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arxiv: 2606.19403 · v1 · pith:V5UUIQ5Onew · submitted 2026-06-17 · ✦ hep-ph · astro-ph.CO

Emergent Gauge Symmetries in Particle Physics and Cosmology

Steven D. Bass This is my paper

Pith reviewed 2026-06-26 20:27 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords emergent gauge symmetriesStandard Modeldark energyMajorana neutrino massesHiggs vacuum stabilityultraviolet phase transitiondark mattergravitational waves
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0 comments X

The pith

Standard Model gauge symmetries dissolve in an ultraviolet phase transition near 10^16 GeV.

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

The paper proposes that the gauge symmetries of the Standard Model are emergent rather than fundamental, arising below a phase transition at energies around 10^16 GeV. In this picture the dark energy density and the masses of light Majorana neutrinos both appear at the same order in an expansion in inverse powers of this high scale. The meta-stability of the Higgs vacuum is taken as a hint that the Higgs field links ordinary particle physics to this deep ultraviolet regime. If the idea holds, dark matter might consist of axions or collective excitations from the higher-scale degrees of freedom, with possible signals in neutrino experiments and primordial gravitational waves.

Core claim

In the emergence scenario the Standard Model gauge symmetries dissolve in a phase transition deep in the ultraviolet. The dark energy scale comes out similar to the size of light Majorana neutrino masses. These two quantities appear at the same order in a low energy expansion in inverse powers of the scale of emergence, about 10^16 GeV. The (meta-)stability of the Higgs vacuum may be pointing to some new critical phenomena at very high energy scales, with the Higgs connecting physics at LHC laboratory energies to that in the deep ultraviolet.

What carries the argument

The emergence scenario in which gauge symmetries dissolve in a phase transition at approximately 10^16 GeV, with the Higgs vacuum meta-stability linking low and high energy regimes.

If this is right

  • Dark energy and light Majorana neutrino masses are of comparable size, both generated at order 1/M^2 where M is the emergence scale about 10^16 GeV.
  • Dark matter candidates include axions and phonon-like excitations of degrees of freedom above the emergence scale.
  • Possible tests involve neutrinos as well as gravitational-wave-related signals from the early Universe sensitive to very high energy scales.

Where Pith is reading between the lines

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

  • Combined measurements of dark energy and neutrino masses could test the predicted similarity at the emergence scale.
  • The Higgs connection suggests that improved calculations of vacuum stability might constrain or support the high-energy phase transition.
  • Gravitational wave observations from the early universe could reveal signatures of the gauge symmetry emergence.

Load-bearing premise

The meta-stability of the Higgs vacuum points to new critical phenomena at very high energy scales that connect LHC energies to the deep ultraviolet.

What would settle it

Observation or calculation showing that the dark energy scale and light Majorana neutrino masses do not appear at the same order in the low energy expansion in inverse powers of a scale near 10^16 GeV would falsify the scenario.

Figures

Figures reproduced from arXiv: 2606.19403 by Steven D. Bass.

Figure 1
Figure 1. Figure 1: Above: Higgs boson couplings to different particles and masses measured [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Running of the Standard Model gauge couplings [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
read the original abstract

Where do gauge symmetries come from? These lectures develop the idea that the Standard Model might be emergent, with its gauge symmetries dissolving in some phase transition deep in the ultraviolet. The (meta-)stability of the Higgs vacuum may be pointing to some new critical phenomena at very high energy scales, with the Higgs connecting physics at LHC laboratory energies to that in the deep ultraviolet. In the emergence scenario, the dark energy scale comes out similar to the size of light Majorana neutrino masses. These two quantities appear at the same order in a low energy expansion in inverse powers of the scale of emergence, about $10^{16}$ GeV. Dark matter candidates include axions and phonon like excitations of degrees of freedom above the scale of emergence. Possible tests of these ideas involve neutrinos as well as gravitational-waves-related signals from the early Universe, which are sensitive to physics at very high energy scales.

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 manuscript develops the idea that Standard Model gauge symmetries are emergent and dissolve in an ultraviolet phase transition, potentially signaled by Higgs vacuum metastability. It argues that an emergence scale of ~10^16 GeV leads to the dark energy scale and light Majorana neutrino masses appearing at the same order in a low-energy expansion in inverse powers of this scale. Dark matter candidates (axions, phonon-like excitations) and tests via neutrinos and early-Universe gravitational waves are also discussed.

Significance. If the emergence mechanism were equipped with explicit derivations fixing the scale independently and demonstrating the operator structure, the framework could offer a dynamical origin for gauge symmetries and a unified account of disparate scales in particle physics and cosmology, with the Higgs providing a bridge from collider energies to the UV.

major comments (2)
  1. [Abstract] Abstract: The claim that dark energy and neutrino masses 'come out similar' at the same order in the low-energy expansion in 1/M with M~10^16 GeV is presented without any explicit effective Lagrangian, list of contributing operators, or power-counting argument showing why the orders coincide.
  2. [Abstract] Abstract: The emergence scale is introduced so that the numerical similarity between dark energy and neutrino masses holds; no independent principle (e.g., from Higgs metastability) is shown to fix M at 10^16 GeV, rendering the matching a consistency check rather than a prediction.
minor comments (1)
  1. The manuscript is framed as lectures; adding explicit references to prior literature on emergent gauge symmetries and clarifying which statements are new versus review would improve accessibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

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

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that dark energy and neutrino masses 'come out similar' at the same order in the low-energy expansion in 1/M with M~10^16 GeV is presented without any explicit effective Lagrangian, list of contributing operators, or power-counting argument showing why the orders coincide.

    Authors: We agree that the abstract would benefit from greater precision on this point. The manuscript is a set of lectures that develops the conceptual framework rather than a complete effective-field-theory calculation. In the body of the text we discuss the low-energy expansion in inverse powers of the emergence scale, but we do not supply an exhaustive operator list or explicit power counting. We will revise the abstract to state the claim more cautiously and will add a short clarifying paragraph in the main text that sketches the relevant operator dimensions and the reason the two scales appear at the same order. revision: yes

  2. Referee: [Abstract] Abstract: The emergence scale is introduced so that the numerical similarity between dark energy and neutrino masses holds; no independent principle (e.g., from Higgs metastability) is shown to fix M at 10^16 GeV, rendering the matching a consistency check rather than a prediction.

    Authors: The emergence scale is motivated by the possible link to Higgs-vacuum metastability, which the manuscript suggests may signal new critical phenomena near 10^16 GeV. However, the text does not contain an explicit derivation that independently fixes the numerical value of M from the metastability condition. We therefore accept the referee’s characterization that the numerical coincidence is presently a consistency check. In revision we will rephrase the relevant sentences to present the scale as a motivated ansatz whose dynamical origin remains to be demonstrated, and we will note the need for further work to elevate it to a genuine prediction. revision: partial

Circularity Check

1 steps flagged

Dark energy/neutrino mass scale matching asserted at same order in 1/M expansion with M~10^16 GeV chosen to produce the coincidence

specific steps
  1. fitted input called prediction [Abstract]
    "In the emergence scenario, the dark energy scale comes out similar to the size of light Majorana neutrino masses. These two quantities appear at the same order in a low energy expansion in inverse powers of the scale of emergence, about 10^{16} GeV."

    The emergence scale is introduced at the specific value ~10^{16} GeV that places both observed quantities at the same order in the expansion; the claimed similarity is therefore enforced by the choice of input scale rather than derived from the scenario's other assumptions or equations.

full rationale

The paper states that dark energy and light Majorana neutrino masses 'appear at the same order in a low energy expansion in inverse powers of the scale of emergence, about 10^{16} GeV' and presents this numerical similarity as a result of the emergence scenario. No independent derivation fixing the emergence scale (e.g., from Higgs vacuum meta-stability or other UV principle) is supplied in the abstract or described claims; the scale is instead selected to align the two quantities at the same order in the 1/M expansion. This reduces the 'prediction' to a consistency check after fitting M to the observed scales rather than an output fixed by other inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

Abstract-only review; the ledger is populated from statements in the abstract. The emergence scale functions as a fitted parameter chosen to equate two observed small quantities. The phase transition and vacuum stability link are domain assumptions without independent derivation shown.

free parameters (1)
  • emergence scale = ~10^16 GeV
    Set to approximately 10^16 GeV so that dark energy and light Majorana neutrino masses appear at the same order in the inverse-power expansion.
axioms (2)
  • domain assumption Gauge symmetries of the Standard Model can dissolve in a phase transition at high energies
    Invoked as the core of the emergence scenario in the abstract.
  • domain assumption Higgs vacuum meta-stability signals new critical phenomena at ultraviolet scales
    Stated as a possible pointer connecting LHC energies to the deep ultraviolet.
invented entities (1)
  • emergence scale no independent evidence
    purpose: Sets the cutoff below which gauge symmetries appear and above which they dissolve
    Introduced to organize the low-energy expansion; no independent falsifiable signature given in the abstract.

pith-pipeline@v0.9.1-grok · 5674 in / 1658 out tokens · 28061 ms · 2026-06-26T20:27:38.130039+00:00 · methodology

discussion (0)

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