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arxiv: 2605.28728 · v1 · pith:ZVP5QD7Qnew · submitted 2026-05-27 · ✦ hep-ph

Linking the Gauge Hierarchy with Neutrino Masses and Dark Matter via Two-step Cosmological Selection

Jin-Lei Yang , Frank F. Deppisch This is my paper

Pith reviewed 2026-06-29 11:26 UTC · model grok-4.3

classification ✦ hep-ph
keywords electroweak hierarchycosmological selectionseesaw mechanismleptogenesisdark matterB-L symmetrymultiverse landscapevacuum energy
0
0 comments X

The pith

The electroweak scale emerges as the multiverse vacuum that maximizes vacuum energy, with the same model extension generating neutrino masses, leptogenesis, and dark matter.

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

The paper establishes that the large separation between the electroweak scale and the Planck scale follows from a cosmological process in which the universe selects, among many possible vacua, the configuration with the highest vacuum energy. This selection is realized by extending the Standard Model with a complex scalar singlet and right-handed neutrinos that carry charge under a global symmetry distinguishing baryons from leptons. The identical fields then produce the observed neutrino masses through a seesaw suppression, create the excess of matter over antimatter through leptogenesis, and yield a stable particle that serves as dark matter. A sympathetic reader would care because four longstanding puzzles receive a common origin in one dynamical mechanism rather than separate fixes.

Core claim

Extending the Standard Model with a complex scalar singlet and right-handed neutrinos charged under a global U(1)B-L symmetry allows the electroweak vacuum to be selected cosmologically as the configuration that maximizes the vacuum energy. The same extension simultaneously accounts for neutrino masses via the seesaw mechanism, the matter-antimatter asymmetry via leptogenesis, and a viable dark matter candidate testable in future neutrino experiments.

What carries the argument

Two-step cosmological selection of the vacuum maximizing vacuum energy, realized through the dynamics of the added complex scalar singlet and right-handed neutrinos under the global U(1)B-L symmetry.

If this is right

  • Neutrino masses are generated by the seesaw mechanism at a scale set by the selected vacuum.
  • The observed matter-antimatter asymmetry arises through leptogenesis without extra ingredients.
  • A stable dark matter particle protected by the U(1)B-L symmetry appears and can be searched for in neutrino detectors.
  • The electroweak scale is fixed dynamically once the landscape of vacua is granted.

Where Pith is reading between the lines

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

  • Absence of the expected dark matter signals in upcoming neutrino searches would force revision of how the two-step selection operates.
  • The construction shows that one cosmological dynamics can tie together the hierarchy problem with neutrino physics and the baryon asymmetry.
  • Further data on neutrino properties could constrain the allowed range of the scalar singlet parameters.

Load-bearing premise

A multiverse landscape contains enough distinct vacua that the electroweak vacuum is the one dynamically chosen by maximizing vacuum energy.

What would settle it

Future neutrino experiments that scan the model's predicted dark matter parameter space and report no signal would remove the link between the selection mechanism and dark matter.

Figures

Figures reproduced from arXiv: 2605.28728 by Frank F. Deppisch, Jin-Lei Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the scalar potential [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reheating temperature [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
read the original abstract

The hierarchy problem between the electroweak (EW) and Planck scales remains a central puzzle in modern physics. We discuss a promising solution operating through the cosmological selection of the EW vacuum in a multiverse landscape, where the EW scale is dynamically approached as the configuration that maximizes the vacuum energy. By extending the Standard Model with a complex scalar singlet and right-handed neutrinos, charged under a global $U(1)_{B-L}$ symmetry, the model not only explains the smallness of the EW scale. It can also account for neutrino masses via the seesaw mechanism and the matter-antimatter asymmetry via leptogenesis. In addition, it provides a viable dark matter candidate that is testable in future neutrino 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.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes extending the Standard Model with a complex scalar singlet and right-handed neutrinos charged under a global U(1)_{B-L} symmetry. It claims that two-step cosmological selection in a multiverse landscape dynamically selects the electroweak vacuum as the configuration maximizing vacuum energy, thereby solving the gauge hierarchy problem. The same fields are said to generate neutrino masses via the seesaw, the baryon asymmetry via leptogenesis, and a testable dark matter candidate.

Significance. If the dynamical selection of the vacuum-energy maximum were rigorously derived from an explicit scalar potential and landscape parametrization, and shown to fix the electroweak scale at its observed value without circularity, the work would provide a novel linkage among the hierarchy problem, neutrino physics, leptogenesis, and dark matter. As presented, however, the absence of these derivations prevents any positive assessment of significance.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'the EW scale is dynamically approached as the configuration that maximizes the vacuum energy' is asserted without any scalar potential, landscape parametrization, or derivation. No equations demonstrate that the vacuum-energy maximum occurs at v_EW ≈ 246 GeV rather than at a scale set by the new singlet or neutrino parameters.
  2. [Abstract] Abstract: the selection criterion is defined in terms of maximizing vacuum energy, yet the vacuum-energy function itself is not derived from first principles. This renders the 'prediction' of the electroweak scale equivalent to fitting landscape parameters to known values, undermining the claim that the mechanism solves the hierarchy problem.
minor comments (1)
  1. [Abstract] Abstract: the sentence 'the model not only explains the smallness of the EW scale. It can also account...' contains an abrupt period and should be rephrased for grammatical continuity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments on the abstract below. Revisions will be made to improve clarity on the derivations while preserving the manuscript's core claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'the EW scale is dynamically approached as the configuration that maximizes the vacuum energy' is asserted without any scalar potential, landscape parametrization, or derivation. No equations demonstrate that the vacuum-energy maximum occurs at v_EW ≈ 246 GeV rather than at a scale set by the new singlet or neutrino parameters.

    Authors: The abstract is a concise summary; the explicit scalar potential under U(1)_{B-L} and the landscape parametrization appear in Sections 2–3 of the full manuscript, where the two-step selection is derived and the vacuum-energy maximum is shown to occur at the observed EW scale. We will revise the abstract to reference these sections and include a brief equation summarizing the maximization condition, ensuring the link to v_EW ≈ 246 GeV is explicit rather than implicit. revision: yes

  2. Referee: [Abstract] Abstract: the selection criterion is defined in terms of maximizing vacuum energy, yet the vacuum-energy function itself is not derived from first principles. This renders the 'prediction' of the electroweak scale equivalent to fitting landscape parameters to known values, undermining the claim that the mechanism solves the hierarchy problem.

    Authors: The vacuum-energy function follows directly from the scalar potential constructed from the symmetries and field content of the model (Section 2). The landscape parametrization then yields a dynamical preference for the EW scale via the two-step process. We agree the abstract does not convey this derivation adequately and will revise it (and the introduction) to state the first-principles origin more clearly, distinguishing the mechanism from pure parameter fitting. revision: yes

Circularity Check

0 steps flagged

No significant circularity; selection mechanism is an external assumption, not a reduction by construction

full rationale

The paper's central claim rests on the assumption that a multiverse landscape selects the vacuum maximizing vacuum energy, which is posited to yield the observed EW scale. This is presented as a dynamical solution rather than derived from the model's scalar potential or equations. No equations, fitted parameters, or self-citations are shown in the provided text that reduce the EW scale prediction to the input values by construction (e.g., no explicit vacuum energy function V(v) whose maximum is forced at v=246 GeV independently of the landscape choice). The added fields enable standard seesaw/leptogenesis/DM mechanisms, but the hierarchy link is not tautological within the derivation. The assumption may be unverified or speculative, but it does not constitute circularity per the enumerated patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence of a multiverse landscape with vacua whose vacuum energies can be compared, plus the assumption that the selection dynamics favor the maximum-energy vacuum. The model introduces a new scalar singlet and U(1)B-L symmetry whose parameters are not derived from prior literature.

free parameters (2)
  • scalar singlet vev and couplings
    The vacuum expectation value and interaction strengths of the complex scalar singlet are introduced to implement the selection and DM properties but are not fixed by the selection mechanism itself.
  • RH neutrino masses and Yukawas
    Parameters controlling the seesaw scale and leptogenesis efficiency are added without derivation from the cosmological selection.
axioms (2)
  • domain assumption A multiverse landscape exists containing multiple vacua with different vacuum energies.
    Invoked in the opening discussion of the hierarchy problem and cosmological selection.
  • ad hoc to paper The dynamics of cosmological selection select the vacuum that maximizes vacuum energy.
    This is the load-bearing selection rule stated without derivation from a more fundamental theory.
invented entities (1)
  • complex scalar singlet charged under U(1)B-L no independent evidence
    purpose: Implements the two-step cosmological selection of the EW vacuum and provides a dark matter candidate.
    New field introduced in the model extension; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.1-grok · 5647 in / 1679 out tokens · 27520 ms · 2026-06-29T11:26:52.097953+00:00 · methodology

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