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Flavour in $SU(5)$ Finite Grand Unified Models
High Energy Physics - Phenomenology · Submitted 25 Jun 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern.
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Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. | contribution 0.99 | 0.84 | 0.07 | asserted 0.93 |
| s1 | The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. | result 0.94 | 0.86 | 0.08 | asserted 1.00 |
| s2 | The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. | result 0.97 | 0.85 | 0.13 | asserted 0.92 |
| s3 | For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. | result 0.97 | 0.86 | 0.16 | asserted 1.00 |
| s4 | One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. | result 0.96 | 0.89 | 0.38 | hedged possibility 0.91 |
| s5 | In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. | result 1.00 | 0.85 | 0.12 | asserted 1.00 |
| s6 | Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings. | contribution 0.71 | 0.91 | 0.17 | asserted 1.00 |
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Original abstract
Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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In this paper, we present the first modular-invariant $Γ_3 ≅A_4$ flavor model within a non-SUSY[In the framework of the ordinary SUSY $SU(5)$ GUT in four dimensions, flavor models have been developed using various conventional non-Abelian symmetry groups, including $S_4$ [ref] and its subgroups $A_4$ [ref] , $S_3$ [ref] , and $D_4$ [ref] .
Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT · Introduction · 0.97
What it cites · 43 sentences without a confident label
Uses the method or tool of 8 papers
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A number of conditions are required (see for example [ref] ) and, following [ref] , we can introduce mass parameters and couplings carrying mass dimension [ref] in the same way as dimensionless couplings.
Perturbative Unification of Soft Supersymmetry--Breaking Terms · Theoretical Basis of Reduction of couplings · 0.80
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The spurion technique [ref] gives all-loop relations among SSB $β$-functions [ref] .
Two-loop renormalization group equations for soft SUSY breaking scalar interactions: supergraph method · Theoretical Basis of Reduction of couplings · 0.88
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The spurion technique [ref] gives all-loop relations among SSB $β$-functions [ref] .
Exact Results for Soft Supersymmetry Breaking Parameters in Supersymmetric Gauge Theories · Theoretical Basis of Reduction of couplings · 0.88
Compares with 2 papers
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[ref] , although in our case it exhibits different discrete symmetries, which could affect the bilinear terms in the soft breaking sector, not analyzed here.
Finite Grand Unified Theories and the Quark Mixing Matrix · Discussion and Conclusions · 0.98
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The $M_d$ mass matrix exhibits a similar structure to the one in [ref] , for a non-supersymmetric 4 Higgs doublet model with $S_3$ symmetry.
Quark sector of S3 models: classification and comparison with experimental data · An TEXT FUT model based on TEXT · 0.99
Cites as background 14 papers
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The FUTA model represents a first approach to the finiteness discussion, in which the superpotential is constructed so that the mass matrices are diagonal, i.e., no mixing terms appear between generations [ref] .
Finite Unified Models · First approach: Diagonal model FUTA · 0.81
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[ref] ), where the finiteness conditions were only applied to the third generation.
Finite Unification: Theory, Models and Predictions · TEXT FUT models based on cyclic symmetries · 0.80
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Once the $SU(5)$ gauge symmetry is broken, it will be assumed that the resulting theory is the MSSM [ref] .
Finite Unification: Theory and Predictions · General Higgs sector rotation of TEXT FUTs, doublet-triplet splitting and fine tuning · 0.82
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