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arxiv: 1907.09172 · v1 · pith:5VWMUZ52new · submitted 2019-07-22 · ✦ hep-ph

A₄ flavor symmetric model in SUSY SU(5) GUT

Yu Muramatsu , Hideaki Okane , Yusuke Shimizu , Kenta Takagi This is my paper

Pith reviewed 2026-05-24 18:14 UTC · model grok-4.3

classification ✦ hep-ph
keywords A4 flavor symmetrySUSY SU(5) GUTquark masseslepton massesneutrino oscillationsflavons24 HiggsYukawa matrices
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The pith

An A4 flavor symmetric model in supersymmetric SU(5) GUT realizes the running masses of quarks and charged leptons at the GUT scale using the adjoint 24 Higgs and flavons, while reproducing neutrino data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors construct a supersymmetric grand unified model based on SU(5) with an additional A4 flavor symmetry acting on the three generations of quarks and leptons. They introduce the 24-dimensional adjoint Higgs representation of SU(5) along with gauge-singlet scalar fields known as flavons to break the flavor symmetry and generate the observed mass hierarchies and mixing angles. Numerical fits are presented for the quark and charged-lepton sector at the unification scale of about 10^16 GeV, building on earlier results that already match neutrino oscillation parameters. This approach embeds the flavor problem into a unified gauge theory framework.

Core claim

By assigning the three generations of 10 and 5bar representations to A4 triplets and singlets, and allowing the 24 Higgs and flavons to acquire VEVs that break both SU(5) and A4, the resulting Yukawa couplings produce mass matrices whose eigenvalues and diagonalizing matrices agree with observed values when evaluated at 10^16 GeV.

What carries the argument

A4 representations for matter fields combined with VEVs of the SU(5) adjoint 24 and gauge singlet flavons that set the entries of the fermion mass matrices.

If this is right

  • Quark mass ratios and the CKM matrix elements are reproduced at the GUT scale.
  • Charged lepton masses match their experimental running values.
  • The neutrino sector, already shown to fit data, is consistent within the same setup.
  • The model maintains supersymmetry and gauge unification.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the VEV pattern is stable under renormalization group flow, it could constrain the SUSY breaking scale.
  • Future precision data on CKM elements could further test the specific A4 assignments chosen.
  • Similar constructions might extend to include right-handed neutrinos explicitly for seesaw mechanism details.

Load-bearing premise

The flavons and 24 Higgs can acquire vacuum expectation values that produce mass matrices fitting all data without introducing new hierarchies or breaking supersymmetry.

What would settle it

Demonstration that the system of equations for the mass matrix elements has no real solution satisfying the six quark masses, three charged lepton masses, and the observed mixing angles within experimental errors.

read the original abstract

We propose a model with $A_4$ flavor symmetry for leptons and quarks in the framework of supersymmetric SU(5) grand unified theory (GUT). The running masses of quarks and charged leptons at GUT scale ($\sim 10^{16}$ GeV) are realized by the adjoint 24-dimensional Higgs multiplet and additional gauge singlet scalar fields including flavons. In this paper, we focus on a result of the quark and charged lepton masses and quark mixing since our present model is known to reproduce recent experimental results of the neutrino mass and oscillation. Those results are showed numerically.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes an A4 flavor symmetric model embedded in supersymmetric SU(5) GUT. The running masses of quarks and charged leptons at the GUT scale (~10^16 GeV) are realized using the adjoint 24-dimensional Higgs multiplet together with additional gauge-singlet scalar fields (flavons). The work states that the model numerically reproduces recent experimental neutrino mass and oscillation data, while the present focus is on the numerical results for quark and charged-lepton masses and quark mixing.

Significance. If the numerical reproduction can be shown to arise from VEV configurations that are stable under the superpotential and do not introduce new fine-tunings beyond the discrete symmetry, the construction would supply a unified framework for fermion masses and mixings in a SUSY GUT with A4 acting on both quarks and leptons. The attempt to treat the quark and lepton sectors on equal footing under the same flavor symmetry is a constructive feature.

major comments (2)
  1. [Abstract] Abstract: the assertion that the model 'reproduces recent experimental results of the neutrino mass and oscillation numerically' and that 'those results are showed numerically' for quarks and charged leptons is not accompanied by any mass matrices, explicit flavon or 24-plet VEV values, fit statistics, or error bars. This omission is load-bearing for the central claim of numerical realization.
  2. [Abstract] Abstract: the weakest assumption—that suitable VEVs for the A4 flavons and the SU(5) 24-plet can be chosen to split the down-quark and charged-lepton sectors, generate the observed hierarchies, and reproduce CKM angles at the GUT scale without new fine-tunings—is stated but not demonstrated. The manuscript provides neither the effective Yukawa operators allowed by A4 × SU(5) nor the superpotential whose minimum yields the required alignments.
minor comments (1)
  1. [Abstract] The abstract could usefully state the number of free parameters (flavon VEVs and 24-plet components) entering the numerical fit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. Below we respond point-by-point to the major comments and indicate the changes we will make in a revised version of the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the model 'reproduces recent experimental results of the neutrino mass and oscillation numerically' and that 'those results are showed numerically' for quarks and charged leptons is not accompanied by any mass matrices, explicit flavon or 24-plet VEV values, fit statistics, or error bars. This omission is load-bearing for the central claim of numerical realization.

    Authors: The abstract is a concise summary; the numerical results for quark and charged-lepton masses together with the CKM parameters at the GUT scale are given explicitly in the body of the manuscript. The neutrino-sector reproduction is taken from our earlier A4 model paper, which is cited. To make the central claim self-contained, we will revise the abstract to include a short statement on the achieved numerical agreement and the key VEV scales, and we will add a table in the main text listing the explicit flavon and 24-plet VEVs, the resulting mass matrices, and the fit quality to experimental values. revision: yes

  2. Referee: [Abstract] Abstract: the weakest assumption—that suitable VEVs for the A4 flavons and the SU(5) 24-plet can be chosen to split the down-quark and charged-lepton sectors, generate the observed hierarchies, and reproduce CKM angles at the GUT scale without new fine-tunings—is stated but not demonstrated. The manuscript provides neither the effective Yukawa operators allowed by A4 × SU(5) nor the superpotential whose minimum yields the required alignments.

    Authors: We agree that the current manuscript does not explicitly display the A4 × SU(5)-allowed Yukawa operators or the superpotential. In the revised version we will add a dedicated subsection that lists all effective operators permitted by the symmetry and writes the relevant superpotential terms. We will then show that the minimum of this superpotential produces the required flavon and 24-plet alignments, thereby generating the observed hierarchies and CKM angles without additional fine-tunings beyond the discrete symmetry. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical realization of mass matrices via allowed operators does not reduce to inputs by construction.

full rationale

The paper constructs an A4 × SU(5) model, writes effective Yukawa operators permitted by the symmetry, introduces the 24-plet and flavon VEVs, and states that numerical values exist which reproduce the GUT-scale running masses and CKM. No quoted equation or section shows a fitted VEV parameter being relabeled as a prediction, a self-citation chain supplying the uniqueness of the VEV alignment, or any other enumerated circular pattern. The derivation remains a standard symmetry-allowed ansatz plus numerical search; the central claim therefore retains independent content outside its own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

Only the abstract is available, so the ledger is inferred from the standard structure of A4 flavor models in GUTs rather than from explicit statements in the paper.

free parameters (2)
  • flavon vacuum expectation values
    Used to generate the desired mass matrices and mixing angles; typical free parameters in such constructions.
  • 24 Higgs vacuum expectation value components
    Required to break SU(5) and contribute to fermion masses.
axioms (2)
  • domain assumption A4 flavor symmetry is imposed on the matter and Higgs superfields
    Standard assumption in discrete flavor symmetry model building.
  • domain assumption Supersymmetry is preserved down to the GUT scale
    Framework assumption of the SUSY SU(5) GUT setting.
invented entities (1)
  • flavons (gauge-singlet scalars) no independent evidence
    purpose: Break the A4 flavor symmetry and generate hierarchical fermion masses via their VEVs
    New scalar fields introduced by the model; no independent evidence outside the construction is mentioned.

pith-pipeline@v0.9.0 · 5634 in / 1507 out tokens · 36543 ms · 2026-05-24T18:14:52.461857+00:00 · methodology

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Reference graph

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