Minimal Leptophilic Dark Matter

• Minimal leptophilic dark matter models are defined by an economical set of new fields that couple dark matter primarily to Standard Model leptons.
• They employ Yukawa interactions, scalar mediators, and seesaw dynamics to achieve relic abundance and link with neutrino mass generation.
• Theoretical constraints such as vacuum stability and experimental limits ensure that these models yield testable predictions in collider and astrophysical searches.

Minimal leptophilic dark matter models constitute a class of frameworks in which the dark matter (DM) candidate couples exclusively or predominantly to Standard Model (SM) leptons, with only the minimal number of new fields and interactions beyond the SM. Such models are motivated by cosmological relic abundance considerations, neutrino mass generation, constraints from direct and indirect detection experiments, and the unique collider signals that arise from the leptonic coupling structure. Central examples span Dirac or Majorana singlet fermions coupled to right-handed charged leptons via scalar mediators, as well as neutral components of vector-like SU(2) multiplets with tailored hypercharge and additional couplings to leptonic sectors via seesaw dynamics or extended gauge symmetries.

1. Fundamental Structure of Minimal Leptophilic Dark Matter Models

Minimal leptophilic DM models are defined by highly economical field content and interaction structure, typically introducing only a DM candidate and one (or at most a few) new mediator fields:

• Fermion singlet DM with a charged scalar mediator: The DM particle is a SM gauge singlet (usually Majorana or Dirac) that interacts with right-handed SM charged leptons via a new scalar S⁺. The Lagrangian includes a Yukawa coupling:

$$\mathcal{L} \supset y_\ell\, \bar{N}\, \ell_R\, S^+ + \text{h.c.}$$

where $N$ is the DM fermion, $\ell_R$ is a right-handed charged lepton, and $S^+$ carries hypercharge +1.

• Vector-like multiplet DM coupled through right-handed neutrinos: The neutral component of a vector-like multiplet $(\Sigma, \Sigma^c)$ with integral weak isospin ($T$) and zero hypercharge ($Y=0$) acts as the DM candidate. New superpotential terms couple this sector to right-handed neutrinos $N_i$:

$$W_\text{new} \supset y_{ij} N_i L_j H_u + \frac{1}{2} h_{ijk} N_i \Sigma_j \Sigma_k$$

This structure links DM production directly to leptogenesis and neutrino mass generation.

Minimality implies that additional new fields are restricted to only those required for stability (imposed by a symmetry such as $Z_2$), viability of the DM relic density, and anomaly cancellation if necessary.

2. Interactions, Symmetries, and Leptophilic Coupling Structure

The characteristic leptophilic interaction is realized by enforcing tree-level couplings only to leptons, while interactions with quarks are either absent or highly suppressed (appearing only at loop level or via kinetic mixing). This has several forms:

• Yukawa interactions: As in singlet fermion plus charged scalar models, sizable Yukawa couplings to right-handed leptons are necessary for relic density production via freeze-out and impact collider signatures and renormalization group (RG) running (Seto et al., 22 Aug 2025).
• Trilinear couplings in effective WIMP models: Trilinear terms $\lambda(\ell \chi) L^* + \text{h.c.}$, where $L$ is a lepton partner with the same SM quantum numbers as the lepton doublet, and $\chi$ is the DM candidate, provide sufficient DM–SM coupling with a simple parameter space (Chang et al., 2014).
• Gauge interactions via Z′ bosons: Some minimal models feature new gauged lepton-number ($U(1)_\ell$) or $B-L$ symmetries, introducing a leptophilic $Z′$ mediator. Purely leptonic Z′ couplings ensure the absence of direct couplings to quarks, with kinetic mixing parameter $\epsilon$ controlling any loop-induced couplings to the quark sector (Bell et al., 2014, Madge et al., 2018, Goudelis et al., 2023).

The DM candidate's stability is typically protected by a discrete parity ($Z_2$ or matter parity), often remnant from the symmetry-breaking pattern (e.g., $(-1)^{3(B-L)}$ in local $U(1)_{B-L}$ extensions (Cai et al., 2018)).

3. Relic Density Generation and Leptogenesis Connection

A central feature of many minimal leptophilic DM models is their deep connection to baryogenesis through leptogenesis and/or neutrino mass generation:

Model Type	DM Production	Leptogenesis/Neutrino Link
Dirac vector-like multiplet via seesaw	Asymmetric from $N_i$ decay	Type I seesaw and leptogenesis
Singlet fermion + charged scalar	Symmetric (thermal freeze-out) or asymmetric via decays	None unless coupled to neutrino sector
Minimal effective operator models	Freeze-in via $lH \to Sf$	Weinberg operator for $\nu$ mass and baryogenesis (Blazek et al., 21 Apr 2025)

• Asymmetry-based production: In models employing the type I seesaw extension, heavy right-handed neutrino decays ($N_1 \to LH_u$ or $N_1 \to \Sigma\Sigma$) generate both lepton and DM asymmetries through CP-violating interference at early times (Chun, 2011). The CP asymmetries are

$$\epsilon_L \simeq \frac{1}{4\pi} \frac{\text{Im}[y_iy_1^*(y_iy_1^* + h_ih_1^*)]}{|y_1|^2 + \frac{3}{4}|h_1|^2}\frac{M_1}{M_i}$$

$$\epsilon_\text{DM} \simeq \frac{1}{2\pi} \frac{\text{Im}[h_ih_1^*(y_iy_1^* + h_ih_1^*)]}{|y_1|^2 + \frac{3}{4}|h_1|^2}\frac{M_1}{M_i}$$

• Effective operator approach: Minimal effective theory models add only a heavy unstable fermion $f$ and a light DM scalar $S$, with the relevant operators

$$\mathcal{L}_\text{eff} = \frac{\lambda}{\Lambda} S\, \bar{f} P_L l H + \frac{\lambda'}{\Lambda} H \bar{l}^c P_L l H + \text{H.c.}$$

The same set of interactions that set the relic density via freeze-in also generate the lepton asymmetry through CP-violating scattering and decay, while the Weinberg operator provides neutrino masses (Blazek et al., 21 Apr 2025).

4. Collider and Astrophysical Signatures

Leptophilic couplings lead to distinctive signatures for both collider and astrophysical searches, often quite distinct from those expected in minimal quark-coupled WIMP scenarios:

• Collider signatures:
  • Long-lived charged scalars and fermions: In scenarios where the DM resides in a multiplet, nearly degenerate charged companions ($\Sigma^\pm$, $\tilde\Sigma^\pm$) are predicted. Decay lengths are often macroscopic (e.g., 100 cm for charged fermions), leading to disappearing charged tracks or slowly moving, highly ionizing tracks (Chun, 2011).
  • Dileptons + missing energy: Pair production and sequential decay of lepton partners (or mediator scalars) leads to final states with multiple leptons (e.g., $\mu^\pm\tau^\mp$) and missing transverse energy (Goudelis et al., 2023, Chang et al., 2014).
  • Mono-Higgs and same-sign charged scalars: At linear colliders, processes such as $e^+e^- \to N_R N_R H$ (mono-Higgs) or $e^-e^-\to H^-H^-$ (same-sign scalar pair) with missing energy offer low-background signals for electroweak-scale DM (Jueid et al., 2021).
• Astrophysical and direct detection:
  • Loop-induced nuclear interactions: Direct detection signals are suppressed, arising at the loop level or through charge radius and dipole moment operators, with cross sections scaling as $b_\chi^2$ or being velocity/anapole suppressed for Majorana DM (Chang et al., 2014, Bell et al., 2014).
  • Solar capture and neutrino signals: Leptophilic DM captured in the Sun exhibits a minimum detectable mass about 1 GeV lower (compared to hadrophilic DM) but requires much larger cross sections for saturation of the annihilation signal (Liang et al., 2018).
  • Neutrino and cosmic ray excesses: Decaying or annihilating leptophilic DM can account for high-energy neutrino fluxes (e.g., PeV-scale events at IceCube) or charged cosmic ray excesses (e.g., DAMPE). In these cases, the dominant energy injection is leptonic, evading gamma-ray and hadronic constraints (Boucenna et al., 2015, Balducci et al., 2018).

5. Theoretical and Renormalization Group Constraints

Minimality and the coupling scale impose stringent theoretical requirements:

• Vacuum stability and perturbativity: Sizable Yukawa couplings (required for the observed relic abundance if $m_N$, $m_{S^+}$ are raised) rapidly affect RG running. The one-loop beta function for the dominant Yukawa is

$$\frac{dy}{d\ln\mu} = \frac{1}{(4\pi)^2}\left(-3g_Y^2 y + 2y^3\right)$$

and similar negative contributions to the quartic scalar couplings can drive vacuum instability. The parameter space for perturbative couplings and a stable potential up to the Planck scale requires $m_N$, $m_{S^+}\lesssim350$ GeV, directly testable at future lepton colliders (Seto et al., 22 Aug 2025).

• Flavor structure: Some models embed flavor symmetries (e.g., DMFV) that control flavor-changing neutral currents and lepton flavor violation. The most restrictive limits arise from lepton flavor violating decays (e.g., $\mu\to e\gamma$), requiring off-diagonal couplings to be suppressed ($\lesssim0.01$–$0.1$ for $m_\psi\sim1$ TeV) (Acaroğlu et al., 2022).

6. Connection to Neutrino Physics and Unified Frameworks

Several minimal leptophilic DM models are constructed to unify dark matter, neutrino masses, and the matter–antimatter asymmetry:

• Weinberg operator realization: The inclusion of the dimension-5 operator $H \bar{l}^c P_L l H$ for neutrino mass ensures that the dynamics responsible for leptogenesis are tightly constrained by observed neutrino mass scales. Successful leptogenesis (via CP violation in scattering/decay of the heavy state $f$) and relic abundance can both be achieved in a model with only two new fields and two effective operators (Blazek et al., 21 Apr 2025).
• Matter parity from gauge origins: In minimal $U(1)_{B-L}$ extensions, spontaneous symmetry breaking renders a nontrivial residual discrete symmetry ($P_M = (-1)^{3(B-L)}$) unbroken, stabilizing the DM and preventing rapid decay, while simultaneously providing the seesaw mechanism required for light neutrino masses (Cai et al., 2018).

7. Summary Table: Salient Model Features

Scenario Type	Key New Fields	Main DM Coupling	Origin of Stability	Collider Signature	Neutrino/Leptogenesis Link
Singlet fermion + charged scalar	$N$, $S^+$	$y_\ell \bar N \ell_R S^+$	$Z_2$ or discrete parity	Long-lived $S^+$, dileptons+MET	Absent unless extended
Vector-like multiplet+seesaw	$\Sigma$, $N$	$h N \Sigma\Sigma$	B–L charge assignments/matter parity	Disappearing tracks, high-ionization	Direct via $N$ decay, seesaw
Effective operator freeze-in	$f$, $S$	$S \bar f P_L l H/\Lambda$	$Z_2$ dark-parity	Missing energy final states	Weinberg operator, leptogenesis
Z′ portal	$Z'$, $\chi$	$g_\chi \bar\chi \gamma^\mu \gamma^5 \chi Z'_\mu$	Gauge symmetry	4-lepton/μ–τ events	Model-dependent

A plausible implication is that, despite their inherent simplicity, minimal leptophilic DM models are heavily constrained by requirements of perturbativity, vacuum stability, and the necessity of reconciling distinct experimental limits from relic density, flavor physics, and direct detection. As such, regions of viable parameter space are highly predictive and often within reach of ongoing or near-future collider and astrophysical experiments. The direct connection to neutrino properties and cosmic matter–antimatter asymmetry in some constructions represents a unifying direction in minimal extension frameworks.