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arxiv: 2606.24571 · v1 · pith:HTORNXRUnew · submitted 2026-06-23 · ✦ hep-ph

Universal two-zero texture in SO(10): implications of JUNO and realization from non-invertible symmetries

Zi-Qiang Chen , Wen-Hao Jiang , Ye-Ling Zhou This is my paper

Pith reviewed 2026-06-25 23:29 UTC · model grok-4.3

classification ✦ hep-ph
keywords universal two-zero textureSO(10)neutrino mass orderingnon-invertible symmetriesJUNODirac CP phaseneutrinoless double beta decay
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The pith

Universal two-zero texture in SO(10) fits nine flavor observables with seven parameters after fixing charged fermion masses.

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

The paper applies the universal two-zero texture simultaneously to all quark and lepton mass matrices inside an SO(10) grand unified theory. With charged-fermion masses fixed at their best-fit values, the construction uses only seven free parameters to describe the remaining nine flavor observables. Updated fits that incorporate the recent JUNO indication for normal neutrino ordering show the texture remains consistent with every current measurement and gains stronger support for that ordering. The Dirac CP phase is restricted to two main intervals, one of which aligns with existing data, while the effective Majorana mass for neutrinoless double beta decay is predicted at the meV scale. The same zero pattern can be generated by non-invertible selection rules that arise from Z_3 gauging of a Z_N symmetry, with the smallest viable case N=7.

Core claim

The universal two-zero texture imposed uniformly on the up-quark, down-quark, charged-lepton and neutrino mass matrices within SO(10) yields a seven-parameter description of nine flavor observables that fits all current data, exhibits an enhanced preference for normal neutrino mass ordering, confines the Dirac phase to two regions, and forecasts a meV-scale m_beta beta; the texture admits a realization from non-invertible selection rules produced by Z_3 gauging of Z_N with minimal N=7.

What carries the argument

Universal two-zero texture (UTZT) applied simultaneously to every quark and lepton mass matrix in the SO(10) framework.

If this is right

  • The texture remains fully compatible with all current flavor data.
  • It exhibits an enhanced preference for normal neutrino mass ordering.
  • The Dirac phase is predicted mainly in two regions, one of which matches existing data.
  • A meV-scale m_beta beta is forecasted, below the reach of next-generation neutrinoless double beta decay searches.
  • The zero pattern can be realized from non-invertible selection rules of Z_3 gauged Z_N symmetry with minimal N=7.

Where Pith is reading between the lines

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

  • Precision data on the Dirac phase from future oscillation experiments could distinguish or exclude one of the two allowed regions.
  • The same non-invertible symmetry mechanism might generate analogous textures inside other grand unified groups without extra light fields.
  • The seven-parameter economy provides a concrete target for testing whether zero textures survive in more complete ultraviolet completions.

Load-bearing premise

The universal two-zero texture must hold simultaneously for the up-quark, down-quark, charged-lepton and neutrino mass matrices inside the SO(10) framework.

What would settle it

A measurement of the Dirac CP phase outside both predicted intervals or an effective Majorana mass m_beta beta significantly above the meV range would rule out the construction.

Figures

Figures reproduced from arXiv: 2606.24571 by Wen-Hao Jiang, Ye-Ling Zhou, Zi-Qiang Chen.

Figure 1
Figure 1. Figure 1: Scan of model parameters with χ 2 ≤ 10. 10 4 10 3 10 2 10 1 10 0 mlightest [eV] 10 3 10 2 10 1 10 0 m [ e V ] KamLAND-Zen Upper Limit JUNO-50T Sensitivity 1 & 3 5 10 15 20 MN1/10 9 [GeV] 1 2 3 MN 3 / 1 0 1 2 [ G e V ] 0 1 2 3 | |(%) 90 180 270 360 l( ) 1 3 1 2 3 MN3/10 12 [GeV] 90 180 270 360 l( ) 1 3 0 2 4 6 8 10 2 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The effective neutrino mass prediction (top left panel) and two-dimensional correlations [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

We apply the universal two-zero texture (UTZT) to all quark and lepton mass matrices in the SO(10) grand unified framework. With charged fermion masses fixed at their best-fit values, this texture contains only seven free parameters to account for nine flavor observables, rendering it highly predictive. Motivated by the recent JUNO indication in favor of the normal ordering of light neutrino masses, we perform an updated analysis of the UTZT in SO(10). The texture remains fully compatible with all current flavor data and exhibits an enhanced preference for normal ordering. The Dirac phase is predicted mainly in two regions, one of which matches very well with current data. A meV-scale $m_{\beta\beta}$ is predicted, beyond the sensitivity bound of future neutrinoless double beta decay measurement. We further explore the origin of the UTZT from non-invertible symmetries, without introducing additional low-energy degrees of freedom. We show that the UTZT can be realized through non-invertible selection rules arising from the $Z_3$ gauging of $Z_N$, with a minimal realization corresponding to $N=7$.

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 / 2 minor

Summary. The manuscript applies a universal two-zero texture (UTZT) simultaneously to all quark and lepton mass matrices (M_u, M_d, M_e, M_νD, M_R) inside an SO(10) GUT. With charged-fermion masses fixed at best-fit values, the texture is stated to involve only seven free parameters for nine flavor observables. An updated numerical analysis, motivated by the JUNO preference for normal ordering, finds full compatibility with current data, an enhanced preference for normal ordering, Dirac-phase predictions concentrated in two regions (one consistent with data), and a meV-scale m_ββ. The texture is further derived from non-invertible selection rules obtained by Z_3 gauging of Z_N (minimal N=7) without additional low-energy degrees of freedom.

Significance. If the UTZT can be consistently realized across all SO(10) sectors while preserving the stated parameter count, the work supplies a compact, predictive framework for flavor observables with direct implications for neutrino mass ordering, CP violation, and neutrinoless double-beta decay. The non-invertible symmetry construction, achieved without extra fields, constitutes a genuine theoretical strength that elevates the model beyond purely phenomenological texture studies.

major comments (2)
  1. [§3] §3 (texture implementation in SO(10)): the central claim that the UTZT reduces to exactly seven free parameters after fixing charged-fermion masses rests on the assumption that the same zero positions can be imposed on M_u, M_d, M_e, M_νD and M_R simultaneously. Because these matrices are linear combinations of the same Y_{10} and Y_{126} with sector-dependent Clebsch-Gordan coefficients, the alignment of zeros is not automatic and may impose additional relations among the underlying Yukawa entries, altering the effective parameter count. This point is load-bearing for the predictivity and compatibility statements.
  2. [Numerical results section] Numerical results section (analysis of neutrino observables): the abstract asserts that the seven-parameter fit remains fully compatible and yields specific predictions (enhanced normal ordering, two Dirac-phase regions, meV-scale m_ββ). Explicit tables or figures reporting the χ² values, the ranges of the seven parameters, and the treatment of SO(10) relations under the fit are required to substantiate that the quoted predictions do not reduce to the input fit itself.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'nine flavor observables' is used without enumeration; listing them explicitly would improve clarity for readers unfamiliar with the precise counting.
  2. [§5] §5 (non-invertible symmetry): the minimal N=7 realization is stated, but a brief table or diagram showing which matrix entries are forbidden by the selection rules in each sector would aid verification that the texture is reproduced uniformly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (texture implementation in SO(10)): the central claim that the UTZT reduces to exactly seven free parameters after fixing charged-fermion masses rests on the assumption that the same zero positions can be imposed on M_u, M_d, M_e, M_νD and M_R simultaneously. Because these matrices are linear combinations of the same Y_{10} and Y_{126} with sector-dependent Clebsch-Gordan coefficients, the alignment of zeros is not automatic and may impose additional relations among the underlying Yukawa entries, altering the effective parameter count. This point is load-bearing for the predictivity and compatibility statements.

    Authors: The UTZT is imposed on the fundamental Yukawa matrices Y_{10} and Y_{126}. The mass matrices are then formed using fixed SO(10) Clebsch-Gordan coefficients, which are representation-theoretic constants and do not generate extra relations among the non-zero entries. The seven parameters are precisely the independent non-zero entries in Y_{10} and Y_{126} once charged-fermion masses are fixed; the neutrino-sector observables follow as predictions. We will add an explicit paragraph in §3 mapping the textured Yukawas through the CG coefficients to confirm no additional constraints arise. revision: partial

  2. Referee: Numerical results section (analysis of neutrino observables): the abstract asserts that the seven-parameter fit remains fully compatible and yields specific predictions (enhanced normal ordering, two Dirac-phase regions, meV-scale m_ββ). Explicit tables or figures reporting the χ² values, the ranges of the seven parameters, and the treatment of SO(10) relations under the fit are required to substantiate that the quoted predictions do not reduce to the input fit itself.

    Authors: We agree that the numerical section would benefit from greater explicitness. The revised manuscript will include a table with best-fit values, 1σ ranges of the seven parameters, and minimum χ² for normal versus inverted ordering. A new figure will show the predicted Dirac-phase and m_ββ distributions. The SO(10) relations are enforced by deriving all mass matrices from the same seven Yukawa parameters via the fixed CG coefficients; the fit minimizes χ² over these parameters only. revision: yes

Circularity Check

0 steps flagged

No significant circularity; texture ansatz and parameter reduction are independent inputs analyzed against data.

full rationale

The abstract states the UTZT is applied to all SO(10) matrices with charged-fermion masses fixed at best-fit values, yielding seven parameters for nine observables. This is a standard ansatz whose consequences (compatibility, normal-ordering preference, Dirac-phase regions, m_beta beta prediction) are then compared to external flavor data. The non-invertible symmetry section explores an origin for the texture without equations or claims that reduce any quoted prediction to a prior fit by construction. No self-citation chains, self-definitional loops, or fitted-input-renamed-as-prediction steps appear in the provided text. The central claim therefore remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the universal two-zero texture being imposed on every mass matrix in SO(10), the fixing of charged-fermion masses to best-fit values, and the construction of the texture from non-invertible selection rules without extra low-energy fields; seven free parameters are introduced to fit the remaining observables.

free parameters (1)
  • seven free parameters of the universal two-zero texture
    After fixing charged-fermion masses at best-fit values, seven adjustable numbers remain to describe nine flavor observables.
axioms (2)
  • domain assumption The universal two-zero texture applies to all quark and lepton mass matrices in the SO(10) framework
    This is the starting assumption that reduces the model to seven parameters.
  • domain assumption SO(10) grand unified theory provides the underlying gauge structure
    The entire construction is performed inside SO(10).
invented entities (1)
  • non-invertible symmetries realized by Z_3 gauging of Z_N (minimal N=7) no independent evidence
    purpose: To generate the universal two-zero texture via selection rules without introducing additional low-energy degrees of freedom
    The abstract states that the texture can be realized through these symmetries.

pith-pipeline@v0.9.1-grok · 5739 in / 1803 out tokens · 28796 ms · 2026-06-25T23:29:43.406684+00:00 · methodology

discussion (0)

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