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arxiv: 2606.19906 · v1 · pith:3GHIEK74new · submitted 2026-06-18 · ✦ hep-ph · hep-ex

New Avenues of Heavy Neutral Lepton at Muon Collider

Fa-Xin Yang , Feng-Lan Shao , Zhi-Long Han , Honglei Li This is my paper

Pith reviewed 2026-06-26 17:14 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords heavy neutral leptonmuon collidervector boson fusionZ primeseesaw modellepton number violationheavy Higgs
0
0 comments X

The pith

New Z' vector boson fusion processes produce heavy neutral leptons at muon colliders without mixing suppression.

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

This paper investigates production of heavy neutral leptons through new vector boson fusion channels involving a Z' gauge boson in U(1) extended seesaw models at a multi-TeV muon collider. It establishes that the channel Z'Z' to H to NN avoids the suppression from the small Higgs mixing angle that affects standard model vector boson fusion. The direct Z'Z' to NN channel remains effective even when the heavy Higgs mass exceeds the available energy. These channels enable searches for lepton number violating signals from the decays of the heavy neutral leptons. Readers would care because they open additional discovery routes for beyond standard model particles at future high energy colliders.

Core claim

Within the U(1) gauged extension of seesaw models, heavy neutral leptons acquire additional interactions with the new Z' gauge boson and heavy Higgs. At the muon collider these lead to the processes Z'Z'→H→NN and Z'Z'→NN that are not suppressed by the Higgs mixing angle α and that work for heavy Higgs masses above the collider center of mass energy, providing alternative pathways to probe the intrinsic features of the heavy neutral lepton through subsequent lepton number violating decays.

What carries the argument

The Z'Z' vector boson fusion processes to heavy neutral lepton pairs, with and without intermediate heavy Higgs, which enable unsuppressed production rates.

Load-bearing premise

The U(1) extension must introduce a Z' boson that couples sufficiently strongly to the heavy neutral leptons and the heavy Higgs to make the fusion processes observable.

What would settle it

Observation of production rates for heavy neutral leptons via Z' fusion that match the suppressed rates expected from standard model vector boson fusion would indicate the new processes do not provide the claimed advantage.

Figures

Figures reproduced from arXiv: 2606.19906 by Fa-Xin Yang, Feng-Lan Shao, Honglei Li, Zhi-Long Han.

Figure 1
Figure 1. Figure 1: FIG. 1. Branching ratio of the heavy Higgs [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Feynman diagrams of the heavy Higgs-strahlung [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Cross sections of the heavy Higgs-strahlung [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Normalized distributions of pseudorapidity of final state muons [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Normalized distributions of number of muons [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The significance of the [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The combined [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Feynman diagrams of the direct heavy neutral lepton pair [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Cross sections of the the direct heavy neutral lepton pair [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Normalized distributions of pseudorapidity of final state muons [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Normalized distributions of number of muons [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The significance of the [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The combined [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
read the original abstract

With initial state radiation, the multi-TeV muon collider can be regarded as an electroweak boson collider. The dominant production mode of the certain process becomes the vector boson fusion channel, because the corresponding cross section typically increases logarithmically at high energies. This also holds true for new physics beyond the standard model. Within the $U(1)$ gauged extension of seesaw models, the heavy neutral lepton has additional interactions with the new gauge boson $Z'$ and heavy Higgs $H$. In this paper, we investigate the production of heavy neutral lepton $N$ via the new vector boson fusion processes $Z'Z'\to H\to NN$ with and $Z'Z'\to NN$ without heavy Higgs at the multi-TeV muon collider. Different from the canonical vector boson fusion processes $WW/ZZ\to H\to NN$, the new process $Z'Z'\to H\to NN$ is not suppressed by the small mixing angle $\alpha$ between the Higgs bosons. Meanwhile, the pair production process $Z'Z'\to NN$ is also viable even for heavy Higgs $m_H> \sqrt{s}$. Therefore, these new avenues provide alternative pathways to probe the intrinsic feature of the heavy neutral lepton. We then perform a detailed analysis of the lepton number violation signals via the new vector boson fusion with heavy Higgs $\mu^+\mu^-\to \mu^+\mu^- H \to \mu^+\mu^- NN$ and without heavy Higgs $\mu^+\mu^-\to \mu^+\mu^- NN$, followed by $N\to \mu^\pm jj$, where the two jets from $W$ boson decay are treated as one fat-jet $J$.

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

3 major / 2 minor

Summary. The paper investigates production of heavy neutral leptons N at a multi-TeV muon collider in a U(1) gauged extension of the seesaw model. It focuses on new vector-boson-fusion channels Z'Z' → H → NN (with heavy Higgs) and Z'Z' → NN (direct), claiming these avoid suppression by the Higgs mixing angle α that affects standard WW/ZZ → H → NN, remain viable for m_H > √s, and enable lepton-number-violating signals via N → μ± jj (fat-jet) in the processes μ+μ− → μ+μ− H → μ+μ− NN and μ+μ− → μ+μ− NN.

Significance. If the U(1) gauged seesaw extension supplies tree-level Z'Z'H, Z'Z'NN and HNN vertices of unsuppressed strength, the proposed channels would furnish model-specific, α-independent production modes for HNLs at future muon colliders, potentially expanding the parameter space accessible beyond canonical VBF and offering concrete LNV search strategies with fat-jet reconstruction.

major comments (3)
  1. [Model section / Lagrangian] The central claim that Z'Z'→H→NN evades α suppression rests on the existence of unsuppressed Z'Z'H and HNN vertices; the manuscript must explicitly derive these couplings from the model Lagrangian (presumably in the model-definition section) and show that they remain O(1) independent of the small α that mixes the two CP-even scalars.
  2. [Process definitions / cross-section calculation] The assertion that Z'Z'→NN is viable for m_H > √s requires demonstration that the direct Z'Z'NN vertex is present at tree level with strength set by the U(1) gauge coupling rather than loop- or mixing-suppressed; without the explicit Feynman rule or cross-section formula, the kinematic claim cannot be verified.
  3. [Phenomenological analysis / event selection] The subsequent LNV analysis (μ+μ− → μ+μ− NN followed by N → μ± jj) must include quantitative signal and background cross sections after fat-jet tagging; the abstract states the final state but does not report the numerical rates or efficiencies needed to establish observability.
minor comments (2)
  1. [Signal topology] Notation for the fat jet (denoted J) and the precise definition of the fat-jet algorithm should be stated explicitly when first introduced.
  2. [Parameter space] The range of free parameters (m_Z', m_H, m_N, α, gauge coupling) over which the new channels dominate should be summarized in a table or plot for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment below and will revise the paper to strengthen the presentation of the model and results.

read point-by-point responses

  1. Referee: [Model section / Lagrangian] The central claim that Z'Z'→H→NN evades α suppression rests on the existence of unsuppressed Z'Z'H and HNN vertices; the manuscript must explicitly derive these couplings from the model Lagrangian (presumably in the model-definition section) and show that they remain O(1) independent of the small α that mixes the two CP-even scalars.

    Authors: We agree that explicit derivation is required for clarity. In the revised manuscript we will expand the model section to present the full U(1) gauged seesaw Lagrangian, including the scalar potential and gauge interactions, and derive the Z'Z'H and HNN vertices step by step. These couplings arise directly from the U(1) charge assignments and the vev of the new scalar; they are independent of the CP-even mixing angle α, which only enters the SM-like Higgs couplings. We will add the resulting Feynman rules and confirm their O(1) strength set by the U(1) gauge coupling. revision: yes

  2. Referee: [Process definitions / cross-section calculation] The assertion that Z'Z'→NN is viable for m_H > √s requires demonstration that the direct Z'Z'NN vertex is present at tree level with strength set by the U(1) gauge coupling rather than loop- or mixing-suppressed; without the explicit Feynman rule or cross-section formula, the kinematic claim cannot be verified.

    Authors: We will add the tree-level Feynman rule for the Z'Z'NN vertex, which follows directly from the U(1) gauge interaction of the heavy neutral leptons with the Z' boson. The vertex strength is proportional to the U(1) gauge coupling g' and does not involve the Higgs mixing angle α or loop factors. We will also include the parton-level cross-section formula for Z'Z' → NN to make the kinematic viability for m_H > √s explicit and verifiable. revision: yes

  3. Referee: [Phenomenological analysis / event selection] The subsequent LNV analysis (μ+μ− → μ+μ− NN followed by N → μ± jj) must include quantitative signal and background cross sections after fat-jet tagging; the abstract states the final state but does not report the numerical rates or efficiencies needed to establish observability.

    Authors: The manuscript performs a detailed LNV analysis with fat-jet reconstruction, but we acknowledge that the numerical signal and background cross sections (after selection cuts and tagging efficiencies) should be reported more explicitly. In the revision we will add tables and figures showing the post-cut cross sections for both signal channels, the dominant backgrounds, and the resulting efficiencies to quantitatively support the observability claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central claims—that the process Z'Z'→H→NN is unsuppressed by the Higgs mixing angle α and that Z'Z'→NN remains viable for m_H > √s—follow directly from the assumed existence of the U(1) gauged seesaw extension and its additional vertices (Z'Z'H, Z'Z'NN, HNN). No equations, fitted parameters, or self-citations are shown that reduce these statements to definitions or prior fits by construction. The analysis is a model-based proposal resting on standard kinematic and interaction assumptions rather than any self-referential derivation, making the chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 2 invented entities

The central claim rests on the existence of the U(1) gauged seesaw extension (introducing Z' and heavy H) and on the standard high-energy collider assumption that ISR turns the muon collider into a vector-boson collider. No independent evidence for the new entities is supplied.

free parameters (2)
  • Higgs mixing angle α
    Small mixing parameter between the two Higgs bosons that the new processes are claimed to evade.
  • m_H, m_Z', m_N
    Masses of the heavy Higgs, Z', and heavy neutral lepton; treated as free inputs in the model.
axioms (1)
  • domain assumption With initial state radiation the multi-TeV muon collider behaves as an electroweak boson collider where vector boson fusion dominates at high energies.
    Invoked in the first paragraph of the abstract as the basis for the production mode.
invented entities (2)
  • Z' gauge boson no independent evidence
    purpose: New gauge boson from the U(1) extension that mediates additional interactions with the heavy neutral lepton.
    Postulated by the model; no independent evidence supplied in the abstract.
  • Heavy Higgs H no independent evidence
    purpose: Additional scalar from the U(1) extension that participates in the fusion process to NN.
    Postulated by the model; no independent evidence supplied in the abstract.

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