Scotogenic Model: Radiative Neutrino Mass

• The Scotogenic model is a radiative neutrino-mass framework that extends the Standard Model with an inert scalar doublet and gauge-singlet fermions, forbidding tree-level neutrino masses.
• Its one-loop mechanism employs Yukawa interactions and a suppressed λ5 term to produce small neutrino masses while facilitating dark matter stability and possible leptogenesis.
• The model’s unified approach links neutrino mass generation with dark matter phenomenology, offering various signatures through its canonical and extended realizations.

The Scotogenic model is a radiative neutrino-mass framework in which the Standard Model is extended by a dark sector whose fields generate neutrino masses at one loop while also furnishing a stable dark matter candidate. In its canonical form, the model adds gauge-singlet fermions and an inert scalar doublet, all odd under an exact discrete symmetry, so that tree-level neutrino masses are forbidden, the lightest odd state is stable, and the same interactions can also support leptogenesis. The framework is routinely described as minimal and economical because neutrino mass generation, dark matter stability, and, in many realizations, baryogenesis are tied to the same structural ingredients (Satapathy, 2023, Bouchand et al., 2012, Escribano, 2021).

1. Canonical structure

The canonical Scotogenic model extends the Standard Model by three gauge-singlet Majorana fermions $N_i$ and one inert scalar doublet, usually denoted $\eta$ or $\Phi_2$, together with an exact $Z_2$ symmetry under which the new fields are odd and all Standard Model fields are even (Satapathy, 2023, Bouchand et al., 2012). In the notation used across the literature summarized here, the new singlets transform as $(1,1,0)$ and the inert scalar doublet as $(1,2,1/2)$ under the electroweak gauge group, with the Standard Model Higgs doublet remaining $Z_2$-even (Satapathy, 2023, Escribano, 2021).

The unbroken discrete symmetry has two immediate consequences. First, the usual tree-level Yukawa coupling $\overline{L}\tilde H N$ is forbidden, so neutrinos are massless at tree level. Second, the lightest $Z_2$-odd state cannot decay into Standard Model particles and is therefore stable, making either a neutral inert-scalar component or a singlet fermion a dark matter candidate, depending on the mass ordering (Bouchand et al., 2012, Escribano, 2021).

After electroweak symmetry breaking, only the Standard Model Higgs acquires a vacuum expectation value, whereas the inert doublet remains without a vacuum expectation value. In the common parametrization,

$\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$

or equivalently

$\eta$0

The exact $\eta$1 then remains intact in the vacuum, preserving the radiative character of neutrino mass generation and the stability of dark matter (Satapathy, 2023, Bouchand et al., 2012).

2. Lagrangian, scalar sector, and loop-induced neutrino mass

The fermionic sector contains Majorana masses for the singlets and Yukawa couplings connecting lepton doublets to the inert scalar,

$\eta$2

or, in equivalent notation,

$\eta$3

The absence of a vacuum expectation value for the inert doublet prevents these couplings from generating a tree-level Dirac neutrino mass (Satapathy, 2023, Bouchand et al., 2012).

The scalar potential in the canonical model is

$\eta$4

which is the inert-doublet-model potential augmented by the real $\eta$5 term (Satapathy, 2023, Bouchand et al., 2012, Escribano, 2021). The neutral-scalar mass splitting is controlled by $\eta$6; in the usual inert-doublet notation,

$\eta$7

and the neutrino mass vanishes in the limit $\eta$8 (Bouchand et al., 2012, Escribano, 2021).

The one-loop neutrino mass matrix takes the standard form

$\eta$9

or equivalently

$\Phi_2$0

In the small-splitting limit, the mass matrix is proportional to $\Phi_2$1, suppressed by the loop factor, and inversely related to the heavy singlet mass scale, yielding an effective seesaw-like structure with a loop-suppressed Weinberg operator coefficient (Satapathy, 2023, Bouchand et al., 2012, Escribano, 2021).

A standard reconstruction of Yukawa couplings uses the Casas–Ibarra parametrization. One convenient form given in the literature is

$\Phi_2$2

with $\Phi_2$3 the PMNS matrix and $\Phi_2$4 an arbitrary complex orthogonal matrix, while in generalized formulations with arbitrary numbers of singlets and inert doublets the one-loop mass matrix can be written in a compact exact form and a small-$\Phi_2$5, small-mixing approximation valid for any $\Phi_2$6 (Satapathy, 2023, Escribano, 2021).

3. Dark matter sector

Because the dark parity remains exact after symmetry breaking, the lightest $\Phi_2$7-odd particle is stable. In the canonical model this can be either the lightest singlet fermion or one of the neutral inert-scalar components. For the inert-doublet realization emphasized in several studies, one typically chooses the lightest neutral scalar, often denoted $\Phi_2$8 or $\Phi_2$9, with a hierarchy such as

$Z_2$0

or equivalently a choice of $Z_2$1 sign that makes $Z_2$2 lighter than $Z_2$3 (Satapathy, 2023, Escribano, 2021).

The dark-matter phenomenology partly mirrors the inert doublet model. In the standard scalar case, relic density is set by annihilation and coannihilation processes involving electroweak gauge interactions and Higgs-portal couplings, while direct detection is governed mainly by Higgs exchange and depends on $Z_2$4 (Satapathy, 2023). In the scale-invariant realization, direct-detection constraints are already severe and leave viable fermionic dark-matter regions roughly below $Z_2$5 GeV and above $Z_2$6 GeV (Ahriche et al., 2016).

Several non-canonical realizations alter this basic picture while preserving the scotogenic logic. In the $Z_2$7 construction, the dark sector carries a new gauge charge, and the dark matter candidate is the lightest Dirac or pseudo-Dirac singlet fermion. The dominant annihilation channels are

$Z_2$8

and

$Z_2$9

with benchmark values such as $(1,1,0)$0 TeV and $(1,1,0)$1 or $(1,1,0)$2 reproducing the observed relic abundance $(1,1,0)$3 in the corresponding limits (Ma et al., 2013).

A recent pseudo-Dirac realization produces a particularly distinctive indirect-detection signal. There, the singlets are organized into pseudo-Dirac pairs and the lightest state annihilates near threshold with a $(1,1,0)$4 branching ratio into neutrino pairs, yielding monochromatic neutrinos while remaining compatible with relic abundance, direct-detection bounds, and neutrino data (Cepedello et al., 6 May 2026). This suggests that the scotogenic framework does not fix a unique dark-matter phenomenology; rather, the common invariant is the stabilization of the dark sector by the same symmetry that forbids tree-level neutrino mass.

4. Leptogenesis and baryon asymmetry

The scotogenic framework also accommodates thermal leptogenesis. In the canonical setup, heavy Majorana singlets decay as

$(1,1,0)$5

violating lepton number and generating a CP asymmetry through the interference of tree-level and one-loop amplitudes (Satapathy, 2023). The CP asymmetry parameter is defined by

$(1,1,0)$6

and in the hierarchical limit takes the approximate form

$(1,1,0)$7

The total decay width is

$(1,1,0)$8

These expressions feed into Boltzmann equations for the heavy-neutrino abundance and the $(1,1,0)$9 asymmetry (Satapathy, 2023).

A standard unflavoured treatment uses

$(1,2,1/2)$0

with decay and washout terms built from inverse decays and $(1,2,1/2)$1 scatterings (Satapathy, 2023). Electroweak sphalerons then convert part of the resulting $(1,2,1/2)$2 asymmetry into baryon asymmetry. For the Standard Model plus one extra inert doublet, the effective conversion factor quoted in the literature is $(1,2,1/2)$3, so that

$(1,2,1/2)$4

and the baryon-to-photon ratio is estimated through

$(1,2,1/2)$5

Suitable choices of Yukawas, $(1,2,1/2)$6, and heavy masses can yield values comparable to the observed $(1,2,1/2)$7 (Satapathy, 2023).

The lower scale of successful leptogenesis is model-dependent. In the canonical model with two right-handed neutrinos and hierarchical masses, the lower bound remains at $(1,2,1/2)$8 GeV, essentially unchanged from standard thermal leptogenesis (Hugle et al., 2018). In the three-right-handed-neutrino case, however, the lower bound can be reduced to around $(1,2,1/2)$9 TeV without any degeneracy in the RHN mass spectrum, provided the $Z_2$0 Yukawa couplings are suppressed, leading to suppressed washout and an active neutrino mass of around $Z_2$1 eV (Hugle et al., 2018). A related singlet–triplet realization lowers the scale further to $Z_2$2 TeV for a spectrum $Z_2$3, again with suppressed washout and a small active neutrino mass, here of about $Z_2$4 eV (Singh et al., 2023). This indicates that low-scale leptogenesis is not generic to all scotogenic models, but it is realizable in specific field-content and flavor configurations.

A different baryogenesis–dark-matter linkage appears in the “asymmetric mediator” extension, where CP-violating decays of right-handed neutrinos simultaneously produce a lepton asymmetry and an asymmetry in a $Z_2$5-odd scalar doublet. The latter is later transferred to a singlet-scalar dark matter candidate through decays of the heavy doublet mediator, providing a scotogenic realization of asymmetric dark matter alongside radiative neutrino mass (Asai et al., 2022).

5. Renormalization, ultraviolet structure, and symmetry origins

The renormalization-group structure of the Scotogenic model differs markedly from tree-level seesaw models because the leading neutrino mass already arises at one loop and depends on scalar-sector lepton-number breaking. The full one-loop RGEs derived for the Ma model show that the quartic coupling $Z_2$6 receives only multiplicative corrections,

$Z_2$7

so if $Z_2$8 at some scale it remains zero at all scales. This reflects the technically natural character of the lepton-number-restoring limit (Bouchand et al., 2012).

Below the heavy-singlet thresholds, the effective theory contains two Weinberg-like operators, $Z_2$9 and $\overline{L}\tilde H N$0, rather than a single coefficient. Their RGEs are coupled through $\overline{L}\tilde H N$1,

$\overline{L}\tilde H N$2

which has no analogue in the minimal type-I seesaw (Bouchand et al., 2012). A concrete numerical study showed that a bimaximal leptonic mixing pattern at the GUT scale can run to a realistic low-energy pattern with large $\overline{L}\tilde H N$3, suggesting nontrivial interplay between the scotogenic mechanism and flavor symmetries (Bouchand et al., 2012).

A separate high-scale issue concerns the stability of the dark parity itself. In generalized scotogenic models with arbitrary numbers of singlet fermions $\overline{L}\tilde H N$4 and inert doublets $\overline{L}\tilde H N$5, the one-loop beta function for the inert mass matrix contains a negative-definite trace term,

$\overline{L}\tilde H N$6

which can drive $\overline{L}\tilde H N$7 negative at high scales, thereby breaking the $\overline{L}\tilde H N$8 symmetry and destroying both the radiative neutrino-mass mechanism and dark matter stability (Escribano, 2021). This does not imply inconsistency, but it requires case-by-case RGE control of Yukawas and quartics.

Several constructions address the ultraviolet origin of the model’s defining ingredients. One ultraviolet completion derives the low-energy $\overline{L}\tilde H N$9 parity as the remnant of a global $Z_2$0 symmetry broken by a singlet scalar $Z_2$1, and dynamically generates the $Z_2$2 term by integrating out a heavy scalar triplet $Z_2$3,

$Z_2$4

The low-energy spectrum then contains, besides the usual scotogenic states, a massive scalar and a massless Goldstone boson, leading to additional signatures in flavor observables, dark matter physics, and invisible Higgs decays (Escribano et al., 2021).

Other works replace the ad hoc discrete parity more radically. A non-invertible $Z_2$5 “no-group” construction reproduces the scotogenic structure, forbids tree-level neutrino masses, and induces an accidental $Z_2$6 that stabilizes dark matter while enforcing a one-zero neutrino mass texture (Nomura et al., 14 Jul 2025). This suggests that the discrete symmetry traditionally imposed by hand can itself emerge from a more structured infrared selection rule.

6. Variants and generalizations

The Scotogenic model has developed into a broad class of radiative neutrino-mass constructions rather than a single fixed lagrangian. The most prominent variants discussed in the literature covered here are summarized below.

Variant	Defining modification	Characteristic outcome
Gauged dark sector	Replace $Z_2$7 by $Z_2$8, exact or broken to $Z_2$9	Dirac or pseudo-Dirac dark matter with dark photon and dark Higgs (Ma et al., 2013)
Flavor-symmetric scotogenic model	Impose $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$0 on $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$1 or $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$2 realizations	Predictive mass textures and correlations for CP violation and $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$3 (Ma et al., 2014)
Dirac scotogenic model	Protect Dirac neutrinos and dark matter with a residual $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$4 from a chiral $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$5	One-loop Dirac neutrino masses and novel low-mass scalar or fermionic dark matter (Chuliá et al., 2024)
Scale-invariant scotogenic model	Remove all tree-level mass scales and add a singlet dilaton	Radiative EWSB plus a light dilaton affecting dark matter and direct detection (Ahriche et al., 2016)
Charged variant	Add charged vector-like fermions and a $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$6 scalar doublet	Only scalar dark matter is viable; new coannihilation regions appear (Romeri et al., 2021)
Singlet–triplet scotogenic model	Add both singlet and triplet Majorana fermions plus a real scalar triplet	Mixed fermion loop states and TeV-scale leptogenesis possibilities (Singh et al., 2023)

The $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$7 model replaces the discrete stabilizing symmetry by a gauged dark symmetry. It contains two inert-like scalar doublets $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$8 with opposite dark charges, three neutral Dirac singlet fermions, and optionally a dark scalar $\Phi_1= \begin{pmatrix} 0\[2pt] \dfrac{v+h}{\sqrt2} \end{pmatrix}, \qquad \Phi_2= \begin{pmatrix} H^+\[2pt] \dfrac{H+iA}{\sqrt2} \end{pmatrix},$9 whose vacuum expectation value breaks $\eta$00. The one-loop neutrino mass matrix is then controlled by scalar mixing,

$\eta$01

with the scalar mixing angle $\eta$02 replacing the role of $\eta$03 in the original model (Ma et al., 2013).

Flavor-symmetric constructions based on $\eta$04 embed both the $\eta$05 and $\eta$06 scotogenic realizations into a non-Abelian discrete symmetry. In one representative texture, the neutrino mass matrix takes the form

$\eta$07

leading, in the parameter region studied, to normal ordering, $\eta$08, and an effective neutrinoless-double-beta mass around $\eta$09 eV (Ma et al., 2014).

Dirac realizations modify the central premise from Majorana to Dirac neutrinos while keeping the radiative-dark-sector logic. In the $\eta$10 model derived from a chiral $\eta$11, the one-loop Dirac neutrino mass matrix is

$\eta$12

and the same residual $\eta$13 simultaneously protects the Dirac nature of neutrinos and stabilizes the dark matter candidate (Chuliá et al., 2024).

More speculative developments include non-invertible symmetry implementations (Nomura et al., 14 Jul 2025) and pseudo-Dirac fermionic dark matter producing monochromatic neutrinos (Cepedello et al., 6 May 2026). A plausible implication is that “scotogenic model” now functions as the name of a mechanism class: radiative neutrino mass generated by fields in a symmetry-protected dark sector, with dark matter stability and neutrino-mass suppression emerging from the same structural input.