Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism

Ang Liu; Fei Huang; Honglei Li; Zhen-Wei Wang; Zhi-Long Han

REVIEW 2 major objections 4 minor 110 references

Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism

T0 review · 2 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper claims that in a gauged U(1)_{B-L} model with two nearly degenerate dark fermions, the conversion mechanism can set the correct dark-matter relic density while keeping the Z' coupling so small that the model evades collider, direc

desk verdict A competent, useful map of GeV–TeV U(1)_{B-L} Z' portal DM with conversion, but two unaddressed issues (kinetic mixing, Z' bath equilibrium at tiny g') keep the 'favored' windows from being fully settled. read the letter →

arxiv 2512.08515 v3 pith:N5LTOD2U submitted 2025-12-09 hep-ph hep-ex

Zhen-Wei Wang , Zhi-Long Han , Fei Huang , Honglei Li , Ang Liu This is my paper

classification hep-phhep-ex

keywords darkmatterZ'portalU(1)_{B-L}inelasticconversionmechanismrelicdensityresonancescenariosecluded

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the usual Z' portal dark-matter scenario is squeezed by collider and direct-detection limits, and constructs a benchmark model where two almost degenerate dark fermions — the lighter, stable one being the dark matter — interact with the Z' only through a small mixing angle. The central claim is that the conversion process (the heavier partner turning into the lighter one inside the dark sector) can produce the observed relic density even when the gauge coupling g' is far too small to annihilate dark matter efficiently. This opens viable parameter space at GeV-to-TeV masses with g' around 10^-5-10^-3 in the resonance case and 10^-8-10^-5 in the secluded case, which the authors report is 'favored' by current constraints in both scenarios.

What carries the argument

The central object is the mass-mixing term δm χ̄₁χ₂ between a U(1)_{B-L}-neutral and a U(1)_{B-L}-charged dark fermion, which produces the small mixing angle θ in the mass eigenstates. This angle suppresses the effective gauge coupling of the dark-matter state χ₁ to Z' (by sin²θ) while keeping the partner χ₂ strongly coupled (by cos²θ), so that conversion reactions involving χ₂ control the abundance of χ₁ without requiring a large coupling to Standard-Model fermions.

What would settle it

A measurement of non-zero kinetic mixing ε ≳ 10^-4 between B-L and hypercharge (e.g. via precision electroweak data or a direct measurement of the Z' couplings to electrons) would generate a Z-Z' mixing that enhances the spin-independent DM-nucleon cross section far above the predicted 10^-50-10^-52 cm² range, ruling out the small-θ conversion windows.

Watch

Extended reading notes

Core claim

In the U(1)_{B-L} Z' model with two Dirac dark fermions χ₁ and χ₂ of nearly equal mass, a small mass-mixing angle θ suppresses the coupling of the dark-matter candidate χ₁ to the Z' (proportional to sin²θ) while leaving the heavier partner χ₂ strongly coupled. The relic density of χ₁ is then set not by χ₁χ₁ annihilation but by inelastic conversion reactions χ₂χᵢ → χ₁χⱼ. The paper demonstrates that in both the resonance regime (m_Z' ≈ 2m_χ₂) and the secluded regime (m_Z' < m_χ₂), the conversion mechanism yields the observed relic abundance with gauge couplings below current limits, making the scenario testable at future colliders, indirect-detection, and CMB experiments.

Load-bearing premise

The paper assumes there is no kinetic mixing between the U(1)_{B-L} gauge boson and the Standard-Model hypercharge gauge boson; if such mixing is non-negligible, the DM-nucleon scattering and the collider limits become much stronger and the 'favored' conversion regions may disappear.

Editorial extensions

If this is right

The correct thermal relic density can be obtained with Z' couplings g' as small as 10^-8-10^-3, far below the values needed in conventional Z' portal dark matter.
Spin-independent direct detection is suppressed by sin⁴θ, so most benchmark points predict cross sections below 10^-50 cm² and escape current and near-future experiments.
In the resonance scenario, the conversion phase survives current collider bounds and could be probed by future colliders at g' ≈ 10^-5-10^-3, while the coannihilation region is instead accessible to future CMB measurements.
In the secluded scenario, conversion is the most promising phase: it can be seen in indirect-detection experiments at g' ≈ 10^-8-10^-5 and, at even smaller couplings, in CMB observations, whereas coannihilation is almost entirely excluded.
The model predicts long-lived dark partners χ₂ at small θ and g', giving distinctive displaced-vertex or missing-energy signatures that complement the search for the Z' itself.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The viability of the small-θ conversion windows relies on the absence of kinetic mixing between U(1)_{B-L} and hypercharge; if even a small mixing parameter ε is present, the Z' would mix with the Standard-Model Z, enhancing the DM-nucleon scattering cross section and strengthening collider bounds, potentially closing the 'favored' regions. Adding ε and recomputing σ_SI would quantify this.
Because the relic density in the secluded scenario is largely independent of g', a natural extension would allow an arbitrarily light Z' acting as a dark-radiation component; the model could then be constrained or discovered by future CMB spectral-distortion or ΔN_eff measurements at couplings below 10^-10.
The same small mixing angle that suppresses direct detection also suppresses the Z'χ₁χ₂ vertex; a dedicated study of mono-photon signals at lepton colliders could target the conversion parameter space with θ ~ 10^-3-10^-2, complementing the CMB and indirect-detection probes envisioned in the paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new piece here is the combined scan of the resonance and secluded Z' scenarios in the GeV–TeV range, with the conversion mechanism separating coscattering, conversion, and coannihilation phases and applying collider, direct detection, CMB, and BBN constraints. That is a legitimate extension of the earlier sub-GeV work and the conversion literature, and the authors use reasonable machinery (micrOMEGAs, standard coupled Boltzmann equations). The central qualitative conclusion — that conversion-dominated windows survive current constraints in both scenarios — is plausible, and the benchmark lines do illustrate the parameter dependence clearly. I give credit for that.

Now the soft spots, in proportion. The reader's listed concerns are real but not all equal. The kinetic mixing issue is the strongest: equation (2) simply omits epsilon F_{Y mu nu} F'^{mu nu} with no discussion. Even loop-induced kinetic mixing is typically nonzero, and even small epsilon can move the direct detection cross sections and collider limits enough to matter for the low-g' windows. The authors should either state the assumption and justify it or run the calculation with a scan over epsilon. This is a genuine gap.

The stress-test about Z' bath equilibrium in the secluded scenario is less fatal than it looks, because the Z' does not need to be in equilibrium with the SM to justify Y_zeta = Y_zeta^eq; it is kept in equilibrium through its large coupling to the dark fermions (g_chi ~ 0.1–1) until freeze-out. Still, the paper never checks that explicitly, and at the very lowest g' values near 1e-10, the Z' lifetime becomes long enough that a separate evolution could matter. That is a referee-level question, not a reason to reject.

The other items — O(10%) uncertainty from not solving the full unintegrated Boltzmann equations, phase criteria borrowed from Ref. [58], and 'favored' based on selected benchmarks rather than a scan statistic — are minor and typical for this subfield. The relic density fits are standard practice, not circular. The lack of code or model files is annoying but common; providing them would make the numbers checkable.

Bottom line: this is a solid phenomenological paper. I would send it to a serious referee, with the request that the authors add a kinetic-mixing discussion (or a scan), state the Z' equilibrium condition, and ideally release the micrOMEGAs model files. The reader's conditional verdict is appropriate, but I would not desk reject it.

Referee Report

2 major / 4 minor

Summary. The paper proposes a U(1)_B-L Z' portal model with two nearly degenerate vector-like dark fermions, chi_1 and chi_2, whose mass mixing induces a small effective coupling of the lighter state chi_1 to the Z'. The authors compute the thermal relic density using micrOMEGAs for two mass regimes: the Z' resonance scenario (r_Z' = m_Z'/m_chi2 = 2) and the secluded scenario (r_Z' < 1). They classify the dominant production mechanisms as coscattering, conversion, and coannihilation, using thermal-rate criteria from Ref. [58]. After imposing collider, direct-detection, indirect-detection, BBN, and CMB constraints, the paper claims that the conversion mechanism is favored in both scenarios, leaving viable parameter windows at small g' (roughly 10^-5--10^-3 in resonance and 10^-8--10^-5 in secluded), with masses from GeV to TeV. The central claim is that conversion solves the tension between relic density and the stringent experimental bounds that affect conventional Z' portal DM.

Significance. If the result holds, the paper identifies new, experimentally promising parameter space for Z' portal DM, particularly in the secluded regime where conversion can be probed by future CMB and indirect-detection experiments. The study is systematic: it uses standard Boltzmann equations, a widely accepted external code (micrOMEGAs), applies a broad set of current and projected constraints, and explicitly shows freeze-out conditions for chi_1. The phase classification and the comparison of resonance versus secluded scenarios are useful and clearly presented. However, the central viability claim depends on two model assumptions that are not adequately justified or tested: the absence of kinetic mixing and the thermal equilibrium of the Z' bath at very small g'. These are not mere presentation issues; they directly affect the relic-density calculation and the derived constraints in the most interesting parameter windows.

major comments (2)

[Sec. IV, Eqs. (15)-(17)] The secluded-scenario calculation assumes that the Z' is part of the thermal bath with equilibrium abundance Y_zeta^eq, including the massive-Z' expression in Eq. (17). This requires the Z' to maintain chemical equilibrium with the SM bath. For the conversion windows highlighted in Sec. IV E (e.g., g' below O(1e-8)), this is not satisfied. For example, with m_Z' ~ 10 GeV and T ~ m_chi/20 ~ 1 GeV, the Z' production rate from SM fermions is roughly g'^2 T/(16 pi) ~ 2e-18 GeV for g'=1e-8, comparable to H ~ 1.4e-18 GeV; for g' below a few times 1e-9 it is smaller than H. At larger m_Z' the threshold is even higher. The paper never checks Gamma_Z' > H for its benchmarks and never evolves Y_Z' separately. The conversion/coscattering terms with Z' in Eqs. (15)-(16) therefore give unreliable relic densities in exactly the small-g' region where the paper claims CMB/indirect-detection promise. The
[Sec. II, Eq. (2)] The Lagrangian in Eq. (2) contains only the direct coupling g' Q_f Z'_mu bar f gamma^mu f and no kinetic-mixing term epsilon F_Y^mu nu F'_mu nu with hypercharge. In U(1)_B-L extensions, such kinetic mixing is generically allowed and is loop-induced even if set to zero at tree level. A non-negligible epsilon would mix the Z' with the SM Z/gamma, contributing to spin-independent DM-nucleon scattering in addition to Eq. (9) and modifying the collider bounds used in Figs. 2 and 7. Since the viability of conversion relies on very small g' and strongly suppressed direct detection, even epsilon ~ 10^-4 could dominate the scattering rate at g' = 1e-8. The paper never states or justifies the assumption epsilon=0. This is a load-bearing model gap. The authors should add a discussion of kinetic mixing, estimate the loop-induced size, and show that the derived constraints and viable windows are robu

minor comments (4)

[Sec. III A, Eqs. (4)-(5)] The text states that the three-body decay chi_2 -> chi_1 f bar f 'has an ignored contribution', but the Boltzmann equations (4)-(5) explicitly include the Gamma_chi2->chi1 f bar f term. Please clarify whether this process is included or neglected; the current wording is contradictory.
[Sec. III A] The authors acknowledge an O(10%) distinction from not solving the full unintegrated Boltzmann equations. This is reasonable, but since the phase boundaries in Figs. 1, 2, 6, and 7 are based on thermal-rate proxies from Ref. [58], it would be helpful to state explicitly how much the benchmark lines and the conversion/coannihilation phase boundaries could shift under a full treatment.
[Sec. IV E] In the discussion of the very small g' limit, the paper requires g' > 1e-10 to avoid BBN constraints on the Z' lifetime. The text could also note that in the range 1e-10 < g' < ~1e-8, the Z' may not be in thermal equilibrium with the SM bath, connecting to the major comment above.
[General] The notation in the figures is often compressed and some labels overlap (e.g., Figs. 1 and 6 with multiple rate curves on a single panel). The phase lines are central to the paper; larger panels or a table of benchmark parameters would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: relic density is solved from coupled Boltzmann equations, benchmark lines are fitted to the observed Omega h^2, and phase labels are diagnostic classifications rather than self-defined predictions.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The relic density is obtained by numerically solving the coupled Boltzmann equations (4)-(5) in the resonance scenario and (15)-(16) in the secluded scenario, with thermal averages computed by micrOMEGAs. The benchmark lines are fitted to the externally measured value Omega_chi1 h^2 = 0.12, which is a standard fitting procedure, not a prediction claimed as independent. The phenomenological statements (collider, direct detection, indirect detection, BBN, CMB) are externally imposed constraints applied after the relic-density calculation, so they do not reduce to an input of the derivation. The classification into coscattering, conversion, and coannihilation is explicitly defined in Section III A by comparing thermal rates; it is a diagnostic used to label regions, not a result that is defined in terms of the conclusion. The central claim that 'conversion is favored' summarizes which fitted benchmark curves remain allowed by external constraints, and the relevant cross sections follow from the Lagrangian in Eq. (2) rather than from the conclusion. The self-citations [50] and [68] are present, but they are used as model motivation and as one of many references for inelastic-conversion cosmology; the scalar-portal suppression is introduced as an explicit parameter assumption (m_phi >> m_chi1,2), not as an unverified uniqueness or ansatz smuggled in solely by citation. Potential physical caveats, such as the neglected kinetic mixing with hypercharge and the assumption that the Z' stays in equilibrium in the very-small-g' secluded region, are model-validity or correctness concerns rather than circular reductions: no equation in the paper is defined in terms of the result it is used to predict, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 4 invented entities

Central claim rests on standard thermal relic calculation, the assumed mass hierarchies, and several simplifications the paper does not fully quantify: scalar portal decoupling, RH neutrino decoupling, zero kinetic mixing, and momentum-independent Boltzmann equations. The six scanned parameters are not predicted; they are chosen by hand to produce the observed relic density.

free parameters (6)

m_chi1 (dark matter mass) = scanned; benchmark values imply m_chi1 up to ~5000 GeV
Sets the DM mass scale; fixed by hand in each benchmark scan (e.g., 100 GeV, 1000 GeV).
Delta_chi = (m_chi2 - m_chi1)/m_chi1 = benchmarks 0.01, 0.04, 0.08; range 1e-3-0.1
Controls whether coscattering, conversion, or coannihilation dominates; chosen by hand in scans.
r_Z' = m_Z'/m_chi2 = 2 (resonance), 0.75 default, 0.3-0.95 varied
Determines resonance vs secluded regime; fixed by hand for each scenario.
g' (B-L gauge coupling) = benchmark lines ~1e-8 to 0.86, varies
Scanned over 1e-10 to 1e-2 (and larger in secluded); strongly constrained by colliders.
g_chi = Q_chi2 g' = benchmarks 0.2, 0.3, 0.5, 1
Dark-sector coupling; controls annihilation and conversion rates; chosen by hand.
theta (dark fermion mixing angle) = 5e-5 to 5e-3 (resonance), 0.003 to 0.1 (secluded)
Suppresses DM-Z' coupling and direct detection; scanned over a wide range.

assumptions (5)

domain assumption U(1)_{B-L} is anomaly-free with three right-handed neutrinos; their mass is set at the seesaw scale and they decouple from DM.
Section I: 'assuming m_N at the canonical seesaw scale O(10^14) GeV'; influence of right-handed neutrino on DM is disregarded.
ad hoc to paper Scalar portal (Yukawa coupling y phi \bar{chi~}_1 chi~_2) is negligible because m_phi >> m_chi1,2.
Section II: 'we further assume that the mass of the new scalar m_phi is much larger than m_chi1,2, so the contribution from phi portal is significantly smaller than Z' portal [50]'. This is a modeling choice without quantified limits.
ad hoc to paper No kinetic mixing between U(1)_{B-L} and hypercharge.
Eq. (2) contains only direct g' Q_f Z'_mu \bar f gamma^mu f couplings; no epsilon F_Y F' term is introduced or discussed. If nonzero, direct detection and collider bounds change.
domain assumption Standard radiation-dominated cosmology with equilibrium thermodynamics; chi1 remains in kinetic equilibrium during freeze-out.
Section III.A: conditions (1)-(3) for coscattering; the authors note that full unintegrated Boltzmann equations could introduce O(10%) differences [53].
domain assumption The coscattering/conversion/coannihilation phase criteria of Ref. [58] are valid proxies for the relic-density production mechanism.
Section III.A and Figure 1: phases are classified by comparing thermal rates Gamma_i with H, following Ref. [58].

invented entities (4)

chi~_1 (mass eigenstate chi1)
purpose: Z2-odd dark fermion with zero B-L charge; the lighter mass eigenstate is the DM candidate with suppressed Z' coupling.
No predicted mass or unique coupling; only indirect DM observables, no independent falsifiable handle outside the model.
chi~_2 (mass eigenstate chi2)
purpose: Z2-odd heavier dark fermion with nonzero B-L charge; enables coscattering, conversion, and coannihilation.
Could give CMB/displaced-vertex signatures, but no specific mass prediction; signatures are parameter-dependent.
phi (dark scalar with B-L charge -Q_chi2)
purpose: Acquires a vev and generates the mass mixing delta m between the two dark fermions.
Assumed heavy and not directly searched; its only role is to generate mixing and Z' mass.
Z' gauge boson of U(1)_{B-L}
purpose: Mediator between dark fermions and SM fermions; central to the portal.
Collider limits constrain it but do not establish it; no positive detection.

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Cite this review

Pith. "Pith review of Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism." pith.science (2026). https://pith.science/paper/N5LTOD2U

@misc{pith2026251208515,
  author       = {Pith},
  title        = {Pith review of: Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N5LTOD2U}},
  note         = {Machine review of arXiv:2512.08515}
}

abstract

In many new physics models with extended gauge symmetry, the new gauge boson $Z'$ could mediate the interactions between the dark matter and standard model particles. For the conventional $Z^\prime$ portal dark matter, the collider and the direct detection constraints typically pose a significant challenge. To address this pressing issue, we present in this paper a new benchmark model based on the gauged $U(1)_{B-L}$ symmetry, which introduces a Dirac dark fermion $\tilde{\chi}_1$ and a heavier partner $\tilde{\chi}_2$ with zero and nonzero $U(1)_{B-L}$ charge, respectively. Including the mass term $\delta m \bar{\tilde{\chi}}_1\tilde{\chi}_2$ results in the dark fermions $\chi_1$ and $\chi_2$ in the mass eigenstate, where the lighter one $\chi_1$ is regarded as the dark matter candidate. Various intriguing processes for the relic density arise with the compressed mass spectrum $m_{\chi_1}\simeq m_{\chi_2}$, such as the coscattering $\chi_2f\to\chi_1f$, the conversion $\chi_2\chi_i\to\chi_1\chi_j$, and the coannihilation $\chi_1\chi_2\to f\bar{f}$ processes. Suppressed by the small mixing angle $\theta$ between the dark fermions, the small effective gauge coupling of dark matter $\chi_1$ to the gauge boson $Z'$ is one distinct feature of this model, rendering phenomenology in many aspects more promising. In this paper, we investigate the production of dark matter through new mechanisms within the frameworks of resonance and secluded scenarios. The impacts of phenomenological constraints from collider, dark matter, and cosmology are also taken into account. We report that the conversion mechanism is both favored by the resonance and secluded scenarios under current constraints.

Figures

Figures reproduced from arXiv: 2512.08515 by the authors.

**Figure 2.** FIG. 2. Constraints on the [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** FIG. 3. The constraints of direct detection experiments in the resonance scenario. The fixed parameters in subfigures [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. The constraints of indirect detection experiments in the resonance scenario. The legends of panels (a)-(d) and [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: FIG. 5. Cosmological constraints on long-lived [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: FIG. 6. The evolutions of various abundances [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

**Figure 7.** Figure 7: FIG. 7. Constraints on the [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

**Figure 8.** Figure 8: FIG. 8. The constraints of direct detection experiments in the secluded scenario. Legends and markers occurring in [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]

**Figure 9.** Figure 9: FIG. 9. The constraints of indirect detection experiments in the secluded scenario. The benchmarks selected in panels [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

**Figure 10.** Figure 10: FIG. 10. Cosmological constraints on long-lived [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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