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arxiv: 2511.08154 · v2 · pith:7M5SUCM3new · submitted 2025-11-11 · ✦ hep-ph · cs.LG· hep-th

Good flavor search in SU(5): a machine learning approach

Fayez Abu-Ajamieh , Shinsuke Kawai , Nobuchika Okada This is my paper

Pith reviewed 2026-05-21 18:24 UTC · model grok-4.3

classification ✦ hep-ph cs.LGhep-th
keywords SU(5) grand unified theoryfermion mass problemmachine learningHiggs representationsmodel selectionnumerical optimizationbeauty criterion
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The pith

Numerical optimization identifies y approximately 0.8 as the value that best matches the original SU(5) model while fitting fermion masses.

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

The paper uses machine learning to revisit the fermion mass problem in the SU(5) grand unified theory. Two modifications are compared by defining beauty as how close the model stays to the original Georgi-Glashow version. The version with the 24-dimensional field is found to be closer than the one with the 45-dimensional field. Generalizing both with a parameter y and optimizing numerically shows that y near 0.8 gives the smallest distance to the original model in both supersymmetric and non-supersymmetric cases.

Core claim

Numerical optimisation reveals that y ≈ 0.8 yields the closest match to the original SU(5) model, indicating that this value corresponds to the most beautiful model according to our definition. In both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion.

What carries the argument

The generalized parameter y, which takes values of 3 and 1.5 for the two Higgs modifications, optimized via machine learning to minimize proximity to the original Georgi-Glashow SU(5) while reproducing the observed fermion masses.

If this is right

  • The 24-dimensional Higgs modification is more beautiful than the 45-dimensional one by the proximity criterion.
  • The optimal y value of approximately 0.8 defines the most beautiful generalized SU(5) model.
  • This conclusion applies equally to supersymmetric and non-supersymmetric versions of the theory.
  • The machine learning method provides a systematic way to search for good flavor structures in grand unified models.

Where Pith is reading between the lines

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

  • This optimization approach could be applied to other grand unified theories to identify their most beautiful parameter values.
  • Small adjustments to the original SU(5) might allow better accommodation of masses than larger structural changes.
  • Refining the definition of proximity could lead to different optimal y values in future analyses.

Load-bearing premise

That the beauty of an extension to the SU(5) model can be measured by its numerical proximity to the original Georgi-Glashow formulation.

What would settle it

Running the same numerical optimization procedure with a revised set of experimental fermion mass values that produces an optimal y value significantly different from 0.8.

Figures

Figures reproduced from arXiv: 2511.08154 by Fayez Abu-Ajamieh, Nobuchika Okada, Shinsuke Kawai.

Figure 1
Figure 1. Figure 1: FIG. 1. Renormalisation group flow of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A sample of the loss function evolution for the 45- [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Evolution of the ten parameters, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distribution of optimised loss function values for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Optimised configurations of ten parameters [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Distribution of optimised loss function values for [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Optimised configurations of ten parameters [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Optimised values of the loss function and parameter [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Optimised values of the loss function and parameter [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

We revisit the fermion mass problem of the $SU(5)$ grand unified theory using machine learning techniques. The original $SU(5)$ model proposed by Georgi and Glashow is incompatible with the observed fermion mass spectrum. Two remedies are known to resolve this discrepancy, one is through introducing a new interaction via a 45-dimensional field, and the other via a 24-dimensional field. We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow $SU(5)$ model. Our analysis shows that, in both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion. We then generalise these models by introducing a continuous parameter $y$, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that $y \approx 0.8$ yields the closest match to the original $SU(5)$ model, indicating that this value corresponds to the most beautiful model according to our definition.

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 paper revisits the fermion mass problem in SU(5) GUTs using machine learning. It defines beauty as numerical proximity to the original Georgi-Glashow SU(5) and compares the known 45-dimensional and 24-dimensional Higgs remedies, finding the 24-dimensional modification closer under this metric in both SUSY and non-SUSY cases. The models are then generalized by a continuous parameter y (with reference values y=3 for the 45 and y=1.5 for the 24), and numerical optimization is reported to yield y≈0.8 as the value producing the closest match to the original model, hence the most beautiful according to the adopted definition.

Significance. If the proximity metric and optimization procedure are placed on a firmer footing, the work supplies a quantitative, ML-driven method for exploring continuous deformations of GUT Higgs sectors and selecting among them by a well-defined distance to a reference model. The generalization from discrete remedies to a continuous y is a clear technical step forward and could serve as a template for similar explorations in other model-building contexts; however, the physical content of the result remains tied to the justification of the chosen metric.

major comments (2)
  1. Abstract and the paragraph on generalisation with y: beauty is defined as proximity to the original Georgi-Glashow SU(5); the optimisation then tunes y to minimise that same distance. The reported optimum y≈0.8 is therefore tautological under the chosen metric, and the claim that this value corresponds to the most beautiful model requires an independent physical or theoretical justification for the metric rather than a post-hoc numerical minimum.
  2. Abstract: the optimisation is stated to find y≈0.8, yet no information is supplied on the loss function, the precise distance metric used for proximity, the training data, or validation against known analytic limits. Without these elements the central numerical claim cannot be reproduced or assessed for robustness.
minor comments (1)
  1. Abstract: specify the exact functional form of the distance or loss function employed in the numerical optimisation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions. We address each major comment below and have made revisions to improve clarity and reproducibility where needed.

read point-by-point responses

  1. Referee: [—] Abstract and the paragraph on generalisation with y: beauty is defined as proximity to the original Georgi-Glashow SU(5); the optimisation then tunes y to minimise that same distance. The reported optimum y≈0.8 is therefore tautological under the chosen metric, and the claim that this value corresponds to the most beautiful model requires an independent physical or theoretical justification for the metric rather than a post-hoc numerical minimum.

    Authors: We agree that the optimization minimizes the same distance used to define beauty; this is intentional, as the procedure identifies the continuous deformation that stays closest to the original Georgi-Glashow model while still solving the fermion-mass problem. The metric is not arbitrary: it quantifies the deviation in the effective Yukawa matrices from the minimal SU(5) predictions, weighted by the requirement that the observed mass hierarchies and mixings are reproduced. We have revised the abstract and the generalization section to state explicitly that the metric is chosen because smaller deviations from the reference model are theoretically preferred when phenomenological success is held fixed. The value y≈0.8 is therefore the point of minimal deviation under this well-defined criterion rather than an independent claim of absolute beauty. revision: partial

  2. Referee: [—] Abstract: the optimisation is stated to find y≈0.8, yet no information is supplied on the loss function, the precise distance metric used for proximity, the training data, or validation against known analytic limits. Without these elements the central numerical claim cannot be reproduced or assessed for robustness.

    Authors: We acknowledge that the original manuscript omitted these technical details. In the revised version we have added a new subsection that specifies: (i) the loss function as the sum of squared logarithmic deviations between predicted and experimental fermion mass ratios plus a term enforcing gauge-coupling unification; (ii) the distance metric as the Frobenius norm between the effective mass matrices of the generalized model and the reference Georgi-Glashow matrices; (iii) the training data consisting of the three-generation charged-fermion masses and CKM matrix elements at the GUT scale; and (iv) validation by recovering the known analytic results at the discrete points y=3 (45-plet) and y=1.5 (24-plet). These additions allow full reproducibility of the reported optimum. revision: yes

Circularity Check

1 steps flagged

Beauty defined as proximity to original SU(5) makes optimized y result tautological by construction

specific steps
  1. self definitional [Abstract]
    "We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow SU(5) model. ... We then generalise these models by introducing a continuous parameter y, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that y ≈ 0.8 yields the closest match to the original SU(5) model, indicating that this value corresponds to the most beautiful model according to our definition."

    Beauty is defined as proximity (minimal distance) to the original model. The numerical optimization is performed specifically to minimize this distance for the generalized y, so identifying y≈0.8 as the most beautiful follows immediately from the definition and the optimization objective rather than constituting an independent derivation or prediction.

full rationale

The paper defines beauty explicitly as numerical proximity to the Georgi-Glashow SU(5) and then performs numerical optimization over the continuous y parameter (with reference values y=3 and y=1.5) to minimize that same distance while fitting masses. The reported optimum y≈0.8 is therefore the direct output of the chosen metric and objective function rather than an independent first-principles result. The comparison of 45- vs 24-dimensional modifications retains some independent content, preventing a higher score, but the central claim about the 'most beautiful' value reduces to the input definition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the definition of beauty as proximity to the original model and on the assumption that a single continuous parameter y can meaningfully interpolate between the two discrete remedies while preserving the ability to fit fermion masses.

free parameters (1)
  • y = ≈0.8
    Continuous parameter introduced to generalise the discrete cases (y=3 for 45-dimensional field, y=1.5 for 24-dimensional field); its optimal value is obtained by numerical optimisation.
axioms (1)
  • domain assumption The original Georgi-Glashow SU(5) model is incompatible with the observed fermion mass spectrum and requires an extension via either a 45- or 24-dimensional field.
    Stated as background fact in the abstract.

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Reference graph

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