arxiv: 2604.04021 · v1 · submitted 2026-04-05 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Reality-constrained Minimal Yukawa Structure in SO(10) GUT

Shaikh Saad , Vasja Susi\v{c}

Authors on Pith no claims yet

Pith reviewed 2026-05-13 17:22 UTC · model grok-4.3

classification ✦ hep-ph

keywords SO(10) GUTminimal Yukawa sectorreality conditionsfermion mass relationsneutrino oscillationsproton decayneutrinoless double beta decay

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The pith

Corrected reality conditions on real scalars in minimal SO(10) Yukawa sector allow viable fits to all Standard Model fermion masses and mixings.

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

The paper studies the smallest set of Higgs representations in an SO(10) grand unified theory that can generate the observed pattern of quark and lepton masses through Yukawa couplings. It derives the exact reality constraints required when the 10 and 120 representations are taken to be real scalars, uncovering a relative sign difference between the two weak doublets inside the 120 that had been missed in earlier work. This sign difference adds one new magnitude parameter to the resulting fermion mass relations. With the corrected relations the authors scan the parameter space and show that the model can match every measured fermion mass and mixing angle, including the latest JUNO solar oscillation data, while producing definite predictions for right-handed neutrino masses, neutrinoless double beta decay, and proton decay channels.

Core claim

In the minimal Yukawa structure built from real 10_R and 120_R scalars together with a 126, the SO(10) reality conditions on the weak-doublet components impose a relative sign difference between the two doublets of the 120_R. This sign difference introduces an extra free magnitude into the effective mass matrices, allowing the model to reproduce the full set of Standard Model fermion masses, the CKM matrix, and the PMNS matrix including recent JUNO precision on solar parameters. The same scan yields a strongly hierarchical right-handed neutrino spectrum at 10^5, 10^12, and 10^15 GeV, a neutrinoless double beta decay parameter m_beta beta of 3-4 meV, and proton decay dominated by the channels

What carries the argument

The reality-constrained Yukawa couplings from the 10_R ⊕ 120_R ⊕ 126 Higgs representations, with the revised relative sign between the two weak doublets of the 120_R.

If this is right

The model reproduces all measured quark and lepton masses and mixings, including JUNO solar parameters.
Both octants of the atmospheric mixing angle theta_23 remain viable while delta_PMNS near 140-220 degrees is mildly disfavored.
Right-handed neutrinos are strongly hierarchical at scales 10^5, 10^12, and 10^15 GeV.
Neutrinoless double beta decay is predicted at m_beta beta approximately 3-4 meV, just below current experimental reach.
Proton decay proceeds mainly through p to pi-plus anti-nu and p to pi-zero e-plus, channels accessible to next-generation detectors.

Where Pith is reading between the lines

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

The revised sign difference may reduce the need for extra Higgs representations in other minimal SO(10) constructions.
The specific proton decay channels provide a sharp experimental test that distinguishes this Yukawa setup from many alternative GUT realizations.
The hierarchical right-handed neutrino spectrum suggests a particular pattern of leptogenesis that could be checked against the observed baryon asymmetry.

Load-bearing premise

The 10_R and 120_R are strictly real scalars whose weak-doublet constituents obey the derived reality conditions with the reported relative sign difference, and the numerical scan has adequately explored the resulting parameter space.

What would settle it

Observation of proton decay in any channel other than p to pi-plus anti-nu or p to pi-zero e-plus, or a neutrinoless double beta decay rate well outside the 3-4 meV window, would rule out the model's predictions.

read the original abstract

We investigate the minimal Yukawa sector of grand unified theories based on $\mathrm{SO}(10)$ symmetry, consisting of a Higgs structure with representations $\mathbf{10}_{\mathbb{R}}\oplus \mathbf{120}_{\mathbb{R}}\oplus\mathbf{126}$. In this framework, where $\mathbf{10}_\mathbb{R}$ and $\mathbf{120}_{\mathbb{R}}$ are real scalars, we derive the associated $\mathrm{SO}(10)$ reality conditions for their weak-doublet constituents -- both by explicit computation and an analytic reframing into a Pati-Salam-like description -- to revisit previously reported fermion mass relations. Our analysis revises these earlier results, in particular by introducing a relative sign difference between the reality constraints on the two weak doublets in $\mathbf{120}_{\mathbb{R}}$, yielding a new parameter (a magnitude) in the fermion mass relations. Our formalism is fully general and provides a systematic framework for deriving Clebsch-Gordan coefficients and implementing reality constraints for arbitrary parent-daughter representation pairs of $\mathrm{SO}(10)$ and its Pati-Salam subgroup. Incorporating these corrections, we perform an extensive numerical scan of the parameter space and find that the model successfully reproduces SM fermion masses and mixings, including recent precision measurements of solar oscillation parameters by JUNO. It accommodates both octants of $\theta_{23}$ while mildly disfavoring $\delta_\mathrm{PMNS}\sim (140^\circ,220^\circ)$. The model predicts a strongly hierarchical right-handed neutrino spectrum $(10^{5},10^{12},10^{15})$ GeV and a neutrinoless double beta decay parameter $m_{\beta\beta}\sim 3$-$4$ meV, just below future experimental sensitivity. Proton decay is dominated by $p\to\pi^+\overline{\nu}$ and $p\to\pi^0 e^+$, making these channels testable in upcoming experiments.

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.

Desk Editor's Note private letter to a colleague

They correct a relative sign in the 120 reality conditions, add a magnitude parameter, and show a numerical fit that works with JUNO data and gives concrete predictions for mbb and proton decay.

read the letter

The main takeaway is that Saad and Susič have spotted and corrected a relative sign difference in the reality constraints applied to the two weak doublets of the 120 representation in their minimal SO(10) setup. This correction introduces an additional magnitude parameter into the fermion mass relations, which revises some earlier results in the literature. They derive these conditions both through direct computation and by recasting the problem in a Pati-Salam framework, and they show that the updated relations allow a viable fit to the observed fermion masses and mixings. Their numerical scan incorporates recent JUNO measurements on solar parameters and finds solutions that work for both octants of theta23 while somewhat disfavoring a range of the CP phase. The model then predicts a strongly hierarchical spectrum for the right-handed neutrinos and a neutrinoless double beta decay effective mass around 3 to 4 meV, along with proton decay branching ratios that favor certain channels. What stands out is the systematic treatment of the Clebsch-Gordan coefficients and reality constraints, which they present in a general form that could apply more broadly. The fit succeeds in reproducing the data without obvious tuning, and the predictions for upcoming experiments give the work some phenomenological bite. On the downside, the abstract provides little information on the details of the parameter scan, such as the range explored, the number of points sampled, or how uncertainties were handled. This makes it difficult to assess how robust the conclusions are. The entire set of predictions hinges on the accuracy of that sign difference, so any error there would invalidate the new results and revert to prior relations. I would want a referee to double-check the derivation step by step. Overall, this is targeted at researchers working on grand unified theories and specifically on constructing realistic Yukawa sectors in SO(10). A reader looking for updated minimal models with concrete experimental implications would find it worthwhile. The work shows clear thinking on the group theory side and engages honestly with fitting the data. I think it deserves to go to peer review rather than a desk rejection, as the correction and the resulting predictions are substantive enough to merit expert scrutiny.

Referee Report

1 major / 2 minor

Summary. The paper claims that by deriving revised reality conditions for the real 10_R and 120_R representations in SO(10), including a relative sign difference for the weak doublets in 120_R that introduces a new magnitude parameter, the minimal Yukawa sector can be fitted to SM fermion masses and mixings through an extensive numerical scan. This includes recent JUNO solar oscillation parameters, accommodates both θ23 octants, mildly disfavors certain δPMNS values, and predicts a hierarchical right-handed neutrino spectrum, mββ ~ 3-4 meV, and dominant proton decay channels p→π+ν¯ and p→π0e+.

Significance. If the reality conditions are correctly derived, the work demonstrates a viable minimal SO(10) GUT with concrete, testable predictions for neutrino physics and proton decay, enhancing the predictive power of GUT models. The systematic framework for reality constraints is a positive contribution, and the numerical success with precision data like JUNO adds to its significance.

major comments (1)

[Derivation of reality conditions] The relative sign difference between the reality constraints on the two weak doublets inside 120_R is critical as it yields the new magnitude parameter in the Yukawa relations. The explicit computation and Pati-Salam reframing should be presented with sufficient detail (e.g., the specific Clebsch-Gordan coefficients or matrix elements) to allow verification, since an error in the sign would revert the mass matrices to the previous form and invalidate the scan results and predictions.

minor comments (2)

[Abstract] The abstract states that an extensive numerical scan was performed but provides no details on the methodology, parameter ranges, or how errors were treated, which is important for evaluating the robustness of the fits to JUNO data and the θ23 octants.
[Numerical results] The right-handed neutrino masses are quoted as (10^5, 10^12, 10^15) GeV; clarify whether these are representative values from the scan or exact predictions from a specific fit point.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the single major comment below and will incorporate the requested details in the revised version.

read point-by-point responses

Referee: The relative sign difference between the reality constraints on the two weak doublets inside 120_R is critical as it yields the new magnitude parameter in the Yukawa relations. The explicit computation and Pati-Salam reframing should be presented with sufficient detail (e.g., the specific Clebsch-Gordan coefficients or matrix elements) to allow verification, since an error in the sign would revert the mass matrices to the previous form and invalidate the scan results and predictions.

Authors: We agree that the derivation requires additional explicit detail to facilitate verification. In the revised manuscript we will expand the relevant section to include the full explicit computation of the reality conditions on the 120_R representation using the SO(10) generators, listing the relevant Clebsch-Gordan coefficients and the resulting matrix elements for each weak doublet. We will also enlarge the Pati-Salam reframing subsection with the explicit transformation matrices that produce the relative sign difference, thereby showing how the new magnitude parameter enters the Yukawa relations. These additions will allow readers to reproduce the sign and confirm that the mass matrices differ from earlier forms. revision: yes

Circularity Check

0 steps flagged

Derivation chain self-contained; reality conditions derived explicitly, predictions follow from constrained fit

full rationale

The paper derives the revised reality conditions on the weak doublets of 10_R and 120_R by explicit computation plus Pati-Salam reframing, yielding a new magnitude parameter in the Yukawa relations. These relations then constrain the numerical scan over Yukawa parameters fitted to SM fermion data. Outputs such as the right-handed neutrino spectrum, m_beta beta ~ 3-4 meV, and dominant proton decay channels are direct consequences of the fitted model under the derived constraints, not inputs or self-definitions. No load-bearing step reduces to a fitted quantity renamed as prediction or to a self-citation chain; the derivation is independent of the target observables.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the SO(10) gauge symmetry with the chosen real Higgs representations, the derived reality conditions, and multiple Yukawa coupling parameters that are fitted to data; no new particles or forces are postulated beyond the standard GUT content.

free parameters (2)

new magnitude parameter from relative sign difference
Arises directly from the corrected reality constraints on the two weak doublets inside 120_R and enters the fermion mass matrices.
Yukawa coupling matrices
Multiple independent Yukawa matrices for the 10, 120, and 126 representations are adjusted to reproduce observed fermion masses and mixings.

axioms (2)

domain assumption SO(10) gauge symmetry with Higgs content 10_R ⊕ 120_R ⊕ 126
Standard minimal choice for Yukawa sector in SO(10) GUTs; invoked throughout the derivation of mass relations.
domain assumption Reality conditions must be imposed on the weak-doublet components of the real 10_R and 120_R scalars
Derived explicitly in the paper; the relative sign difference is the key new element.

pith-pipeline@v0.9.0 · 5649 in / 1730 out tokens · 59918 ms · 2026-05-13T17:22:16.651245+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We derive the associated SO(10) reality conditions for their weak-doublet constituents... yielding a new parameter (a magnitude) in the fermion mass relations.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the revised reality conditions introduce one additional parameter (magnitude) relative to previous analyses.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

Towards Precision Neutrino Fits in GUTs: Relevance of One-Loop Finite Corrections
hep-ph 2026-05 unverdicted novelty 6.0

One-loop corrections in minimal SO(10) GUTs cause 30-40% shifts in neutrino observables from tree-level fits, requiring their inclusion for reliable parameter space exploration.

Reference graph

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