Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Two Puzzles, One Solution: Neutrino Mass and Secluded Dark Matter

Mattia Di Mauro

Abstract

We present a minimal secluded dark-matter (DM) framework based on an extra $U(1)_X$ gauge symmetry. The model contains a Dirac DM particle $χ$, three heavy neutrinos $N_I$ with masses $M_{N,I}$, and a singlet scalar $R$ that mixes with the Standard Model Higgs doublet $Φ$ by an angle $α$. A symmetry forbids the $Φ$-$R$ portal at tree level; the leading portal then arises at one loop from the same Yukawa structures that generate active neutrino masses $m_{ν,I}$, implying $\tan(2α) \propto \sum_I m_{ν,I} M^2_{N,I}/(v_h m_H^2)$, where $v_h$ and $m_H$ are the SM Higgs VEV and mass. For heavy-neutrino masses in the multi-TeV range, this yields a naturally tiny mixing, $\tan(2α)\sim 5\times 10^{-11}\left(M_N/10~\mathrm{TeV}\right)^2$, which strongly suppresses DM signals in direct, indirect, and collider searches. For PeV-scale heavy neutrinos the DM-nucleon cross section can instead enter the reach of direct-detection experiments. The visible and dark sectors thermalize at temperatures of order a few times the mass of the lightest heavy neutrino, then subsequently decouple, and typically evolve with a slightly hotter dark bath. In the secluded regime, with $\tan(2α)\ll 1$ and $m_χ>m_{H_p}$, the relic density is set by $p$-wave annihilation $χ\barχ\to H_p H_p$ (with $H_p$ the Higgs-like particle of the dark sector), and the dark-sector Yukawa couplings required to reproduce the observed abundance are $\sim(0.1\text{-}1)$, as in the standard WIMP case. For heavy-neutrino masses $\gtrsim 10~\mathrm{TeV}$, the mediator decays before nucleosynthesis without spoiling BBN observables, while the tiny portal suppresses present-day signals below current and near-future sensitivities. This links two long-standing puzzles, the absence of DM signals and the smallness of neutrino masses, within a predictive thermal framework.

Two Puzzles, One Solution: Neutrino Mass and Secluded Dark Matter

Abstract

We present a minimal secluded dark-matter (DM) framework based on an extra gauge symmetry. The model contains a Dirac DM particle , three heavy neutrinos with masses , and a singlet scalar that mixes with the Standard Model Higgs doublet by an angle . A symmetry forbids the - portal at tree level; the leading portal then arises at one loop from the same Yukawa structures that generate active neutrino masses , implying , where and are the SM Higgs VEV and mass. For heavy-neutrino masses in the multi-TeV range, this yields a naturally tiny mixing, , which strongly suppresses DM signals in direct, indirect, and collider searches. For PeV-scale heavy neutrinos the DM-nucleon cross section can instead enter the reach of direct-detection experiments. The visible and dark sectors thermalize at temperatures of order a few times the mass of the lightest heavy neutrino, then subsequently decouple, and typically evolve with a slightly hotter dark bath. In the secluded regime, with and , the relic density is set by -wave annihilation (with the Higgs-like particle of the dark sector), and the dark-sector Yukawa couplings required to reproduce the observed abundance are , as in the standard WIMP case. For heavy-neutrino masses , the mediator decays before nucleosynthesis without spoiling BBN observables, while the tiny portal suppresses present-day signals below current and near-future sensitivities. This links two long-standing puzzles, the absence of DM signals and the smallness of neutrino masses, within a predictive thermal framework.

Paper Structure

This paper contains 39 sections, 174 equations, 7 figures, 1 table.

Table of Contents

  1. General Details of the Model
  2. Lagrangian and Particle Content
  3. $R$–$\Phi$ Mixing
  4. Interaction Terms in the Mass Basis
  5. (i) SM fermions.
  6. (ii) Dark matter.
  7. (iii) Heavy (right-handed) neutrinos.
  8. (iv) Light–heavy neutrino Yukawas (Dirac sector).
  9. (v) Scalar potential (for reference).
  10. Useful Decay Rates and Annihilation Cross Sections
  11. Decay rate of $H_p$
  12. Tree-level χχ→HpHp and the p-wave coefficient
  13. Light and heavy neutrino masses, interactions, and the seesaw mechanism
  14. Light and heavy neutrino Yukawa interactions
  15. Type-I seesaw mechanism
  16. ...and 24 more sections

Figures (7)

  • Figure 1: Box Feynman diagram describing the one-loop generation of the mixed quartic $(R^\dagger R)(\Phi^\dagger \Phi)$.
  • Figure 2: Values of the heavy-neutrino mass $M_N$ and dark scalar mass $m_{H_p}$ for which the decay of $H_p$ occurs before BBN. We fix $y_N=1$ and $m_\nu=0.05~\text{eV}$.
  • Figure 3: Per-particle rates vs. expansion rate for the neutrino-portal processes as a function of $\xi=M_N/T$: decay/inverse decay $N \leftrightarrow LH$ (red solid), $\Delta L=1$ scatterings (blue dashed), $N R \leftrightarrow L_\alpha H$ (black dotted), and $\Delta L=2$ scatterings (orange dot-dashed). We fix $M_{N}=20~\mathrm{TeV}$, $m_\nu=0.05~\mathrm{eV}$, and $y_N=1$. The green band shows $H(T)$; the cyan band reflects the uncertainty on the coefficient $c_1$ in the $\Delta L=1$ rate. The vertical yellow band marks the transition to the non-relativistic regime for $N$ where its abundance becomes Boltzmann suppressed.
  • Figure 4: Representative neutrino-portal processes maintaining thermal contact between the SM, the heavy neutrinos $N_I$, and the dark sector at $T\gg M_I$.
  • Figure 5: One-loop generation of the mixed quartic $(\Phi^\dagger \Phi)(R^\dagger R)$. Left: box diagram with two $Y_N$ and two $Y_\nu$ insertions and internal $N,L$ lines. Right: effective contact interaction with coupling $\kappa_{\rm loop}$ obtained by integrating out the heavy neutrinos for $p^2 \ll M_N^2$.
  • ...and 2 more figures