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Multi-component secluded WIMP dark matter and Dirac neutrino masses with an extra Abelian gauge symmetry

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper builds a complete dark-sector model in which two WIMP dark matter candidates, a dark photon, and a dark Higgs arise from one extra Abelian gauge symmetry, and claims this sector alone can produce the observed relic abundance…

desk verdict A solid first phenomenology scan of a specific chiral secluded WIMP benchmark; the thermal-equilibrium assumption is the main thing to push on. read the letter →

arxiv 2412.02027 v3 pith:QVRBRLOC submitted 2024-12-02 hep-ph

Kimy Agudelo , Diego Restrepo , Andrés Rivera , David Suarez This is my paper · ORCID
classification hep-ph
keywords secludedWIMPdarkmatterphotonHiggsDiracneutrinomassscotogenicmechanismtwo-componentU(1)Dgaugesymmetryanomaly-freechiralfermions
topics Dark Matter
open problems Dark Matter
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 constructs a complete, renormalizable extension of the Standard Model in which dark matter is not one particle but two weakly interacting massive fermions that annihilate inside an isolated 'secluded' dark sector. The central claim is that one extra Abelian gauge symmetry, broken by a dark Higgs, leaves a dark photon and a dark Higgs as the only portals, and that this sector can reproduce the observed relic abundance $\Omega h^{2}\approx 0.12$ even when the kinetic mixing between the dark photon and the Standard Model is set to zero. The same sector, through two inert scalars that never acquire vacuum values, generates small Dirac masses for the three Standard Model neutrinos at one loop, matching current oscillation data by construction. A sympathetic reader would care because it shows a UV-complete example of a class of models—chiral, anomaly-free, multi-component dark sectors with radiative neutrino masses—that survives cosmological and laboratory constraints and leaves some parameter space within reach of next-generation direct-detection experiments.

What carries the argument

The central object is the anomaly-free charge vector $D=[(1,-10),(1,-10),(-4,-5),9,9,9]$ under $U(1)_D$, with dark Higgs charge $S=9$. This vector solves the anomaly equations, gives three massive Dirac pairs after symmetry breaking (one of which is a two-flavor system whose lightest mass eigenstate is the first dark matter candidate, and a one-generation Dirac fermion is the second), and leaves three massless charge-9 right-handed neutrinos. A dark photon $Z'$ and a dark Higgs $h_2$ mediate annihilation; two inert scalars, a doublet $\eta$ and a singlet $\Phi$, close the one-loop 'scotogenic' Dirac neutrino mass diagram, meaning neutrinos remain massless at tree level. The load-bearing equation is the coupled Boltzmann system, whose conversion term $\langle\sigma_{2211}v\rangle$ couples the two number densities and is what makes the two-component nature change the relic density.

What would settle it

Measure the dark photon's invisible decay to neutrinos at a beam-dump or fixed-target experiment over the 1-100 GeV mass range; if a $Z'$ with the required coupling is absent, or its lifetime exceeds one second so it survives to Big Bang nucleosynthesis, the model's central compatibility claim is ruled out.

Watch

Extended reading notes

Core claim

The central claim is that a single self-consistent charge assignment $D=[(1,-10),(1,-10),(-4,-5),9,9,9]$ under $U(1)_D$, with a dark Higgs of charge $9$, yields all the ingredients at once: two stable Dirac fermions (the lightest state of a two-flavor pair and a single one-generation Dirac fermion), a dark photon that decays directly into three right-handed neutrinos, and a radiative Dirac neutrino mass from a decoupled inert scalar sector. Solving the two coupled Boltzmann equations with the conversion process $\Psi_2\Psi_2\to\Psi_1\Psi_1$, the paper finds parameter regions where the two components together saturate $\Omega h^{2}=0.12$, with dark matter masses from about 1 GeV to a few TeV. The neutrino decay mode of the dark photon opens a channel that keeps the model consistent with Big Bang nucleosynthesis and $\Delta N_{\text{eff}}$ even at zero kinetic mixing, and a scan under all constraints leaves viable points above the projected sensitivity of future liquid-xenon direct-detection experiments.

Load-bearing premise

The dark sector and the Standard Model plasma came into thermal equilibrium in the early Universe, and the same tiny couplings later decoupled it before Big Bang nucleosynthesis; the paper takes this equilibrium as a starting point rather than deriving it from a full thermal-history calculation.

Editorial extensions

If this is right

  • With zero kinetic mixing, the relic abundance can still reach $\Omega h^{2}=0.12$, because the dark photon's decay into right-handed neutrinos provides the connection back to the Standard Model without needing $\epsilon$.
  • Whenever the two dark matter candidates are close in mass and the dark Yukawa coupling $y_c$ is above about 0.1, the conversion process $\Psi_2\Psi_2\to\Psi_1\Psi_1$ affects the heavier component's abundance, so isolated single-component freeze-out calculations are not reliable in this model.
  • Spin-independent direct detection is dominated by the vector portal and scales as $\epsilon^{2}$, so the $\epsilon=0$ region is currently invisible; nonetheless a slice of the viable parameter space lies above the projected sensitivity of the next generation of xenon-based detectors.
  • Annihilation into the Standard Model is dominated by neutrino final states, making the model effectively dark for gamma-ray telescopes; the strongest experimental probes are therefore direct detection, collider searches, and possibly neutrino telescopes.
  • The neutrino spectrum is Dirac and radiatively generated, so the model predicts no neutrinoless double beta decay, in contrast with Majorana seesaw constructions.

Reading between the lines

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

  • An extension the authors do not pursue: because the dark photon decays predominantly to neutrinos, its most direct experimental signature may be missing-energy events in beam-dump and fixed-target searches rather than dilepton resonances.
  • The charge assignment studied here is one benchmark from a family of about a thousand anomaly-free solutions, and the paper's own comparison suggests the same two-mediator, two-component phenomenology can be realized by other charge vectors; whether the relic-density behavior is identical for the rest of the family is a testable extension.
  • The near-decoupled dark Higgs, with mixing angle below $10^{-3}$ and mass near 550 GeV, could still be probed by precision measurements of the 125 GeV Higgs couplings at future colliders, giving a complementary handle on the viable points that direct detection cannot reach.
  • Quantifying the cascade annihilation $\Psi\Psi\to Z'Z'\to 4\nu$ at neutrino telescopes could make the model's otherwise dark indirect signal visible; the paper notes the neutrino-flux enhancement but leaves the calculation for future work.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents a UV-complete, anomaly-free extension of the Standard Model with a secluded U(1)_D gauge symmetry. The new fields (Table I) comprise a dark Higgs S that breaks U(1)_D, a dark photon Z', a dark Higgs h2, nine chiral fermions including three massless right-handed neutrinos charged under U(1)_D, and a decoupled inert scalar sector (eta, Phi). Two Dirac fermions, Psi1 and the lighter of the two mixed states Psi_2^1, are stable dark matter candidates; the right-handed neutrinos plus the inert scalars generate Dirac neutrino masses at one loop (Fig. 2), with the couplings y_nR solved from the measured neutrino masses and PMNS matrix (App. A). The relic density is computed in a one-component WIMP limit (Eqs. (24)-(25), App. C) and with micrOMEGAs 6.0.3 for the full two-component system (Eqs. (18), Figs. 6-7) over the scan ranges of Table III, selecting points with Omega h^2 equal to about 0.12. The paper shows direct-detection prospects (Figs. 9-10) and claims compatibility with invisible-decay, BBN, and Delta N_eff constraints, including for zero kinetic mixing (epsilon = 0).

Significance. The paper's main asset is completeness: it is the first phenomenological exploration of the model class catalogued in Ref. [23], with an explicit anomaly-free charge assignment, one-loop Dirac neutrino masses, and relic densities computed with standard tools. The analytic one-component calculation is cross-checked against micrOMEGAs (Fig. 5), and the annihilation cross-sections in App. C reproduce known vector and axial-vector limits. The fits are transparently labelled: y_nR is fixed 'by construction' (App. A) to reproduce neutrino data, and the scan is filtered on Omega h^2 = 0.12, so the results establish existence of viable parameter regions and falsifiable direct-detection targets (Fig. 9) rather than sharp predictions. The significance is tempered by the two gaps identified below: the assumed early-universe thermal history of the dark sector, and the epsilon = 0 Delta N_eff claim; both are load-bearing for the headline 'even without kinetic mixing' statement.

major comments (3)
  1. [Sec. IV; App. F] The stress-test concern about the thermal history is warranted. Section IV opens with 'Since the dark sector is in thermal equilibrium,' and the same section asserts that the visible and dark sectors decouple when epsilon ~ 10^-6, theta < 10^-3, and m_Xi > 1 TeV, citing Ref. [24]; neither statement is derived for the model's own couplings. This assumption is load-bearing because the Boltzmann equations (18), the analytic relic density (24), and the Delta N_eff treatment of Appendix F all presuppose a single thermal bath at temperature T with standard equilibrium initial abundances. At epsilon = 0 the only channels connecting the dark sector to the SM are the scalar mixing theta and the y_nL Yukawa couplings to inert scalars with m_Xi > 1 TeV, and it is a parametric question (depending on the Table III ranges) whether these equilibrate the dark sector at T larger than about m_Psi/25 and later decouple it before BBN. If the dark sector never equilibrated, the correct computation would be freeze-in or a two-temperature Boltzmann system, and Figs. 5-7 would not determine the relic abundance. I request a rate-versus-Hubble comparison for the dominant DS-SM equilibration processes for the benchmark of Fig. 5 and for representative epsilon = 0 points, or a coupled T_DS/T_SM evolution.
  2. [App. F; Fig. 9] The epsilon = 0 Delta N_eff claim is not supported by the presented calculation. Appendix F computes Gamma_nuR only for the kinetic-mixing-mediated coupling (Eqs. (F2)-(F3)), and the text concludes that the blue epsilon = 0 region in Fig. 9 has 'zero contribution to the relativistic degrees of freedom at tree level.' But at epsilon = 0 the dark sector is still populated (the freeze-out mechanism requires it), and after freeze-out the DM annihilation energy is transferred to Z' and h2, which decay predominantly into the massless right-handed neutrinos; that nu_R population is a decoupled dark-radiation component whose contribution to Delta N_eff is not computed anywhere in the paper. The magenta-region constraint in Fig. 9 therefore reflects only the kinetic-mixing channel, and the abstract and Sec. VI claims of compatibility with Delta N_eff 'even without kinetic mixing' need either a computation of this channel or a quantitative demonstration that it is negligible (e.g., early decoupling and entropy dilution).
  3. [Eq. (21); Table III; Figs. 6-10] The paper's headline statements are existence claims, and the reader should be able to judge how representative the viable regions are. The scan filters on Omega h^2 = 0.12 (Eq. (21)) and fixes y_nR from neutrino data (Eqs. (A13)-(A14)); the manuscript should report the fraction of randomly scanned points that pass Eq. (21) and all other constraints, and how the viable regions shift under the Table III bounds. Note also a quantitative inconsistency: Eq. (21) imposes Omega h^2 = 0.1200 +- 0.0012, while Fig. 6 and its text use a 10% band; the actual filter used to produce Figs. 6-10 should be stated once, precisely.
minor comments (5)
  1. [Eq. (F1)] Equation (F1) is dimensionally inconsistent as printed: Gamma_nuR has dimension of energy while 3H n_nuR has dimension of energy to the fourth power; the intended condition is presumably Gamma_nuR > 3H, so the 'n_nuR' should be removed.
  2. [Figs. 5-7] The notation for the second dark matter fermion is hard to parse: the mass eigenstates are written as m_Psi1_2 and m_Psi2_2 in the Fig. 5 caption and as Psi_2^1, Psi_2^2 elsewhere; a consistent notation such as m_{Psi_2^{(1)}} and m_{Psi_2^{(2)}} would remove the ambiguity with the first DM candidate Psi1.
  3. [Sec. V (Fig. 7 discussion)] The text says the relic abundance is 'almost always dominated by annihilation processes directly to the SM particles,' but in Table II the classes 1100 and 2200 include final states with Z' and h2, and the secluded regime is dominated by annihilation into dark mediators; the phrase should be reconciled with the classification.
  4. [Sec. V] Please state whether the SARAH/SPheno/micrOMEGAs model files and the scan-filtering code will be made available; the reproducibility of Figs. 6-10 depends on these.
  5. [Abstract; Sec. V] Minor typos and infelicities: 'Bolztmann equations' (Sec. V), 'the branching ratio of Standard model particles into invisible' (abstract), and 'that is below the current limit of XENONnT for the two DM components' (Sec. V) should be reworded.

Circularity Check

1 steps flagged · score 6.0 of 10

Neutrino mass generation reduces to a fit: ynR is solved from measured masses and the PMNS matrix, so reproducing oscillation data is true by construction; relic-density and direct-detection results remain genuine outputs.

  1. self definitional [Section V (scan paragraph) and Appendix A, Eqs. (A13)-(A14)]
    "Finally, the Yukawa couplings (ynR)αi in Lagrangian (6) were parameterized in terms of the (ynL)iα Yukawa couplings, the neutrino masses mνα and the Pontecorvo-Maki-Nakagawa-Sakata matrix [67] as described in Appendix A. In this model, the new Yukawa couplings reproduce the current neutrino oscillation data by construction [37]."

    In Appendix A, Eqs. (A13)-(A14) explicitly solve the couplings ynR in terms of the target observables: the measured masses mν2, mν3 and the PMNS matrix U. Feeding these couplings back into the one-loop mass formula (A5) reproduces those masses by construction. Therefore the paper's stated success that the model 'generates Dirac neutrino masses' and is compatible with neutrino oscillation data is an inversion of the input data rather than a first-principles prediction. The loop diagram and the functional form are genuine model content, but the neutrino mass eigenvalues themselves are fitted inputs, so this headline result is built in by definition.

full rationale

The only identifiable circular step is the neutrino sector, where Eqs. (A13)-(A14) invert the one-loop formula to determine ynR from the measured neutrino masses and PMNS matrix, making the subsequent agreement with oscillation data tautological; the paper itself labels this 'by construction,' and it is central to the title and abstract. The rest of the analysis is not circular in the same sense: the relic density is imposed as a constraint (Ωh^2 = 0.1200 ± 0.0012) and points are filtered, not fitted and then renamed as a prediction; the DM conversion fractions ζ and the direct-detection cross sections of Eqs. (26)-(27) are computed outputs that were not used as inputs; and the ΔNeff/BBN and invisible-decay checks are comparisons against external constraints. The early-universe thermal-equilibrium statement in Section IV is an unproved premise and a correctness risk, but it is an assumption rather than a derivation from the model's outputs. Self-citations to Refs. [23] and [25] provide the charge classification and scotogenic framework, but they do not force the relic-density or direct-detection conclusions. Score 6 rather than 8 because the DM relic-density content and direct-detection predictions retain independent content; score not lower because a headline 'prediction' — Dirac neutrino masses matching oscillation data — is explicitly fitted by construction.

Assumptions & free parameters 10 free parameters · 6 assumptions · 5 invented entities

Most of the quantitative success is purchased through free parameters: the relic density and neutrino masses are imposed by scanning or fitting, and the new particles have no independent experimental confirmation. The model is still a legitimate UV completion because the particle content is fixed by anomaly cancellation and the Lagrangian is renormalizable, but the ratio of assumed input to derived output is high.

free parameters (10)
  • g_D (dark gauge coupling) = 10^-3 to 1 (scan)
    Sets dark photon interactions; scanned in Table III; central to relic density and direct detection.
  • y_c (Yukawa coupling for Psi1) = 10^-3 to 1 (scan)
    Determines the mass of the first dark matter candidate and the DM conversion cross section.
  • m_Z' (dark photon mass) = 1 to 1000 GeV (scan)
    Input scan variable, effectively set by g_D, v_s, and kinetic mixing; controls annihilation and decay.
  • m_h2 (dark Higgs mass) = 125 to 5000 GeV (scan)
    Determines s-channel annihilation and the scalar portal to the Standard Model.
  • theta (scalar mixing angle) = 10^-6 to 10^-3 (scan)
    Chosen small to suppress scalar direct detection; controls DM-SM coupling and BBN-related decays.
  • epsilon (kinetic mixing) = 10^-12 to 10^-2 (scan)
    Controls vector-portal direct detection and Delta Neff; scanned in Table III.
  • ynL (neutrino Yukawa matrix entries) = 10^-4 to 1 (scan)
    Free inputs; ynR are then solved from neutrino masses and PMNS by construction, so neutrino data is fitted.
  • Dark sector mass splittings and inert scalar masses = ranges in Table III
    Mass splittings and m_eta, m_Phi, mu_c are chosen to set the DM hierarchy and decouple the inert scalars.
  • Quartic scalar couplings lambda_k = 10^-4 to 1 (scan)
    Scanned in Table III; affect scalar spectrum and the one-loop neutrino mass calculation.
  • Dark fermion mixing angles theta_L, theta_R = 10^-3 to 2 pi (scan)
    Control the Psi2 mass eigenstates and their couplings; scanned with implications for relic density.
assumptions (6)
  • standard math Anomaly cancellation conditions (sum Zi = 0 and sum Zi^3 = 0) are the full consistency requirement for the U(1)_D sector.
    Used in Sec. II to classify charge assignments; relies on Refs. [22,27,29].
  • domain assumption The dark sector was in thermal equilibrium with the Standard Model in the early Universe.
    Sec. IV opens with 'Since the dark sector is in thermal equilibrium'; supports freeze-out and BBN reasoning, but this is not derived for the tiny couplings adopted.
  • domain assumption A residual discrete Z_|S| symmetry after spontaneous symmetry breaking stabilizes the lightest dark fermion.
    Sec. II uses Ref. [35] to guarantee DM stability; standard group-theoretic result for the dark Higgs VEV.
  • ad hoc to paper The inert scalar sector (eta, Phi) does not develop VEVs and is heavy and decoupled with m_Xi above 1 TeV.
    Required to keep the scotogenic loop as the neutrino mass source and to avoid extra dark matter states; imposed in Table III.
  • domain assumption Numerical codes SARAH, SPheno, and micrOMEGAs 6.0.3 correctly implement the model and solve the two-component Boltzmann system.
    All quantitative results in Sec. V depend on these tools; no independent cross-check or code release is provided.
  • domain assumption Neutrino oscillation data (normal ordering, m_nu1 = 0) can be reproduced by the one-loop formula with perturbative couplings.
    Appendix A forces ynR to fit PDG masses and PMNS; assumes this yields acceptable couplings, and perturbativity is not audited.
invented entities (5)
  • Dark photon Z'
    purpose: Mediates DM annihilation and conversion, and decays into active and right-handed neutrinos; this decay channel relaxes kinetic-mixing bounds.
    A new gauge boson postulated by the model; mass and coupling are scanned, with no external experimental evidence offered.
  • Dark Higgs S (mass eigenstate h2)
    purpose: Breaks U(1)_D, generates dark fermion masses and the dark photon mass, and provides a scalar portal to the SM.
    Model input; no independent evidence, and its mixing with the SM Higgs is constrained by the scan.
  • Chiral dark fermions Psi1 and Psi2^1 (two-component DM)
    purpose: Serve as the two thermal relic dark matter candidates with a conversion process between them.
    New fermions introduced to cancel anomalies and to provide dark matter; no external detection.
  • Massless right-handed neutrinos nu_R^alpha with charge -9
    purpose: Complete the anomaly-free fermion set, generate Dirac neutrino masses at one loop, and provide the Z' decay channel into neutrinos.
    No independent evidence; their existence is part of the model setup.
  • Inert scalars eta (SU(2)_L doublet) and Phi (singlet)
    purpose: Realize the one-loop scotogenic Dirac neutrino mass while remaining without VEVs.
    Introduced for neutrino mass generation; assumed heavy, with no external handle.

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Cite this review

Pith. "Pith review of Multi-component secluded WIMP dark matter and Dirac neutrino masses with an extra Abelian gauge symmetry." pith.science (2026). https://pith.science/paper/QVRBRLOC

@misc{pith2026241202027,
  author       = {Pith},
  title        = {Pith review of: Multi-component secluded WIMP dark matter and Dirac neutrino masses with an extra Abelian gauge symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QVRBRLOC}},
  note         = {Machine review of arXiv:2412.02027}
}
read the original abstract

Scenarios for secluded WIMP dark matter models have been extensively studied in simplified versions. This paper shows a complete UV realization of a secluded WIMP dark matter model with an extra Abelian gauge symmetry that includes two-component dark matter candidates, where the dark matter conversion process plays a significant role in determining the relic density in the Universe. The model contains two new unstable mediators: a dark Higgs and a dark photon. It generates Dirac neutrino masses and can be tested in future direct detection experiments of dark matter. The model is also compatible with cosmological and theoretical constraints, including the branching ratio of Standard model particles into invisible, Big Bang nucleosynthesis restrictions, and the number of relativistic degrees of freedom in the early Universe, even without kinetic mixing.

Figures

Figures reproduced from arXiv: 2412.02027 by the authors.

Figure 1
Figure 1. A schematic picture that shows our model setup with two secluded DM particles. Ψ [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Diagram for neutrino masses at one-loop. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. DM(Ψ1, Ψ1 2 ) annihilation channels (we do not show the corresponding u-channels.). The DM annihilation into SM model particles via mass mixing of the scalars hi or kinetic mixing is extremely suppressed. Ψ2 Ψ2 h2 Ψ1 Ψ1 Ψ2 Ψ2 Z ′ Ψ1 Ψ1 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: DM conversion channels Ψ1 ↔ Ψ1 2 mediated by the dark Higgs h2 or the dark photon Z ′ . Dirac neutrinos, the dark Higgs h2, and the dark photon Z ′ . Also, we show the DM conversion processes in [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Relic density in the limit of one DM component Ψ [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: DM relic density for the two fermionic DM candidates (Ψ [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: DM conversion impact. The green darker points represent models where the conversion [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Spin independent interactions of DM (Ψ1, Ψ1 2 ) with nuclei: vector (left) and scalar (right) portals. where µ = MNmΨi /(MN + mΨi ) is the reduced mass, MN ≈ 939 MeV is the nucleon mass (neutron or proton), BΨ1 = (qχL − qχR ) = 1, BΨ2 = (qψL − qψR ) = 9 (see Tab. I). O…
Figure 9
Figure 9. Figure 9: SI cross-section for elastic scattering of DM with nuclei scaled by [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: XENONnT contours limits for some dark photon masses projected in the plane of the [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

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94 extracted references · 16 canonical work pages · cited by 1 Pith paper

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    , (11) with UΞ =   cos θΞ sin θΞ − sin θΞ cos θΞ   . (12) Regarding the fermion spectrum, in this model, we have two DM particles (DM1 and DM2) that are connected by the dark photonZ ′ and the Higgs portal S as is shown in Fig. 1. According to the Lagrangian 6 and after electroweak and U (1)D symmetry breaking, we get a Dirac fermion DM candidate, Ψ 1...

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    annihilation channels (we do not show the corresponding u-channels.). The DM annihilation into SM model particles via mass mixing of the scalars hi or kinetic mixing is extremely suppressed. Ψ2 Ψ2 h2 Ψ1 Ψ1 Ψ2 Ψ2 Z′ Ψ1 Ψ1 Figure 4. DM conversion channels Ψ 1 ↔ Ψ1 2 mediated by the dark Higgs h2 or the dark photon Z′. Dirac neutrinos, the dark Higgs h2, and...

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    with nuclei: vector (left) and scalar (right) portals. where µ = MN mΨi/(MN + mΨi) is the reduced mass, MN ≈ 939 MeV is the nucleon mass (neutron or proton), BΨ1 = (qχL − qχR) = 1, BΨ2 = (qψL − qψR) = 9 (see Tab. I). On the other hand, the contribution of the scalar portal (ri...

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