Scalar DM–Neutrino Portal Model

• The paper introduces a minimal sterile-neutrino framework where a stable scalar dark matter particle (φ) attains the relic density through φφ → NN annihilation.
• The model employs a neutrino portal, linking the dark sector and the Standard Model via Yukawa-like interactions without relying solely on Higgs mediation.
• The approach structurally connects neutrino mass generation with dark matter phenomenology while satisfying relic density, direct detection, and indirect search constraints.

The scalar DM–neutrino portal model denotes a class of dark-sector extensions in which a scalar dark matter candidate communicates with the Standard Model through neutrino-sector states rather than primarily through the ordinary Higgs portal. In the minimal sterile-neutrino realization, the dark sector contains a scalar $\phi$ and a fermion $\Psi$, both singlets under the Standard Model gauge group but charged under an exact dark symmetry $G_{\rm dark}$, while sterile neutrinos $N$ are singlets under both sectors. For the hierarchy $m_\phi<m_\Psi$, the scalar is stable and can obtain the observed relic abundance predominantly through $\phi\phi\to NN$, with the sterile neutrinos subsequently decaying to Standard Model states via their active–sterile mixing. This makes the scalar case a genuine alternative to standard singlet-scalar Higgs-portal dark matter (Escudero et al., 2016).

1. Minimal sterile-neutrino construction

In the canonical realization, the dark sector contains two new fields, a scalar $\phi$ and a fermion $\Psi$, both charged under an exact dark symmetry $G_{\rm dark}$, chosen so that the bilinear $\overline{\Psi}\phi$ is neutral under $\Psi$0. Because all Standard Model fields and the sterile neutrinos are neutral under the dark symmetry, while $\Psi$1 and $\Psi$2 are charged, the lighter of $\Psi$3 and $\Psi$4 is stable. The scalar-DM regime is defined by

$\Psi$5

so that $\Psi$6 is the stable dark matter particle and $\Psi$7 is the heavier dark fermion mediator (Escudero et al., 2016).

The defining neutrino-portal interaction is

$\Psi$8

This Yukawa-like operator directly couples the scalar $\Psi$9, the dark fermion $G_{\rm dark}$0, and the sterile neutrino $G_{\rm dark}$1. The dark sector is connected to the Standard Model through the usual type-I-seesaw interaction

$G_{\rm dark}$2

with $G_{\rm dark}$3. The resulting interaction chain is

$G_{\rm dark}$4

The scalar sector also contains the renormalizable singlet-scalar Higgs portal

$G_{\rm dark}$5

A crucial assumption is that $G_{\rm dark}$6 does not acquire a vacuum expectation value. The dark symmetry therefore remains unbroken, and the scalar remains stable. This assumption is structurally central rather than cosmetic, because the portal phenomenology only uses the fact that the symmetry is exact and stabilizes the lightest dark-sector particle.

2. Relic-density mechanism and freeze-out structure

The central scalar-DM annihilation channel is

$G_{\rm dark}$7

through $G_{\rm dark}$8-channel exchange of $G_{\rm dark}$9. The channel is open only for

$N$0

so the scalar-DM regime of interest is

$N$1

This differs from the earlier effective-operator regime in which sterile neutrinos are heavier than the dark sector and can be integrated out, generating

$N$2

In the scalar portal regime under discussion, the sterile neutrinos are instead real final states controlling freeze-out (Escudero et al., 2016).

For $N$3, emphasized in the numerical analysis, the annihilation remains $N$4-wave and the rate scales roughly as

$N$5

The threshold factor $N$6 suppresses annihilation as $N$7, while a heavy mediator suppresses the process through the propagator. This is why the scan finds that the mediator mass should not be too large if one wants perturbative couplings and the correct relic density; imposing $N$8 effectively yields $N$9 TeV. The explored scalar-DM ranges are

$m_\phi<m_\Psi$0

A defining phenomenological result is that the relic abundance need not be controlled by $m_\phi<m_\Psi$1. In ordinary scalar singlet dark matter, the same Higgs-portal coupling controls both annihilation and direct detection, generating the familiar low-mass tension. Here, by contrast, direct-detection and invisible-Higgs limits can force $m_\phi<m_\Psi$2 to be small while the relic density is still fixed by $m_\phi<m_\Psi$3. Below about $m_\phi<m_\Psi$4 GeV, annihilation into Standard Model final states through the Higgs portal cannot account for freeze-out once those bounds are imposed, whereas annihilation into sterile neutrinos remains open and dominant. In the low-mass region the paper finds

$m_\phi<m_\Psi$5

rising to order unity only for $m_\phi<m_\Psi$6 GeV or near the Higgs resonance $m_\phi<m_\Psi$7. After current bounds, scalar dark matter with masses from $m_\phi<m_\Psi$8 GeV to $m_\phi<m_\Psi$9 TeV can still reproduce the observed relic abundance, with the neutrino portal dominant over most of the parameter space (Escudero et al., 2016).

3. Neutrino masses, mediator decays, and portal observables

The sterile neutrinos simultaneously generate active neutrino masses through the standard type-I seesaw. In the seesaw limit,

$\phi\phi\to NN$0

and diagonalization yields three light mostly-active neutrinos and heavy mostly-sterile states. The mixing matrix is written as

$\phi\phi\to NN$1

with leading-order entries

$\phi\phi\to NN$2

$\phi\phi\to NN$3

The portal therefore inherits the usual HNL decay phenomenology, but the dark-sector couplings $\phi\phi\to NN$4 are not fixed by neutrino masses (Escudero et al., 2016).

This distinction resolves a common misconception. The sterile neutrino mediator links the relic-density calculation and the neutrino-mass sector, but the main annihilation strength is controlled by the independent dark-sector parameters $\phi\phi\to NN$5, while the decay of the sterile neutrinos to Standard Model particles is governed by the seesaw Yukawas $\phi\phi\to NN$6 and the induced mixings $\phi\phi\to NN$7. The model therefore correlates neutrino physics and dark matter structurally, but not through a one-parameter relation.

Indirect detection follows the cascade

$\phi\phi\to NN$8

If $\phi\phi\to NN$9, the heavy neutrino decays through off-shell gauge bosons with a typical width

$\phi$0

For $\phi$1, two-body decays dominate, with widths scaling as

$\phi$2

Because scalar annihilation can be $\phi$3-wave, indirect detection is meaningful; estimates based on Fermi-LAT and H.E.S.S. suggest that indirect searches may probe or exclude scalar dark matter masses around and below

$\phi$4

especially when the sterile-neutrino decays produce significant $\phi$5-lepton final states. The same analysis finds CMB constraints weaker than Fermi-LAT under the same rough rescaling, while IceCube limits are far above the predicted rate (Escudero et al., 2016).

4. Direct detection, Higgs-sector limits, and viable parameter space

The principal non-cosmological constraints on the scalar portal are ordinary scalar-singlet constraints, but their role is changed by the neutrino portal. Direct detection proceeds through tree-level Higgs exchange, so the rate is controlled primarily by $\phi$6. The standard invisible-Higgs channel,

$\phi$7

is especially restrictive for $\phi$8. Using

$\phi$9

the scalar case acquires strong upper bounds on $\Psi$0. Direct-detection searches, treated as in standard singlet-scalar Higgs-portal models, likewise require $\Psi$1 to be small (Escudero et al., 2016).

This produces the characteristic viable regime: small enough $\Psi$2 to evade direct detection and invisible-Higgs limits, together with sufficiently large $\Psi$3 and an open $\Psi$4 final state to reproduce the relic density. The practical perturbativity/narrow-width bound used is

$\Psi$5

The main constraints shaping the scalar-DM parameter space are: relic density, invisible Higgs decay, tree-level Higgs-mediated direct detection, indirect detection from $\Psi$6 cascades, perturbativity/narrow-width consistency, neutrino-sector consistency, and the assumption that $\Psi$7 does not acquire a vev.

A second misconception is that any dark-sector model involving neutrinos and scalars is automatically a scalar DM–neutrino portal. Several closely related constructions are not. The UV-complete neutrino-portal models of (González-Macías et al., 2016) and (González-Macías et al., 2016) contain both a scalar and a fermion in the dark sector, but their main phenomenological regime is $\Psi$8, so the relic is fermionic and the scalar is a heavier partner/mediator. Likewise, radiative inverse-seesaw and doubly charged-scalar constructions such as (Ahriche et al., 2016) and (Hierro et al., 2016) connect dark matter to neutrino-mass generation but are not direct scalar DM–neutrino portals in their main implementation.

5. Broader model space and major variants

The term also covers related but phenomenologically distinct realizations. The main variants differ in whether the mediator is a sterile neutrino or a Dirac fermion, whether the portal is tree-level or loop-induced, and whether the scalar couples to left-handed neutrinos, right-handed neutrinos, or an extended Higgs sector.

Variant	Core interaction	Distinctive result
Direct left-handed-neutrino portal	$\Psi$9	relic density and collisional damping set coupling-independent lower mass bounds
Loop-induced scalar portal	$G_{\rm dark}$0 via a one-loop triangle with Majorana $G_{\rm dark}$1	loop-induced annihilation can dominate freeze-out
Seesaw-portal light scalar DM	$G_{\rm dark}$2	sub-GeV to GeV thermal scalar DM via forbidden and non-forbidden channels

In the direct scalar–left-handed-neutrino model, a scalar DM particle $G_{\rm dark}$3 couples to left-handed neutrinos through a Dirac mediator $G_{\rm dark}$4 via

$G_{\rm dark}$5

The same coupling controls both thermal annihilation into neutrinos and elastic DM–neutrino scattering. For complex scalar DM, annihilation is $G_{\rm dark}$6-wave and elastic scattering scales as $G_{\rm dark}$7; for real scalar DM, annihilation is $G_{\rm dark}$8-wave and elastic scattering scales as $G_{\rm dark}$9. Combining thermal relic abundance with collisional-damping constraints yields

$\overline{\Psi}\phi$0

for complex scalar DM and

$\overline{\Psi}\phi$1

for real scalar DM, while thermal coupling to neutrinos and Planck $\overline{\Psi}\phi$2 pushes the viable mass scale up to approximately

$\overline{\Psi}\phi$3

for both cases (Boehm et al., 2017).

A conceptually distinct variant is the loop portal. In the scalar-DM realization of “Neutrino Portal via Loops,” the real scalar $\overline{\Psi}\phi$4 annihilates through a one-loop triangle into $\overline{\Psi}\phi$5, with the mediator required to be a Majorana fermion. The effective operator is

$\overline{\Psi}\phi$6

and the thermally averaged cross section is

$\overline{\Psi}\phi$7

This realizes the nonstandard possibility that loop-induced annihilation, rather than tree-level annihilation, sets the thermal relic abundance (Chao, 2020).

Later light-DM embeddings preserve the same basic logic while altering the mediator sector. In the type-I-seesaw portal with an additional Higgs doublet $\overline{\Psi}\phi$8, the real singlet scalar $\overline{\Psi}\phi$9 is stabilized by an exact $\Psi$00, and the dominant neutrinophilic annihilation channel is

$\Psi$01

The model targets the range $\Psi$02 to $\Psi$03, uses forbidden and non-forbidden channels, and suppresses charged final states to evade CMB bounds (Borah et al., 2024). A related sterile-neutrino portal in $\Psi$04THDM introduces a scalar singlet $\Psi$05 and a Dirac fermion singlet $\Psi$06, both $\Psi$07-odd, such that for $\Psi$08 the scalar is dark matter and can annihilate through

$\Psi$09

recovering an effective scalar-DM–sterile-neutrino portal in a UV-complete setting (Liu et al., 2022).

6. Conceptual significance and unresolved boundaries of the category

The central conceptual novelty of the scalar DM–neutrino portal is the partial decoupling of relic abundance from direct detection. In ordinary singlet-scalar dark matter, the same Higgs-portal coupling controls thermal freeze-out and spin-independent scattering. In the sterile-neutrino portal realization, freeze-out can instead be dominated by

$\Psi$10

set by $\Psi$11, while direct detection remains controlled mainly by $\Psi$12. This is why the framework is especially important below about $\Psi$13 GeV, where ordinary scalar Higgs-portal dark matter is strongly constrained (Escudero et al., 2016).

At the same time, the category has clear boundaries. Some models are only indirect matches. “Neutrino Masses and Scalar Singlet Dark Matter” introduces a real singlet scalar $\Psi$14 and a neutrino-mass sector with an isospin-$\Psi$15 scalar $\Psi$16, but the connection is through the quartic $\Psi$17, not through a direct DM–neutrino portal; the dominant new annihilation final states are $\Psi$18 multiplet states rather than neutrinos (Bhattacharya et al., 2016). “Higgs portal dark matter and neutrino mass and mixing with a doubly charged scalar” likewise links scalar DM to a neutrino-mass-generating scalar sector without introducing a direct neutrino portal (Hierro et al., 2016). Such models materially modify scalar-DM phenomenology, but they are more accurately described as Higgs-portal scalar DM augmented by a neutrino-sector extension.

The unresolved theoretical issues are correspondingly model-dependent rather than universal. In the minimal sterile-neutrino portal, the exact dark symmetry is assumed rather than derived, $\Psi$19 is assumed not to obtain a vev, and detailed vacuum-stability conditions beyond that assumption are not developed. Indirect-detection projections for cascade final states depend on rescaling limits derived for direct annihilation into Standard Model particles. In broader constructions, the scalar may be a stable relic, a coannihilating partner, or a long-lived decaying state, and the portal may operate through tree-level, loop-induced, WIMP, or FIMP cosmologies. What unifies the class is narrower: a scalar dark sector whose dominant communication with the Standard Model runs through neutrino-sector mediators rather than through the Higgs alone.