Neutrino Portal Dark Matter Models

• Neutrino portal dark matter is a framework where sterile neutrinos generate neutrino masses via the seesaw mechanism and mediate interactions between dark matter and the Standard Model.
• Key processes include dark matter annihilation via t-channel scalar exchange and subsequent sterile neutrino decay, producing observable gamma-ray and cosmic-ray signals.
• Model extensions with large Yukawa and Higgs-portal couplings offer complementary search strategies while balancing relic abundance constraints and multi-messenger indirect detection limits.

Neutrino portal dark matter refers to a broad class of theories in which the Standard Model (SM) is extended by new neutral fermions (right-handed or sterile neutrinos) that simultaneously participate in the origin of light neutrino masses and act as mediators between a stable dark-matter (DM) candidate and the SM. The defining property of these constructions is that the dominant connecting interactions involve SM neutrinos (the "neutrino portal"), leading to experimentally distinctive features and unique phenomenological constraints.

1. Theoretical Framework and Model Structure

Neutrino portal dark matter models introduce at minimum: (i) a sterile Majorana neutrino $N$, (ii) a Dirac or Majorana dark fermion $\chi$ (the dark matter candidate), and (iii) a real singlet scalar $\phi$ as a mediator. Stability of $\chi$ is enforced by a discrete symmetry, typically $\mathbb{Z}_2$ with $\chi,\phi\to-\chi,-\phi$. The Lagrangian is

$${\cal L} \supset -\frac{1}{2} M_N N^c N - m_\chi \bar\chi \chi - \frac{1}{2} m_\phi^2 \phi^2 - \left[ y_\nu L \tilde{H} N + g_\chi \bar{N} P_L \chi \phi + \text{h.c.}\right]$$

where $L$ is the SM lepton doublet, $\tilde{H} = i \sigma_2 H^*$, $y_\nu$ is the neutrino Yukawa coupling, $M_N$ is the Majorana mass of the sterile neutrino, and $g_\chi$ is the dark-sector Yukawa coupling.

After electroweak symmetry breaking, active neutrino masses are generated via the Type I seesaw: $m_\nu \simeq \frac{y_\nu^2 v^2}{M_N}$ Requiring $m_\nu \sim 0.05$ eV (the atmospheric mass scale) fixes $y_\nu \simeq 10^{-6} \sqrt{M_N/100\,\mathrm{GeV}}$. The active–sterile mixing is $\theta \simeq y_\nu v/M_N$, giving $\theta \lesssim 10^{-6}$ for $M_N \sim 100$ GeV (Batell et al., 2017).

2. Dark Matter Annihilation and Relic Density Mechanisms

When $m_\chi > M_N$, the dominant DM annihilation in the early universe is $\chi\chi \to N N$ mediated by $t$-channel $\phi$ exchange. The $s$-wave annihilation cross section at low velocity (assuming $m_\phi \gg m_\chi, M_N$) is

$$\langle \sigma v \rangle_{\chi\chi\to NN} \simeq \frac{g_\chi^4 m_\chi^2}{16\pi m_\phi^4}$$

The correct relic abundance ($$\langle \sigma v \rangle \simeq 2.2 \times 10^{-26}\,\mathrm{cm}^3/\mathrm{s}$$) requires $g_\chi \sim 0.1$–$1$ for $m_\chi \sim 10$–$100$ GeV. Partial-wave unitarity ($g_\chi \lesssim \sqrt{4\pi}$) and avoidance of dark matter overclosure require $m_\chi \lesssim 20$ TeV (Batell et al., 2017).

3. Indirect Detection Signatures via Sterile-Neutrino Decay

The sterile neutrino $N$ produced from $\chi\chi \to N N$ promptly decays through its small active–sterile mixing ($\theta$) into SM states: $$N \to \ell W^*,\quad N \to \nu Z^*,\quad N \to \nu h^*$$ with decay width (for $M_N > m_W$): $$\Gamma(N \to \ell W) = \theta^2 \frac{M_N^3}{16\pi v^2} (1-m_W^2/M_N^2)^2 (1+2 m_W^2/M_N^2)$$ These decays inject gamma rays, antiprotons, electrons, and neutrinos with spectra computed via MadGraph5→Pythia8 simulation and Lorentz boosting (Batell et al., 2017). The gamma-ray and antiproton ($\bar{p}$) spectra are peaked at $E\sim \mathcal{O}(10\,\mathrm{GeV})$ for $m_\chi\sim 200$ GeV; the $e^\pm$ spectrum features a hard component from $N \to W \ell$. These multi-particle final states yield observable astronomical signatures from dark matter annihilations.

4. Experimental Constraints and Future Sensitivity

The combined indirect-detection and cosmological constraints are summarized as follows (Batell et al., 2017):

Probe	Excluded $m_\chi$ Range	Comments
Planck (CMB)	$m_\chi \lesssim 20$ GeV	Independent of $M_N$, $f_\mathrm{eff}$ taken into account
Fermi–LAT GC	$m_\chi \lesssim 10$ GeV	Assuming NFW profile
Fermi dSphs	$m_\chi \lesssim 50$–$80$ GeV	$M_N$-dependent, uses stacked $J$ factors
AMS-02 $\bar{p}$	$m_\chi \sim 20$–$80$ GeV	Propagation/halo $O(\mathrm{few})$ uncertainty

Thermal $\chi\chi\to NN$ is ruled out for $m_\chi\lesssim 50$ GeV, with strongest limits from Fermi dSphs and AMS-02 antiprotons. Future Fermi observations (with 15 yr/60 dSphs) can reach up to $m_\chi\sim 100$–$200$ GeV; CTA (100 hr GC) can cover $m_\chi\sim 200$ GeV–1 TeV, although systematics are non-negligible.

5. Interpretation of Gamma-Ray Excess and Parameter Space

The Fermi Galactic Center (GC) excess, a $1$–$3$ GeV residual, can be interpreted within the neutrino portal model: the best-fit is at $m_\chi\approx 41$ GeV, $M_N\approx 23$ GeV, $\langle \sigma v \rangle\approx 3.1\times10^{-26}$ cm$^3$/s. Allowed $1\sigma$–$3\sigma$ regions span $m_\chi\sim 30$–$60$ GeV, $M_N\sim 10$–$40$ GeV. This region, however, is in mild tension with dSph and AMS-02 $\bar{p}$ limits, subject to astrophysical uncertainties in the $J$-factor and cosmic-ray propagation (Batell et al., 2017).

6. Model Extensions: Large Yukawas and Higgs-Portal Couplings

• Large neutrino Yukawas: In inverse-seesaw or extended seesaw realizations, $y_\nu$ can reach $10^{-2}$–$10^{-1}$ while retaining phenomenologically realistic $m_\nu$. The active–sterile mixing $\theta$ can then be $\mathcal{O}(10^{-3})$–$\mathcal{O}(10^{-2})$, permitting direct detection via 1-loop Higgs/Z exchange, accelerator production of $N$, and new $\chi\chi\to\nu\nu$ annihilation via $s$-channel Z/h processes. This restores complementarity with direct and collider searches.
• Higgs portal: The scalar $\phi$ can couple to the Higgs via $\lambda_{\phi H} \phi^2 |H|^2$. For $\lambda_{\phi H}\sim10^{-2}$, this induces spin-independent $\chi$–nucleon scattering and invisible Higgs decay $h\to\phi\phi\to NN\chi\chi$, possibly yielding displaced vertex signatures when $N$ is light. Even if $\lambda_{\phi H}=0$ at tree level, radiative corrections generate $$\lambda_{\phi H}\sim g_\chi^2 y_\nu^2/(16\pi^2)\sim 10^{-17}$$–$10^{-14}$ for minimal $y_\nu$; UV completions can enhance/suppress this coupling significantly.

7. Synthesis and Phenomenological Outlook

Neutrino portal dark matter provides a highly economical, UV-completable connection between the mechanisms of neutrino mass generation and dark matter interactions. Minimal Type I seesaw constructions predict very weak active–sterile mixing ($\theta\sim 10^{-6}$), precluding present direct or collider detection, but nonetheless produce robust multi-messenger indirect-detection signals via $\chi\chi\to NN$ annihilations with subsequent $N$ decay (Batell et al., 2017).

Current data exclude thermal candidates with $m_\chi\lesssim 50$ GeV; future gamma-ray and cosmic-ray experiments (Fermi, CTA) will probe up to the TeV scale. Interpreting the Fermi GC excess is possible but challenged by tension with indirect constraints. Extensions with larger $y_\nu$ and/or substantial Higgs-portal couplings open up complementary search strategies, including direct detection and collider production or decay signatures.

The broader implication is that models of this type generically predict characteristic indirect-detection features (multi-channel spectra, possible monochromatic neutrino lines in alternative realizations (Macias et al., 2015)), allow consistent cosmological histories, and motivate a confluence of astrophysical and laboratory searches for both sterile neutrinos and dark matter.

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References: (Batell et al., 2017, Macias et al., 2015)