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The $S_{3}$ symmetry: Flavour and texture zeroes

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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F. González Canales, A. Mondragón

High Energy Physics - Phenomenology · Submitted 20 Jan 2011

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

The authors' main claim This classification reduce the number of phenomenologically viable textures for the non-singulars mass matrices of $3\times3$, from thirty three down to only eleven independent sets of matrices.

how it is stated · asserted 1.00 read the record →

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arXiv ID1101.3807 (version 1)
Pith ID7ZPUKCNZ, Pith's permanent record of this paper and its review
CitationA. Mondrag\'on, F. Gonz\'alez Canales. "The $S_{3}$ symmetry: Flavour and texture zeroes." arXiv:1101.3807 (2011). https://pith.science/paper/7ZPUKCNZ
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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, 4,302 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We use the permutational symmetry group $S_{3}$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. In this framework all mass matrices of the fermions in the theory have the same form with four texture zeroes of class of I. Also, with the help of six elements of real matrix representation of $S_ {3}$ as transformation matrices of similarity classes, we make a classification of the sets of mass matrices with texture zeroes in equivalence classes. This classification reduce the number of phenomenologically viable textures for the non-singulars mass matrices of $3\times3$, from thirty three down to only eleven independent sets of matrices. Each of these sets of matrices has exactly the same physical content.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We use the permutational symmetry group $S_{3}$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. contribution 0.55 0.87 0.12 asserted 1.00
s1 In this framework all mass matrices of the fermions in the theory have the same form with four texture zeroes of class of I. result 0.76 0.78 0.25 asserted 1.00
s2 Also, with the help of six elements of real matrix representation of $S_ {3}$ as transformation matrices of similarity classes, we make a classification of the sets of mass matrices with texture zeroes in equivalence classes. method 0.89 0.92 0.08 asserted 1.00
s3 This classification reduce the number of phenomenologically viable textures for the non-singulars mass matrices of $3\times3$, from thirty three down to only eleven independent sets of matrices. result 0.99 0.89 0.41 asserted 1.00
s4 Each of these sets of matrices has exactly the same physical content. result 0.58 0.80 0.21 asserted 1.00

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

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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 use the permutational symmetry group $S_{3}$ as a symmetry of flavour, which leads to a unified treatment of masses and mixings of the quarks and leptons. In this framework all mass matrices of the fermions in the theory have the same form with four texture zeroes of class of I. Also, with the help of six elements of real matrix representation of $S_ {3}$ as transformation matrices of similarity classes, we make a classification of the sets of mass matrices with texture zeroes in equivalence classes. This classification reduce the number of phenomenologically viable textures for the non-singulars mass matrices of $3\times3$, from thirty three down to only eleven independent sets of matrices. Each of these sets of matrices has exactly the same physical content.

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References
How the literature uses it

8 arXiv papers cite this in 9 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 · 4 sentences without a confident label

Cites it as background 5 papers

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