a nearly TB mixing have been suggested in the last years [ref] .

Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions · Introduction · 0.96

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