Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}

Lal Singh; Radha Raman Gautam; S. Dev

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Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}

S. Dev, Radha Raman Gautam, Lal Singh

High Energy Physics - Phenomenology · Submitted 18 Jan 2012

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

The authors' main claim This scheme of breaking S3 symmetry can reproduce a relatively large reactor mixing angle as suggested by the recent T2K results.

how it is stated · hedged possibility 0.74 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,449 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.49 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the effects of breaking S3 symmetry in the neutrino mass matrix for the masses and mixing matrix of neutrinos. At zeroth order the model gives degenerate neutrino masses and accommodates tribimaximal mixing. We introduce perturbations in terms of a small and complex parameter. The perturbations are introduced in a manner such that the S3 symmetry is broken by its elements in the same representation. Successive perturbations introduce mass splitting, sizable non-zero reactor mixing angle and CP violation. This scheme of breaking S3 symmetry can reproduce a relatively large reactor mixing angle as suggested by the recent T2K results. The effective neutrino mass is predicted to be large which is testable in the ongoing and forthcoming neutrinoless double beta decay experiments.

background contribution method result interpretation main claim

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 study the effects of breaking S3 symmetry in the neutrino mass matrix for the masses and mixing matrix of neutrinos.	contribution 0.99	0.87	0.05	asserted 0.73
s1	At zeroth order the model gives degenerate neutrino masses and accommodates tribimaximal mixing.	result 0.54	0.63	0.07	asserted 0.99
s2	We introduce perturbations in terms of a small and complex parameter.	method 0.96	0.88	0.03	asserted 0.99
s3	The perturbations are introduced in a manner such that the S3 symmetry is broken by its elements in the same representation.	method 0.98	0.84	0.05	asserted 0.99
s4	Successive perturbations introduce mass splitting, sizable non-zero reactor mixing angle and CP violation.	result 0.98	0.82	0.47	asserted 1.00
s5	This scheme of breaking S3 symmetry can reproduce a relatively large reactor mixing angle as suggested by the recent T2K results.	result 0.53	0.59	0.34	hedged possibility 0.74
s6	The effective neutrino mass is predicted to be large which is testable in the ongoing and forthcoming neutrinoless double beta decay experiments.	result 0.66	0.80	0.23	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study the effects of breaking S3 symmetry in the neutrino mass matrix for the masses and mixing matrix of neutrinos. At zeroth order the model gives degenerate neutrino masses and accommodates tribimaximal mixing. We introduce perturbations in terms of a small and complex parameter. The perturbations are introduced in a manner such that the S3 symmetry is broken by its elements in the same representation. Successive perturbations introduce mass splitting, sizable non-zero reactor mixing angle and CP violation. This scheme of breaking S3 symmetry can reproduce a relatively large reactor mixing angle as suggested by the recent T2K results. The effective neutrino mass is predicted to be large which is testable in the ongoing and forthcoming neutrinoless double beta decay experiments.

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References

Forward citations

Cited by 2 Pith papers

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

Analysis of an extended scalar sector with $S_3$ symmetry
hep-ph 2014-04 conditional novelty 5.0 of 10

Tree-level unitarity plus vacuum stability in the S3-symmetric three-Higgs-doublet model force all nonstandard scalars below roughly 1 TeV and predict suppressed h to gamma gamma and h to Z gamma signal strengths.
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.

How the literature uses it

14 arXiv papers cite this in 15 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 · 6 sentences without a confident label

Compares with it 1 paper

In comparison, one will be left with $δ= 0$ in the limit of the flavor democracy [ref] or $S^_3$ permutation symmetry [ref] .

Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S^{}_3$ reflection symmetry · Introduction · 0.99

Cites it as background 8 papers

singlet under $S_3$ [ref] .

Quark sector of S3 models: classification and comparison with experimental data · Introduction · 0.81
Models based on this approach have been discussed extensively (see, e.g., [ref] for some recent works) and they often lead to intriguing mixing patterns, including the well-known tribimaximal mixing (TBM) [ref] and bimaximal mixing (BM) [ref] .

Neutrino Mixing and Discrete Symmetries · Introduction · 0.97
Such a symmetry has been explored extensively in the context of the SM gauge group [ref] .

An $S_3$ flavored left-right symmetric model of quarks · Introduction · 0.93

What it cites · 11 sentences without a confident label

Builds on 1 paper

In the present work, we generalized the approach used in Ref. [ref] for breaking $S_3$ symmetry in the neutrino mass matrix by considering a small but complex perturbation parameter.

Broken $S_3$ Symmetry in the Neutrino Mass Matrix · Summary · 0.99

Uses data or values from 2 papers

The experimental constraints on neutrino parameters at 1, 2 and 3$σ$ [ref] are given in Table 1.

Where we are on $\theta_{13}$: addendum to "Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters" · Numerical results · 0.97
Cosmological observations put an upper bound on the sum of neutrino masses [equation] The WMAP data [ref] limit $Σ$ to be less than $0.67 eV$ at $95 %$ C.L..

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · Numerical results · 0.98

Compares with 1 paper

In Ref. [ref] the breaking of $S_3$ symmetry generated a non-zero $θ_13$ but the deviation from zero was small.

Broken $S_3$ Symmetry in the Neutrino Mass Matrix · Introduction · 0.81

Cites as background 4 papers

The most studied phenomenological Ansätz for the neutrino mixing matrix arising from discrete symmetries was proposed by Harrison, Perkins and Scott [ref] known as tribimaximal mixing (TBM) is given by [equation] Non-Abelian flavor symmetries [ref] have been invoked to account for TBM.

The Horizontal Symmetry for Neutrino Mixing · Introduction · 0.99
A large number of papers [ref] have presented detailed models based on $S_3$ symmetry.

Perturbed S3 neutrinos · Introduction · 0.98
Democratic mass matrix in the neutrino sector with terms breaking $S_3$ symmetry to $μ-τ$ symmetry has been discussed in [ref] .

Three-parameter Lorentz-violating texture for neutrino mixing · $S_3$ invariant neutrino mass matrix · 0.95

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