Muonphilic Dark Matter Models

• Muonphilic dark matter refers to models where DM interacts predominantly through muon-specific mediators, leading to suppressed direct detection and distinct astrophysical and collider signals.
• These models incorporate frameworks like secluded scalar, U(1)ₗ₍μ₋τ₎ gauge extensions, and 2HDM to reconcile relic abundance, the Galactic Center Excess, and the muon (g-2) anomaly.
• Experimental probes range from lepton and muon colliders to neutron star observations and gamma-ray searches, providing multiple avenues to test these theories.

Muonphilic dark matter (DM) refers to the class of models in which dark matter communicates with the Standard Model (SM) sector dominantly or exclusively via couplings to the muon. This design feature produces a host of phenomenological consequences: suppressed direct detection rates, characteristic astrophysical signals, possible solutions to the muon anomalous magnetic moment, and distinctive collider and fixed-target opportunities. Muonphilic DM arises in a variety of frameworks, from minimal scalar or fermionic singlets coupled through scalar or vector mediators, to UV-complete constructions involving extended Higgs or new gauge sectors.

1. Theoretical Frameworks of Muonphilic Dark Matter

Models of muonphilic dark matter commonly introduce a new mediator particle, either a scalar ($\phi$), a pseudoscalar, or a vector boson (e.g., $Z'$), with interaction Lagrangians specifically engineered so that the mediator couples predominantly to muons. Representative scenarios include:

• Secluded Scalar Models: A scalar DM candidate ($\chi$) interacts via a contact term with a mediator scalar ($\phi$). The mediator $\phi$ is assigned Yukawa-like couplings to SM leptons, typically proportional to their mass (i.e., $$\mathcal{L} \supset \alpha\,\sum_{\ell}(m_\ell/v)\,\phi\,\bar{\ell}\ell$$), rendering the coupling muon-dominated for kinematically viable parameters, especially for light $\phi$ (Ghorbani, 2023).
• $U(1)_{L_\mu-L_\tau}$ Gauge Extensions: The SM is extended by an anomaly-free gauge symmetry $U(1)_{L_\mu-L_\tau}$ with a new gauge boson $Z'$ and DM candidate $\chi$ charged under this group. The $Z'$ couples to $\mu$, $\tau$, and their neutrinos, but not to electrons or quarks at tree level, yielding a strict muonphilic profile (Garani et al., 2019).
• Two-Higgs-Doublet Models (2HDM): Type-X (leptophilic) 2HDMs enable the introduction of a light, predominantly muon-coupled neutral scalar ($H$), which serves as the bridge between a real scalar DM ($S$) and the visible sector (Herms et al., 2022).
• Fermionic and Vector DM with Scalar Mediators: Comprehensive operator analyses (e.g., $L_3, L_9, L_{13}$) show that, after imposing muon $g-2$, relic abundance, and direct detection constraints, only s-channel scalar-mediated models (with both scalar and fermionic DM) remain viable for muonphilic scenarios (Abdughani et al., 2021, Chen et al., 26 Nov 2025).

Characteristic features of these models are summarized in the following table:

Model Class	Mediator Spin	DM Spin	Muon Coupling Structure
Secluded scalar	0 (scalar)	0 (scalar)	$\alpha (m_\mu/v)\,\phi\,\bar\mu\mu$
$U(1)_{L_\mu-L_\tau}$	1 (vector $Z'$)	0/1/½	$g' Z'_\mu\,\bar\mu\gamma^\mu\mu$
2HDM Type-X (leptophilic)	0 (scalar $H$)	0 (scalar)	$Y_{\mu\mu} H\,\bar\mu\mu$
Fermion DM + scalar med.	0 (scalar $\phi$)	½	$g_D\bar\chi i\gamma^5\chi\,\phi$, $g_\mu\bar\mu\mu\,\phi$

2. Relic Abundance, Annihilation Channels, and Resonance Phenomena

Muonphilic DM relic abundance is governed through thermal freeze-out processes mediated by the muonphilic portal.

• For sub-10 GeV scalar models, the main process is $\chi\chi\to\phi\phi$, with $\phi$ subsequently decaying to $\mu^+\mu^-$ or $\gamma\gamma$ ($$\Gamma(\phi\to\ell^+\ell^-) \propto \alpha^2 m_\ell^2/v^2$$) (Ghorbani, 2023).
• In the 2HDM scenario, $SS\to \mu^+\mu^-$ is possible via $s$-channel exchange of a light $H$, with forbidden-channel kinematics ($m_S < m_\mu$) ensuring that annihilations cease after freeze-out, evading late-time constraints (Herms et al., 2022).
• For heavier DM ($m_\chi\sim 40$–$80$ GeV), annihilation is optimized through s-channel scalar resonance when $m_\phi\sim 2m_\chi$, allowing sufficient present-day annihilation to account for the Galactic Center Excess (GCE) without violating relic abundance (Abdughani et al., 2021). The thermally averaged cross-section near resonance,

$$\langle \sigma v \rangle_{2\mu} \sim \frac{(g_Dg_\mu)^2\,m_\chi^2\sqrt{1-m_\mu^2/m_\chi^2}}{(4m_\chi^2 - m_\phi^2)^2 + m_\phi^2\Gamma_\phi^2}$$

is resonantly enhanced for $m_\phi\to 2m_\chi$.

• $U(1)_{L_\mu-L_\tau}$ scenarios allow $\chi\chi\to \mu^+\mu^-$ via $Z'$ exchange; the cross-section saturates in the geometric limit when DM-muon interaction rates are large (Garani et al., 2019).

3. Connections to the Muon Anomalous Magnetic Moment

Muonphilic mediators naturally induce loop-level contributions to the anomalous magnetic moment of the muon, $\Delta a_\mu=(g-2)_\mu/2$.

• For scalar mediators,

$$\Delta a_\mu = \frac{\alpha^2 m_\mu^2}{v^2}\int_0^1 dy\,\frac{(1+y)(1-y)^2}{(1-y)^2 + y(m_\phi/m_\mu)^2}$$

allowing GCE- and relic-density-compatible regions to simultaneously explain the $(g-2)_\mu$ anomaly for specific parameter ranges (e.g., $m_\phi\sim 0.2$–$1$ GeV, $\alpha\sim 0.1$–$0.5$) (Ghorbani, 2023, Abdughani et al., 2021).

• $U(1)_{L_\mu-L_\tau}$ models with $Z'$ masses of 10 MeV ($g'\sim 5\times10^{-4}$) can also produce the requisite $\Delta a_\mu$ (Garani et al., 2019).
• 2HDM-derived light scalars with $Y_{\mu\mu} \sim 3\times 10^{-4}$–$10^{-3}$ account for the full $(g-2)_\mu$ discrepancy with mediator masses $m_H\sim 110$–$150$ MeV (Herms et al., 2022).
• Only s-channel, scalar mediator models allow the correct sign and magnitude of $\Delta a_\mu$, as vector and axial interactions yield either the wrong sign or insufficient magnitude (Abdughani et al., 2021).

4. Astrophysical and Terrestrial Detection Prospects

Direct and indirect signals of muonphilic DM exhibit several important features:

• Suppressed Direct Detection: Tree-level DM-nucleon or DM-electron interactions are absent. Elastic DM–electron and DM–nucleon scattering arise only at one or two loops, yielding $\sigma_e\sim 10^{-43}$–$10^{-46}\,\mathrm{cm}^2$ and $\sigma_{\rm SI}\sim10^{-48}\,\mathrm{cm}^2$, generally below current XENON1T and PandaX-4T limits, but possibly accessible to next-generation experiments (Ghorbani, 2023, Abdughani et al., 2021, Chen et al., 26 Nov 2025).
• Neutron Star Heating: Neutron stars, with degenerate muon populations, are unique targets for DM that interacts solely with muons. Captured DM heats the star kinetically or via annihilation, elevating the surface temperature ($T_{\mathrm{kin}}\sim1700\,\mathrm{K}$, $T_{\mathrm{ann}}\sim2500\,\mathrm{K}$), which could be observable via next-generation infrared telescopes and is insensitive to tiny model-dependent loop-induced nucleon couplings (Garani et al., 2019).
• Gamma-Ray and Secondary Signals: DM annihilation to muons ($\chi\chi \to \mu^+\mu^-$) or to mediators ($\phi\phi$ with $\phi\to\mu^+\mu^-$) explains the Fermi GCE for $m_\chi \sim 40$–$70$ GeV, $$\langle \sigma v \rangle_{2\mu}\sim 4\times10^{-26}\,\mathrm{cm^3/s}$$ (Abdughani et al., 2021, Chen et al., 26 Nov 2025). In sub-GeV models, indirect searches target characteristic sharp $\gamma$-ray lines from loop-suppressed processes such as $SS\to \gamma\gamma$ (Herms et al., 2022).
• Collider Probes: Searches in $e^+e^-$ and (future) muon colliders, including visible and invisible decays of the mediator, can probe much of the viable parameter space. For example, a 3 TeV muon collider with $4.4\,\mathrm{ab}^{-1}$ can reach $g_\mu\sim 10^{-4}$–$10^{-3}$ for mediator masses $m_\phi=20$ GeV–1 TeV (Chen et al., 26 Nov 2025).

5. Viable Parameter Space and Phenomenological Benchmarks

The confluence of cosmological, collider, and astrophysical constraints delineates a tightly restricted parameter space for muonphilic DM models.

• In secluded scalar scenarios, successful benchmarks reflect $m_\chi\sim 1$–$5$ GeV, $m_\phi\sim0.2$–$1$ GeV, $\lambda\sim0.1$–$0.5$, $\alpha\sim0.1$–$0.5$, matching $\Omega_\chi h^2=0.12$, $\Delta a_\mu\simeq2$–$3\times 10^{-9}$, and $\sigma_e\sim 10^{-43}$–$10^{-45}\,\mathrm{cm}^2$ (Ghorbani, 2023).
• For GCE-compatible models (with or without resonance enhancement), $m_\chi\sim 50$–$70$ GeV, $m_\phi\sim100$–$140$ GeV, $g_D g_\mu\sim10^{-2}$–$10^{-1}$, and mediator widths $\Gamma/m_\phi\sim10^{-3}$–$10^{-2}$ satisfy all present bounds (Abdughani et al., 2021, Chen et al., 26 Nov 2025).
• In the sub-GeV forbidden annihilation regime, $m_S\sim 100$–$105$ MeV, $m_H \sim 110$–$150$ MeV, and $g_\chi g_\mu\sim 10^{-7}$ yield the correct relic density and full $(g-2)_\mu$ shift without violating CMB or direct-detection constraints (Herms et al., 2022).

6. Experimental Probes and Future Prospects

Multiple orthogonal experimental avenues can probe or exclude the muonphilic DM framework:

• Lepton Colliders: BABAR and Belle II (and proposed $\mu^+\mu^-$ and $Z$ factories) test mediator production in $e^+e^-\to\mu^+\mu^-\phi$ and $\phi$ decay channels, covering most of the $(g-2)_\mu$ and relic density favoured parameter band for $m_\phi\lesssim3.5$ GeV (Ghorbani, 2023).
• Muon Colliders: Projected reach at a 3 TeV $\mu^+\mu^-$ machine excludes $g_\mu\sim10^{-4}$–$10^{-3}$ for $m_\phi=20$ GeV–1 TeV, accessing nearly the entirety of the non-resonant GCE-favoured region (Chen et al., 26 Nov 2025).
• Muon Beam Dumps: Experiments such as NA64-$\mu$ plan sensitivity to $Y_{\mu\mu}\sim2\times10^{-4}$ in the sub-GeV regime (Herms et al., 2022).
• Indirect Detection: Next-generation MeV–GeV telescopes (e.g., AMEGO, e-ASTROGAM) may detect monochromatic $\gamma$-ray lines from loop-induced annihilation of sub-GeV DM (Herms et al., 2022); AMS-02 and Fermi may further constrain annihilations into secondary leptons.
• Neutron Star Observations: Infrared surveys targeting old neutron stars in DM-rich environments can uniquely test muonphilic scenarios, particularly those with suppressed direct-detection signals (Garani et al., 2019).

7. Summary and Open Questions

Muonphilic dark matter models, with efficiently suppressed direct detection rates and characteristic collider and astrophysical signatures, provide compelling target scenarios for DM phenomenology. The frameworks discussed reconcile the Galactic Center Excess, the muon $(g-2)_\mu$ anomaly, and the observed relic abundance via parameter tuning near s-channel scalar resonance or, for sub-GeV models, forbidden Boltzmann-suppressed channels.

Key open questions include the UV completion of these simplified models (e.g., embedding in 2HDM or vectorlike fermion portals), systematic exploration of resonance regions at colliders, and discrimination from alternative leptophilic or flavor-specific DM scenarios. Advancements in IR neutron-star observations, MeV gamma-ray, and high-luminosity lepton and muon collider programs collectively provide a comprehensive experimental probe into the full parameter space of muonphilic dark matter (Ghorbani, 2023, Abdughani et al., 2021, Chen et al., 26 Nov 2025, Herms et al., 2022, Garani et al., 2019).