arxiv: 2604.05270 · v1 · submitted 2026-04-07 · ✦ hep-ph

Recognition: no theorem link

Reply to "Comment on `Unified neutrino mixing and approximate μ-τ reflection symmetry'[arXiv:2603.00885]''

Yuta Hyodo , Teruyuki Kitabayashi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 20:11 UTC · model grok-4.3

classification ✦ hep-ph

keywords neutrino mixingmu-tau reflection symmetryinverted orderingneutrino mass sumeffective Majorana massneutrino hierarchyreflection symmetry

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The pith

Inverted neutrino ordering remains excluded by the sum of neutrino masses under approximate μ-τ reflection symmetry.

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

This reply addresses a comment on an earlier analysis of unified neutrino mixing under approximate μ-τ reflection symmetry. The authors concede they overlooked real-value conditions for the symmetry but defend their finding that inverted neutrino mass ordering is disfavored. They clarify that although recent data on the effective mass |M_ee| may permit inverted ordering, the constraint from the total neutrino mass sum ∑ m_ν still creates tension within the model's parameter space. Readers interested in neutrino physics would care because resolving the mass ordering is key to understanding the neutrino mass mechanism and its implications for cosmology and particle physics models.

Core claim

The authors argue that inverted ordering is still excluded by the experimental upper bounds on the sum of neutrino masses ∑ m_ν, when approximate μ-τ reflection symmetry is imposed, even though it may be compatible with bounds on the effective Majorana mass |M_ee| from neutrinoless double beta decay experiments.

What carries the argument

Approximate μ-τ reflection symmetry, which imposes relations on neutrino mass matrix elements that constrain mixing parameters and the mass hierarchy.

Load-bearing premise

The model parameter space from the original work accurately captures the constraints imposed by approximate μ-τ reflection symmetry on the neutrino mass sum.

What would settle it

An experimental upper limit on the neutrino mass sum ∑ m_ν low enough to permit inverted ordering while still satisfying the approximate symmetry conditions would remove the claimed tension.

read the original abstract

Huang and Li [arXiv:2603.00885] have raised the following two points regarding our previous work [arXiv:2502.18029]:(1) The real-value conditions associated with $\mu$-$\tau$ reflection symmetry were overlooked. (2) Inverted Ordering (IO) remains viable when the latest experimental data are taken into account. As they have pointed out, we overlooked an important real-value condition. However, with regard to point (2), we believe that there may be a misunderstanding. In our original study, we excluded IO based on the constraint on the sum of neutrino masses, $\sum m_\nu$. In contrast, they argue that IO remains viable when considering the effective neutrino mass, $|M_{ee}|$. While IO may indeed remain allowed in light of the latest $|M_{ee}|$ data, it is still in tension with the experimental bounds on $\sum m_\nu$ under approximate $\mu-\tau$ symmetry within the discussed model parameter space.

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

This reply correctly flags that the original exclusion of inverted ordering used the neutrino mass sum rather than |M_ee|, but it offers no updated scan or derivation once the real-value conditions are restored.

read the letter

The main thing to know is that the authors accept they missed the real-value conditions required for approximate mu-tau reflection symmetry, yet they maintain that inverted ordering is still ruled out by the experimental bound on the sum of neutrino masses inside their model. They argue the comment conflated that sum with the effective mass |M_ee| from neutrinoless double beta decay. That distinction is stated plainly and is worth noting if one is tracking the exchange. Beyond the clarification, the paper contains no new fits, no revised parameter ranges, and no explicit check that the tension survives after the symmetry conditions are enforced. The exclusion claim therefore continues to rest on the original, incomplete setup. This is a narrow point that matters only to the handful of people already working on mu-tau symmetric neutrino models and mass-ordering constraints. It adds a modest amount of clarity to the back-and-forth but does not resolve whether the inverted ordering remains viable once the model is made consistent with the comment. I would not cite it, would not bring it to a reading group, and would not send it for peer review; a short private note or an appendix in a follow-up paper would have been enough.

Referee Report

1 major / 1 minor

Summary. This short reply addresses a comment on the authors' earlier work on unified neutrino mixing under approximate μ-τ reflection symmetry. It acknowledges that real-value conditions required for the symmetry were overlooked but maintains that inverted ordering (IO) remains excluded by experimental bounds on the neutrino mass sum ∑m_ν (as opposed to |M_ee|) within the model parameter space of the original analysis.

Significance. If the central claim is substantiated, the reply would help clarify the distinction between different neutrino mass observables and preserve the reported tension between approximate μ-τ symmetry and current ∑m_ν limits for IO. However, because the manuscript provides no new scan, derivation, or quantitative update that incorporates the admitted real-value conditions, its contribution to the literature is modest and primarily clarificatory.

major comments (1)

[Abstract] The manuscript asserts that IO 'is still in tension with the experimental bounds on ∑m_ν under approximate μ-τ symmetry within the discussed model parameter space' (abstract), yet it contains no updated numerical analysis or explicit demonstration that this tension survives once the real-value conditions for the symmetry are enforced. The original exclusion therefore rests on a parameter space that the authors themselves now recognize as incomplete.

minor comments (1)

[Abstract] The abstract would be strengthened by a brief quantitative indication (e.g., the range of ∑m_ν values obtained under the symmetry) rather than a purely qualitative statement of tension.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our short reply and for highlighting the need to substantiate the persistence of the tension under the corrected symmetry conditions. We address the major comment below and indicate where a revision will strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] The manuscript asserts that IO 'is still in tension with the experimental bounds on ∑m_ν under approximate μ-τ symmetry within the discussed model parameter space' (abstract), yet it contains no updated numerical analysis or explicit demonstration that this tension survives once the real-value conditions for the symmetry are enforced. The original exclusion therefore rests on a parameter space that the authors themselves now recognize as incomplete.

Authors: We acknowledge that the real-value conditions for μ-τ reflection symmetry were overlooked in the original analysis, as correctly noted by the referee and by Huang and Li. The reply manuscript is deliberately concise and focuses on clarifying the distinction between the observables: our exclusion of IO was based on the cosmological bound on ∑m_ν, not on |M_ee|. Within the approximate symmetry framework of the original parameter space, the symmetry relations force a higher minimum value of ∑m_ν for IO than is compatible with current limits, independent of the specific phase constraints. The real-value conditions further restrict the allowed CP phases but do not open new regions that would relax the ∑m_ν tension for IO. Because this is a reply rather than a full re-analysis, we did not repeat the numerical scan; however, the qualitative conclusion drawn from the original scan remains valid. We will revise the abstract and main text to explicitly note the oversight, restate that the tension is with ∑m_ν (not |M_ee|), and add a sentence clarifying that a dedicated re-scan incorporating the real-value conditions would be a natural follow-up but lies beyond the scope of the present comment reply. revision: partial

Circularity Check

1 steps flagged

Reply's ∑ m_ν exclusion of IO under μ-τ symmetry reduces to self-cited original parameter space without incorporating admitted real-value conditions

specific steps

self citation load bearing [Abstract]
"In our original study, we excluded IO based on the constraint on the sum of neutrino masses, ∑ m_ν. In contrast, they argue that IO remains viable when considering the effective neutrino mass, |M_ee|. While IO may indeed remain allowed in light of the latest |M_ee| data, it is still in tension with the experimental bounds on ∑ m_ν under approximate μ-τ symmetry within the discussed model parameter space."

The claim that IO is 'still in tension' with ∑ m_ν bounds under the symmetry is asserted by invoking the 'discussed model parameter space' from the authors' own prior paper. The reply acknowledges the overlooked real-value conditions for μ-τ reflection symmetry (point 1 from the comment) but provides no new derivation or re-scanned parameter space to demonstrate that the exclusion holds after those conditions are included. The justification therefore reduces to the self-citation.

full rationale

The paper is a short reply defending the original conclusion by noting a possible misunderstanding between |M_ee| and ∑ m_ν bounds. However, the load-bearing assertion that IO remains excluded by ∑ m_ν under approximate μ-τ symmetry is justified solely by reference to the authors' prior work and its parameter space. The reply explicitly admits overlooking the real-value conditions required for the symmetry but offers no updated scan, derivation, or re-analysis to show the tension survives once those conditions are restored. This makes the central claim dependent on the self-citation without independent external support or correction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No new free parameters, axioms, or invented entities are introduced; the paper references the symmetry and mass constraints from the authors' earlier work.

pith-pipeline@v0.9.0 · 5490 in / 1003 out tokens · 35721 ms · 2026-05-10T20:11:19.079701+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · 1 internal anchor

[1]

Comments on

Chao-Shang Huang and Wen-Jun Li, “Comments on ”Unified neutrino mixing and approximate µ−τreflection symmetry”, arXiv:2603.00885

work page internal anchor Pith review arXiv
[2]

Unified neutrino mixing and approximateµ−τreflection sym- metry

Y. Hyodo and T. Kitabayashi,“Unified neutrino mixing and approximateµ−τreflection sym- metry”, Modern Physics Letters A 40 (2025), 2550097. arXiv:2502.18029. 2

work page arXiv 2025