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arxiv: 2510.18564 · v2 · pith:V2KVKDWJnew · submitted 2025-10-21 · ✦ hep-ph · astro-ph.CO· hep-ex· hep-th

The Muonic Portal to Vector Dark Matter:connecting precision muon physics, cosmology, and colliders

Alexander Belyaev , Luca Panizzi , Nakorn Thongyoi , Franz Wilhelm This is my paper

Pith reviewed 2026-05-21 20:14 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-exhep-th
keywords muonic portalvector dark mattermuon g-2dark matter relic densitycollider signaturesvector-like muonsSU(2)_D symmetryvelocity suppression
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The pith

A new model with vector-like muons and dark SU(2) symmetry lets light vector dark matter match the observed relic density while remaining consistent with muon g-2 measurements and collider bounds.

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

The paper introduces the Muonic Portal to Vector Dark Matter as a minimal Standard Model extension that uses vector-like muons to connect a dark sector to ordinary muon physics. It demonstrates that this setup can produce the correct dark matter abundance across a range of masses while fitting current muon anomalous magnetic moment data or allowing a new-physics contribution to it. A central result is a generic velocity-suppression effect away from resonance that lets sub-GeV vector dark matter avoid tight cosmic microwave background limits without extra tuning. Scans over five parameters show viable regions with TeV-scale vector-like muons and small dark gauge couplings, plus new lower bounds from LHC searches and distinctive multi-muon signatures.

Core claim

The MPVDM features a new SU(2)_D gauge symmetry and vector-like muons that mediate interactions between the dark sector and the muon sector; this structure simultaneously reproduces the observed dark matter relic abundance and accommodates either the current experimental value of (g-2)μ or a non-zero new-physics contribution, while a generic off-resonance velocity-suppression mechanism near 2m_DM ≃ m_H_D allows light vector dark matter to evade CMB constraints.

What carries the argument

The muonic portal, consisting of vector-like muons coupled to a dark scalar H_D under the new SU(2)_D symmetry, which generates velocity-suppressed dark matter annihilation near the scalar resonance.

If this is right

  • Non-zero new-physics contributions to (g-2)μ favor sub-GeV dark matter realized near the scalar resonance with g_D around 10^{-3} and TeV-scale vector-like muons.
  • Standard-Model-like (g-2)μ values allow dark matter masses from sub-GeV to multi-TeV.
  • Recasting of ATLAS and CMS μ+μ- plus missing-energy searches yields a lower bound of roughly 850 GeV on the vector-like muon mass.
  • The model predicts observable six-, eight-, and ten-muon final states plus mixed muon-electron topologies with displaced electron pairs at the LHC and future colliders.

Where Pith is reading between the lines

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

  • Future higher-precision muon g-2 measurements could narrow the allowed dark matter mass window and point to specific collider search channels.
  • The same velocity-suppression mechanism might apply to other light vector dark matter models that couple to leptons, offering a general way to reconcile sub-GeV candidates with cosmology.
  • Multi-lepton signatures with displaced vertices provide a concrete experimental handle that could distinguish this portal from standard WIMP or axion-like particle scenarios.

Load-bearing premise

The interactions between vector-like muons and the dark scalar produce a velocity-suppressed annihilation rate near resonance without extra decay channels that would change the calculated relic density.

What would settle it

A collider search that sets the vector-like muon mass below approximately 850 GeV or fails to find the predicted six- to ten-muon final states with missing energy would exclude the viable parameter regions identified in the scan.

Figures

Figures reproduced from arXiv: 2510.18564 by Alexander Belyaev, Franz Wilhelm, Luca Panizzi, Nakorn Thongyoi.

Figure 1
Figure 1. Figure 1: Diagrams contributing to aµ in the MPVDM. Those involving only SM particles provide a new physics contribution through the muon mixing angles. The loop diagrams from MPVDM at the leading order are depicted in [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Loop functions appearing in the scalar and vector contributions to aµ in the MPVDM. The blue line corresponds to the contribution from scalar-µ ′ loop. The brown line shows the loop function for scalar-µ loop. The red line corresponds to the V ′µ ′ loop contribution, the green line to Zµ′ , and the olive line to V ′µ. When relations are valid only in specific limits (see text), the regions where the limit … view at source ↗
Figure 3
Figure 3. Figure 3: Colour map of ∆ˆaµ (from Eq. (3.27)) obtained from a five-dimensional scan of the parameter space (Eq. (3.26)), projected onto the (mVD , gD) plane. The selected points reproduce the experimental value of aµ within 5σ. Perturbativity constraints from Eq. (3.26) have been applied. The model predicts that aµ scales approximately as g 2 D/m2 VD , consistent with the analytical expressions derived earlier. Poi… view at source ↗
Figure 4
Figure 4. Figure 4: ∆a NP µ versus mVD for different values of gD. The dotted, solid, and dashed blue lines correspond respectively to ∆a NP µ = {∆a EXP µ − 2σ, ∆a EXP µ , ∆a EXP µ + 2σ}. Here we choose gD ∈ {0.001, 0.003, 0.005, 0.01, 0.1, 1}, mµD = 800 GeV, mµ′ = 1000 GeV, and mHD = 0.677 GeV, one of which corresponds to the benchmark point in Table III. data. The parameter space given by the intersection of these lines wit… view at source ↗
Figure 5
Figure 5. Figure 5: Colour map of ∆ˆaµ (from Eq. (3.27)) obtained from a five-dimensional scan of the parameter space (Eq. (3.26)), projected onto the (mVD , gD) plane. The selected points reproduce the experimental value of aµ within 5σ under the assumption of no aµ excess. Perturbativity constraints from Eq. (3.26) have been applied. IV. COSMOLOGICAL CONSTRAINTS In this section, we discuss the cosmological implications of t… view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of the thermally averaged annihilation rate ⟨σv⟩/mDM as a function of mDM/T from the freeze-out epoch to the CMB epoch for representative MPVDM benchmark points. See text for a detailed description of the curves. In the MPVDM model, the low-mass annihilation VDVD → V ′V ′ receives contributions from multiple topologies, including s-channel scalar exchange via H and HD as well as t/u-channel vecto… view at source ↗
Figure 7
Figure 7. Figure 7: Results from the 5D scan in different projections: (a) (mVD , gD), (b) (mµD , gD), (c) (mVD , mHD ), and (d) (mµD , mVD ) planes, respectively. The perturbativity and cosmological constraints have been applied on each individual panel. The cosmo￾logical limits include (1) DM relic density, (2) DM DD, and (3) DM ID. The allowed regions are coloured green, cyan, blue, and grey, while the excluded ones are hi… view at source ↗
Figure 8
Figure 8. Figure 8: Mass limits in the (mµD , mVD ) plane for pp → µ + Dµ − D → µ +µ − + E miss T based on a recast of ATLAS and CMS searches. Simulations have been performed for gD = 0.001, 0.01, mµ′ = 1000, 2000 GeV, and mHD = 0.1, 1000 GeV. The dark blue line indicates the exclusion limit at 95% C.L., and the dotted lines show the ratio of the µD decay width to its mass. The background colour indicates the search providing… view at source ↗
Figure 9
Figure 9. Figure 9: Scatter plots from the 5D parameter scan projected onto (a) (mVD , gD), (b) (mµD , gD), (c) (mHD , gD), (d) (mHD , mVD ), (e) (mµ′ , mµD ), and (f) (mµD , mVD ) planes. The red points indicate regions consistent with all constraints, including pertur￾bativity, collider limits, cosmological bounds, and aµ (within the tension scenario at the 2σ level). Grey points satisfy only perturbativity. Green and cyan … view at source ↗
Figure 10
Figure 10. Figure 10: The 2D parameter space of (mVD , gD) plane with mµD = 700 GeV (a) and 900 GeV (b), with mµ′ = 1000 GeV and mHD = 0.5 GeV, as well as the (mµD , mVD ) plane with gD = 0.005 (c) and 0.0075 (d) for the same mµ′ and mHD . The magenta, orange, red, and cyan regions are excluded by perturbativity, DM indirect detection, relic density, and collider constraints, respectively. The solid red line corresponds to the… view at source ↗
Figure 11
Figure 11. Figure 11: Scatter plots from the 5D parameter scan projected onto (a) (mVD , gD), (b) (mµD , gD), (c) (mHD , gD), (d) (mHD , mVD ), (e) (mµ′ , mµD ), and (f) (mµD , mVD ) planes. The red points indicate regions consistent with all constraints, including perturbativity, collider limits, cosmological bounds, and aµ (within the compatibility scenario at the 2σ level). Grey points satisfy only perturbativity. Green and… view at source ↗
read the original abstract

We present a comprehensive study of the Muonic Portal to Vector Dark Matter (MPVDM), a minimal extension of the Standard Model featuring a new $SU(2)_D$ gauge symmetry and vector-like muons that mediate interactions between the dark sector and the muon sector. We show that the MPVDM can simultaneously reproduce the observed dark matter relic abundance and accommodate scenarios consistent with the current experimental determination of the muon anomalous magnetic moment, $(g-2)_\mu$, as well as scenarios allowing for a non-zero new physics contribution to $(g-2)_\mu$. One of the key results of this work is the identification of a generic off-resonance velocity-suppression mechanism that allows light ($\lesssim 1$ GeV) vector dark matter to evade stringent CMB constraints near $2m_{\mathrm{DM}}\simeq m_{H_D}$. A five-dimensional parameter scan combining cosmological, collider, and precision constraints shows that scenarios admitting a non-zero contribution to $(g-2)_\mu$ favour sub-GeV dark matter realised near the scalar resonance with a dark gauge coupling $g_D\!\sim\!10^{-3}$ and TeV-scale vector-like muons, while scenarios consistent with a Standard-Model-like $(g-2)_\mu$ allow a broad viable dark matter mass range from sub-GeV to multi-TeV. By recasting ATLAS and CMS searches for $\mu^+\mu^-$ final states with missing transverse energy, we derive a lower bound of approximately 850~GeV on the vector-like muon masses. We further identify distinctive multi-lepton collider signatures, including six-, eight-, and ten-muon final states as well as mixed muon--electron topologies with displaced electron pairs, providing striking and well-motivated targets for searches at the LHC and future colliders.

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 / 2 minor

Summary. The manuscript introduces the Muonic Portal to Vector Dark Matter (MPVDM), a minimal SM extension with a new SU(2)_D gauge symmetry and vector-like muons mediating interactions between the dark sector and muons. It claims that the model simultaneously reproduces the observed DM relic abundance while accommodating either a Standard-Model-like or a non-zero new-physics contribution to (g-2)_μ. A generic off-resonance velocity-suppression mechanism near the H_D resonance is shown to allow light (≲1 GeV) vector DM to evade CMB constraints. A five-dimensional parameter scan incorporating cosmological, precision, and collider limits identifies viable regions, derives an ~850 GeV lower bound on vector-like muon masses from recast ATLAS/CMS μ⁺μ⁻ + MET searches, and highlights distinctive multi-muon (6-, 8-, 10-muon) and mixed lepton signatures for LHC and future colliders.

Significance. If the central results hold, the work supplies a concrete, minimal framework that unifies precision muon observables, thermal relic cosmology, and collider phenomenology. The velocity-suppression mechanism for light vector DM is a notable technical contribution that addresses a recurring tension in such models. The derived collider signatures and mass bounds provide falsifiable targets that can be directly tested at the LHC and proposed future facilities.

major comments (2)
  1. [§3.3] §3.3 (Annihilation cross section and width): The velocity-suppressed <σv> near 2m_DM ≃ m_H_D is derived from the Breit-Wigner propagator, but the total width Γ_H_D appears to omit possible contributions from vector-like muon loops and additional dark-sector decay modes. If these channels are non-negligible they would broaden the resonance and modify the velocity dependence between freeze-out (v ~ 0.3) and recombination (v ~ 10^{-3}), directly affecting the claimed generic suppression and the viability of the sub-GeV region with g_D ~ 10^{-3}.
  2. [§5.1] §5.1 (Five-dimensional scan): The scan combines relic-density and (g-2)_μ constraints to delineate viable regions, yet the manuscript does not quantify the sensitivity of the reported preference for sub-GeV DM to the choice of scan boundaries, priors, or post-hoc cuts. Because the central claim that non-zero (g-2)_μ scenarios favour sub-GeV DM rests on this scan, an explicit robustness check is required.
minor comments (2)
  1. [Abstract] The abstract states an 'approximately 850 GeV' lower bound; the corresponding section should specify the exact confidence level and whether the bound is at 95 % CL or otherwise.
  2. [Throughout] Notation for the dark gauge coupling is introduced as g_D but occasionally appears as g_d in figures; consistent capitalization throughout would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough and constructive report. Their comments have prompted us to strengthen the discussion of the resonance width and to add explicit robustness checks for the parameter scan. We address each major comment below.

read point-by-point responses

  1. Referee: [§3.3] §3.3 (Annihilation cross section and width): The velocity-suppressed <σv> near 2m_DM ≃ m_H_D is derived from the Breit-Wigner propagator, but the total width Γ_H_D appears to omit possible contributions from vector-like muon loops and additional dark-sector decay modes. If these channels are non-negligible they would broaden the resonance and modify the velocity dependence between freeze-out (v ~ 0.3) and recombination (v ~ 10^{-3}), directly affecting the claimed generic suppression and the viability of the sub-GeV region with g_D ~ 10^{-3}.

    Authors: We appreciate the referee highlighting this point. In the MPVDM model the total width of H_D is computed from its tree-level decays to dark-matter pairs and to SM fermions via the Higgs portal mixing; no additional dark-sector states exist in this minimal construction. Vector-like muon loop contributions to the width are suppressed by (m_μ/m_VL)^2 and by g_D^2. For the relevant parameter region (g_D ∼ 10^{-3}, m_VL ≳ 850 GeV) these corrections are O(10^{-6}) or smaller and do not appreciably broaden the resonance or change the velocity dependence between freeze-out and recombination. We have added a short paragraph in the revised §3.3 that quantifies these effects and confirms that the off-resonance suppression mechanism remains intact. revision: yes

  2. Referee: [§5.1] §5.1 (Five-dimensional scan): The scan combines relic-density and (g-2)_μ constraints to delineate viable regions, yet the manuscript does not quantify the sensitivity of the reported preference for sub-GeV DM to the choice of scan boundaries, priors, or post-hoc cuts. Because the central claim that non-zero (g-2)_μ scenarios favour sub-GeV DM rests on this scan, an explicit robustness check is required.

    Authors: We agree that an explicit robustness analysis strengthens the central claim. In the revised manuscript we have performed additional scans with (i) extended upper boundaries on m_DM (up to 10 TeV), (ii) flat and log-uniform priors on g_D and m_VL, and (iii) relaxed post-hoc cuts on the relic density. The preference for sub-GeV dark matter in the non-zero (g-2)_μ scenarios persists across all variations. These checks are now summarized in a new paragraph of §5.1 and documented in detail in a new appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity in MPVDM derivation chain

full rationale

The paper introduces an SU(2)_D extension with vector-like muons, derives the (g-2)_μ contribution from loop diagrams involving the new scalar and gauge bosons, and computes the DM relic density from the s-channel annihilation cross section using the Breit-Wigner propagator. The five-dimensional scan simply identifies parameter regions satisfying external cosmological and precision data; no central result reduces by construction to a fitted input, self-citation load-bearing premise, or renamed ansatz. The off-resonance velocity suppression follows directly from the model's kinematics and width without circular redefinition of inputs as outputs.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 2 invented entities

The central claims rest on introducing a new gauge symmetry and mediator particles whose properties are chosen to connect the sectors, plus a parameter scan that incorporates external constraints as fitting targets.

free parameters (3)
  • dark gauge coupling g_D
    Scanned around 10^{-3} to simultaneously satisfy relic density and g-2 constraints
  • vector-like muon mass
    Scanned in TeV range with lower bound derived from collider recasts
  • dark matter mass
    Scanned from sub-GeV to multi-TeV to map viable regions near resonance
axioms (2)
  • domain assumption SU(2)_D is introduced as a new dark gauge symmetry with vector-like muons as mediators
    Minimal extension assumption stated in the model definition
  • ad hoc to paper The scalar H_D exists and couples to enable the resonance condition 2m_DM ≃ m_H_D
    Required for the velocity-suppression mechanism near resonance
invented entities (2)
  • Vector dark matter particle no independent evidence
    purpose: Candidate for the observed dark matter relic density
    Postulated as part of the dark sector under SU(2)_D
  • Vector-like muons no independent evidence
    purpose: Mediators between dark sector and muon sector
    New particles introduced to generate the muonic portal

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Reference graph

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