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arxiv: 2605.28923 · v1 · pith:XZCHHSOFnew · submitted 2026-05-27 · ✦ hep-ph · astro-ph.CO

A Minimal Dark SU(2) Origin of a Massless Dirac Neutrino

P. S. Bhupal Dev , Julia Gehrlein , Amartya Sengupta , Amarjit Soni This is my paper

Pith reviewed 2026-06-29 11:12 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords neutrino mass matrixDirac neutrinosdark SU(2) gauge symmetrymassless neutrinodark matteranomaly cancellationZ4 symmetryconfining dark sector
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0 comments X

The pith

A minimal dark SU(2) gauge symmetry enforces a rank-two Dirac neutrino mass matrix with one exactly massless neutrino.

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

The paper shows how charging one right-handed neutrino under a new dark SU(2) gauge symmetry forbids its Yukawa coupling to the Higgs, producing a Dirac mass matrix of rank two. This texture automatically sets one neutrino mass to zero while leaving the other two free to fit oscillation measurements. Quantum consistency of the gauge theory requires a second dark fermion doublet to cancel the Witten anomaly, and a discrete Z4 symmetry keeps the pair vectorlike so that no Majorana masses appear. The same structure generates a secluded confining dark sector that supplies a dark matter candidate without conflicting with cosmological bounds.

Core claim

The mechanism relies on a minimal dark SU(2)_D gauge symmetry under which one right-handed-neutrino-like Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Cancellation of the Witten anomaly requires a second fermionic SU(2)_D doublet, while a discrete Z4 symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector with a viable dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.

What carries the argument

The dark SU(2)_D gauge symmetry acting on one right-handed neutrino-like fermion, completed by a vectorlike pair of SU(2)_D doublets required for anomaly cancellation and protected by a Z4 symmetry.

If this is right

  • The neutrino mass matrix is forced to have rank two, so exactly one Dirac neutrino remains massless.
  • The remaining two neutrino masses can be chosen to reproduce all current oscillation data.
  • The dark sector confines at low energies and supplies a stable dark matter particle.
  • No tree-level Majorana masses are generated for the neutrinos or the dark fermions.

Where Pith is reading between the lines

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

  • Precision measurements of the neutrino mass ordering could distinguish this exact zero from small corrections induced by higher-dimensional operators.
  • The shared dark fermions open a possible link between the neutrino sector and the dynamics that set the dark matter relic density.
  • Collider searches for new gauge bosons or long-lived particles from the dark sector could provide an independent test of the same symmetry that protects the massless neutrino.

Load-bearing premise

A discrete Z4 symmetry must be present to forbid Majorana mass terms for the dark fermions.

What would settle it

Detection of three neutrinos each carrying a non-zero mass that cannot be accommodated by a rank-two Dirac texture, or the absence of any dark matter candidate matching the predicted secluded confining sector, would rule out the construction.

Figures

Figures reproduced from arXiv: 2605.28923 by Amarjit Soni, Amartya Sengupta, Julia Gehrlein, P. S. Bhupal Dev.

Figure 1
Figure 1. Figure 1: FIG. 1. Absolute-mass predictions for the zero-column rep [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark $SU(2)_D$ gauge symmetry under which one right-handed-neutrino-like Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic $SU(2)_D$ doublet, while a discrete $Z_4$ symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector with a viable dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.

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

0 major / 2 minor

Summary. The paper proposes a gauge-symmetry origin for a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino. A minimal dark SU(2)_D symmetry charges one right-handed neutrino under a doublet, forbidding its Standard Model Yukawa coupling. Witten anomaly cancellation requires a second fermionic doublet; a discrete Z4 symmetry then permits a vector-like mass term for the pair while forbidding Majorana operators. The resulting anomaly-free, secluded confining dark sector supplies a viable dark matter candidate, with the construction asserted to be consistent with neutrino oscillation data and cosmological constraints.

Significance. If the symmetry construction and its implications hold, the work supplies a minimal, gauge-theoretic explanation for the protected massless neutrino state without ad-hoc parameter tuning in the neutrino sector, while simultaneously generating a dark matter candidate through infrared dynamics of the dark gauge group. This links two a priori separate puzzles (neutrino texture and dark matter) through anomaly cancellation and discrete symmetry, offering a concrete realization that could be probed via dark-sector searches or precision neutrino measurements.

minor comments (2)
  1. The abstract asserts consistency with oscillation data and cosmological constraints, but the manuscript should include an explicit numerical example or fit of the resulting Dirac mass matrix to current oscillation parameters (e.g., in a dedicated subsection after the mass-matrix derivation) to make the claim quantitative rather than qualitative.
  2. Notation for the dark-sector fields and charges (e.g., the two SU(2)_D doublets and their Z4 assignments) should be introduced with a clear table or list early in the model-building section to improve readability for readers unfamiliar with the construction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, including the recognition of its significance in linking a protected neutrino texture to dark-sector dynamics via anomaly cancellation and discrete symmetry. We note the recommendation for minor revision and will incorporate any editorial improvements accordingly.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper constructs a neutrino mass texture via explicit gauge symmetry assignments (one RH neutrino charged under SU(2)_D to forbid its Yukawa) plus standard anomaly cancellation (Witten anomaly requiring a second doublet) and a discrete Z4 to enforce vector-like pairing while forbidding Majorana terms. These steps are self-contained symmetry arguments that do not reduce to fitted inputs, self-citations, or redefinitions of the target massless state. No equations or claims in the provided text exhibit the enumerated circular patterns; the resulting dark sector is a derived consequence rather than an input.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 2 invented entities

The central claim rests on the introduction of new symmetries and entities without independent evidence or derivation details in the abstract.

axioms (3)
  • standard math The Standard Model particle content and gauge symmetries form the base.
    The model extends the SM.
  • domain assumption Witten anomaly must be canceled by adding a second SU(2)_D doublet.
    Stated as fixing the minimal completion.
  • ad hoc to paper A discrete Z4 symmetry is imposed to forbid Majorana masses.
    Introduced to allow vectorlike pair.
invented entities (2)
  • SU(2)_D dark gauge symmetry no independent evidence
    purpose: To charge one right-handed neutrino-like fermion and forbid its SM Yukawa coupling
    New gauge group postulated to protect the masslessness.
  • Z4 discrete symmetry no independent evidence
    purpose: To forbid Majorana masses and allow vectorlike pairing of dark doublets
    New symmetry introduced in the model.

pith-pipeline@v0.9.1-grok · 5680 in / 1571 out tokens · 50440 ms · 2026-06-29T11:12:12.164814+00:00 · methodology

discussion (0)

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Reference graph

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