Scotoseesaw Model: Neutrino Mass & Dark Matter

• Scotoseesaw Model is a hybrid framework that combines a tree-level seesaw with radiative corrections to explain small neutrino masses while providing a stable dark matter candidate.
• It leverages discrete symmetries and anomaly cancellation to enforce dark matter stability and naturally generate the observed neutrino mass hierarchy.
• The model offers testable predictions through lepton flavor violation signals, collider searches, and dark matter phenomenology, aligning with current experimental constraints.

The scotoseesaw model refers to a class of neutrino mass models in which the pattern of observed light neutrino masses and mixings arises via a hybrid mechanism: one component from a conventional (typically type‐I or linear) seesaw at tree level, and a radiative component generated at loop level, often in a dark or symmetry-protected sector. The scotoseesaw paradigm provides a unified framework that both accounts for small neutrino masses (with natural suppression) and incorporates a viable, stable dark-matter candidate, with stability typically furnished by a discrete symmetry remnant of a dark gauge or flavor symmetry. The minimal realization relates the nontrivial flavor assignment of right-handed neutrinos (or other sterile fermions) under such symmetries, anomaly cancellation, and radiative mass-generation channels.

1. Field Content and Symmetries

Baseline constructions introduce, beyond the Standard Model (SM) fields:

• Three right-handed neutrinos with nontrivial transformation properties under a new symmetry: e.g., a dark gauge symmetry $U(1)_D$ with anomaly-free charges $D=0,-1,+1$ for $\nu_{1,2,3R}$ (Dong et al., 2023, Dong et al., 2024), a flavor-dependent $U(1)_X$ (Loi et al., 2024), or a $Z_3$ subgroup as the center of $SU(3)_C$ (Luong et al., 15 Jan 2025).
• Additional scalar fields:
  • Inert $SU(2)_L$ doublet(s) $\eta$, possibly also singlets $\chi$, $\xi$, with parity-odd assignments.
  • A SM-singlet scalar $\phi$ with charge to effect spontaneous symmetry breaking, leaving a discrete $Z_2$ or $Z_3$ stabilizing symmetry.
• New Dirac or Majorana neutral fermions, typically introduced as mediators in the radiative channel.
• In some variants, modular symmetry (e.g., non-holomorphic $A_4$) and modular weights distinguish the tree and loop sectors (Nasri et al., 10 Jan 2026). Flavon fields and vector-like fermions UV-complete the flavor structure in some models (Loi et al., 15 Jun 2025).

The table below summarizes representative field assignments in a popular $U(1)_D$ realization (Dong et al., 2023, Dong et al., 2024):

Field	SM Gauge	$D$	Residual Parity	Role
$\nu_{1R}$	1,1,0	0	$+1$	Seesaw (tree)
$\nu_{2,3R}$	1,1,0	$-1,+1$	$-1$	Loop/radiative
$\eta$	2,½	$+1$	$-1$	Inert doublet
$\chi$, $\xi$	1,0	$-1$	$-1$	Inert singlet
$\phi$	1,0	$+2$	$+1$	$U(1)_D$ breaking

2. Neutrino Mass Mechanism

The core of the scotoseesaw structure is the partitioning of light neutrino masses into distinct origins:

1. Tree-level (Seesaw) Contribution:
   • The $U(1)_D$- or parity-even neutral fermion (often only one right-handed neutrino) couples to SM leptons and the Higgs, yielding a rank-1 mass matrix at tree level after $\phi$ acquires a vacuum expectation value (VEV). For type-I seesaw:

   $$(m_\nu^{\rm tree})_{ab} \simeq - \frac{v^2}{2M_1} h_{a1}^\nu h_{b1}^\nu$$

   This predicts only one massive neutrino eigenvalue (Dong et al., 2023, Dong et al., 2024, Loi et al., 2024).

2. Radiative (Scotogenic) Contribution:
   • Dark parity-odd states couple to the SM lepton doublet only via inert doublets and run in the loop with other parity-odd neutral fermions, giving a one-loop (or higher) correction. In the minimal one-loop structure [Ma-type], the mass is

   $$(m_\nu^{\rm rad})_{ab} = \sum_{j} \frac{h_{a2}^\nu h_{b2}^\nu U_{2j}^2 M_j}{32\pi^2} \Bigl[ I(M_j^2, m_{R_1}^2) - I(M_j^2, m_{I_1}^2) \Bigr]$$

   where $I(M^2, m^2) = \frac{m^2}{M^2 - m^2} \ln(M^2/m^2)$, and $U_{2j}$ diagonalizes the neutral-fermion mass matrix (Dong et al., 2023, Dong et al., 2024).

3. Combined Light Neutrino Mass:
   • The neutrino mass matrix becomes

   $m_\nu = m_\nu^{\rm tree} + m_\nu^{\rm rad}$

   yielding typically $m_1 = 0$, $m_2 \sim m^{\rm rad}$ (solar scale), $m_3 \sim m^{\rm tree}$ (atmospheric scale). The observed mass hierarchy $\Delta m^2_{31} \gg \Delta m^2_{21}$ thus arises naturally (Dong et al., 2024).

Extensions exist with three-loop radiative mass generation (Abada et al., 2024), linear scotoseesaw variants with softly broken lepton number (Batra et al., 2023), and $A_4$ modular-weight separated sectors (Nasri et al., 10 Jan 2026).

3. Discrete Dark Symmetries, Anomaly Cancellation, and DM Stability

Residual discrete symmetries ($Z_2$, $Z_3$) responsible for dark matter stability are not ad hoc, but remnants of broken gauge symmetries. Anomaly cancellation for nontrivial $U(1)_D$ or $U(1)_X$ charge assignments uniquely fixes the pattern of assignments, typically:

• $D_1 + D_2 + D_3 = 0$, $$D_1^3 + D_2^3 + D_3^3 = 0 \Rightarrow D = (0, -1, +1)$$ (Dong et al., 2023, Dong et al., 2024).
• For $Z_3$ as $SU(3)_C$ center, RH neutrinos are assigned $1, w, w^2$ with $w^3 = 1$ (Luong et al., 15 Jan 2025).
• Breaking the associated symmetry by $\langle \phi \rangle$ of suitable charge leaves a residual $P_D = (-1)^D$ or $Z_3$ matter parity (Dong et al., 2023, Luong et al., 15 Jan 2025).

Under these symmetries, all SM fields are even, while the lightest odd field (e.g., parity-odd scalar or neutral fermion) is an absolutely stable dark matter candidate. This structure tightly links the origin of DM stability to the ultraviolet completion of the flavor or dark sector.

4. Dark Matter Phenomenology

The scotoseesaw framework generically admits both fermionic and scalar dark matter candidates:

• Fermionic DM: The lightest parity-odd neutral fermion (e.g., $N_2$ in $U(1)_D$, $N_{2R}$ in $Z_3$) annihilates via Higgs-portal or heavy mediator resonance:

$$\langle \sigma v \rangle_{N_2 N_2 \to t\bar t} \sim \frac{s_\varphi^2 m_t^2 M_2^2}{8\pi v^2 w^2 (4M_2^2 - m_{H_2}^2)^2}$$

Typical relic density constraints prefer TeV-scale masses and small portal mixing angles ($s_\varphi \sim 10^{-2}$) (Dong et al., 2023, Dong et al., 2024).

• Scalar DM: The lightest neutral component of the inert sector (e.g., mostly $\eta^0$ or admixtures with singlets) may be DM, with annihilation via the Higgs portal or gauge interactions, and possible coannihilations (Batra et al., 2023, Dong et al., 2023, Dong et al., 2024).

Direct-detection rates are controlled by the Higgs-portal couplings and inert scalar content, constrained to

$\sigma_{\rm SI} \lesssim 10^{-46}\,\mathrm{cm}^2$

for TeV-scale DM, compatible with current XENONnT and LZ bounds (Dong et al., 2023, Dong et al., 2024). Indirect detection constraints can also be relevant, depending on the DM mass and annihilation channels.

5. Lepton Flavor Violation and Collider Phenomenology

Hybrid scotoseesaw models involve new sources of lepton-flavor violation (LFV), both from heavy–light neutrino mixing ($M_D$ in the seesaw) and loops involving inert scalars and dark fermions. Critical processes include $\mu \to e\gamma$, with present limits requiring

$\mathrm{BR}(\mu \to e\gamma) < 4.2 \times 10^{-13}$

and Yukawa couplings $|\mathrm{Yukawa}| \lesssim \mathcal{O}(10^{-2})$ for $m_{\rm inert} \sim 1$ TeV (Batra et al., 2023, Dong et al., 2023, Nasri et al., 10 Jan 2026).

Collider searches target:

• Long-lived charged inert scalars (e.g., $\eta^\pm$), nearly mass-degenerate with DM, producing disappearing charged tracks. ATLAS excludes $m_{\eta^\pm}$ up to $\sim 560$ GeV (Nasri et al., 10 Jan 2026).
• Heavy $Z'$ bosons from broken $U(1)_D$/$U(1)_X$, with limits $m_{Z'} / g_X \gtrsim 10$–$20$ TeV from LEP II/LHC di-lepton searches (Loi et al., 2024, Loi et al., 15 Jun 2025).
• Deviations in electroweak precision observables (oblique $S$, $T$, $Z$-pole), with typical constraints on new VEV scales $w \gtrsim 10$ TeV (Loi et al., 15 Jun 2025).

6. Model Variants and Extensions

Several concrete variants exemplify the scotoseesaw principle:

• Dark linear scotoseesaw: Soft breaking of lepton number by a singlet–doublet–doublet scalar sector and loop-induced small $m_S$ entry, yielding a low-scale linear-seesaw (Batra et al., 2023).
• Gauge-completed $Z_3$ scotoseesaw: RH neutrinos assigned $Z_3$ charges, stabilized by the center of $SU(3)_C$ or residual $U(1)_{B-L}$ symmetry; both tree (inverse) seesaw and scotogenic loop terms tied to singlet VEVs (Luong et al., 15 Jan 2025).
• Flavor-dependent $U(1)_X$: The scotoseesaw mechanism realized in a flavor-dependent Abelian symmetry, with anomaly constraints selecting three generations and one unique $Z_2$-odd sterile neutrino $N_R$ as DM (Loi et al., 2024).
• Non-holomorphic modular $A_4$ scotoseesaw: Modular weights strictly separate even and odd sectors, ensuring minimal coupling, and $A_4$ modular forms shape all Yukawa matrices; successful leptogenesis is achievable via dark-portal loops (Nasri et al., 10 Jan 2026).
• Fully-flipped inert doublet frameworks: Three SM-family-dependent $U(1)_{Y_a}$ and a separated $U(1)_D$ for RH neutrinos, naturally yielding a hybrid seesaw, CKM hierarchies, and realistic DM (Loi et al., 15 Jun 2025).
• Three-loop scotoseesaw extensions: Further suppression of light neutrino mass at three loops, producing small masses even for $\mathcal{O}(0.1)$ Yukawas and explaining the W-mass anomaly for suitable parameter choices (Abada et al., 2024).

7. Outlook and Experimental Prospects

The scotoseesaw paradigm offers a robust link between neutrino mass generation and dark-matter stability, traced to residual discrete symmetries from UV-complete gauge or flavor extensions. Combined, these models accommodate:

• Natural smallness and hierarchy of light neutrino masses,
• Stable dark-matter candidates (either scalar or fermion),
• Compatibility with oscillation data, direct/indirect DM detection, LFV, and collider constraints,
• Predictivity for Higgs-portal signals, long-lived charged tracks, and new heavy gauge bosons.

Current and future experiments—LZ, XENONnT, DARWIN, MEG II, Belle II, multi-TeV colliders—are poised to probe large regions of the parameter space relevant for scotoseesaw models (Dong et al., 2023, Dong et al., 2024, Nasri et al., 10 Jan 2026, Loi et al., 15 Jun 2025).