Sterile neutrino dark matter in conformal Majoron models

TL;DR

This work analyzes keV-scale sterile neutrino dark matter within a classically conformal U(1)' extension of the Standard Model, where three right-handed neutrinos and a Majoron-like scalar generate neutrino masses through a radiatively broken type-I seesaw. The lightest sterile state N_1 serves as a nonthermal DM candidate produced via freeze-in through feeble Z' and h_2 portals, with its phase-space distribution solved from a Boltzmann equation and confronted with Lyman-α and X-ray constraints; a 7 keV benchmark shows compatibility with a potential 3.5 keV line. The study also explores multi-component decaying DM to address the S_8 tension, identifying a narrow region where N_2 decays can suppress small-scale power while preserving the total relic abundance. A highly fine-tuned scenario is discussed for a >100 PeV DM to explain a KM3NeT event, but this requires extreme near-threshold production. Overall, the keV freeze-in mechanism in a conformal U(1)' framework yields a consistent, data-compatible DM picture with testable implications for small-scale structure and X-ray signals, while offering intriguing but less favored paths to ultra-heavy DM interpretations.

Abstract

We study sterile neutrino dark matter (DM) in a classically conformal U(1)' extension of the Standard Model with three right-handed neutrinos and a Majoron-like singlet scalar that generate the observed pattern of active neutrino masses and mixing via the type-I seesaw mechanism. Working in the regime of strongly suppressed active-sterile mixing, we show that the observed DM abundance can be produced through freeze-in from feeble interactions mediated by the heavy Z' and the conformal scalar. We solve the Boltzmann equation for the nonthermal phase-space distribution and confront the scenario with Lyman-$α$ data by computing the matter power spectrum. For keV-scale sterile neutrinos we identify the viable parameter space consistent with structure-formation and X-ray bounds, including regions compatible with a tentative 3.5 keV line. If a second sterile state is long-lived, late decays can realize a two-component setup that alleviates the $S_8$ tension. In a highly fine-tuned variant of the model, the 220 PeV KM3NeT event can also be explained by invoking the decay of a superheavy sterile neutrino.

Figures (7)

• Figure 1: Production rate of $N_1$ divided by the Hubble expansion rate, $\mathcal{R}(\text{SM\;SM} \to N_I N_I)/H$, as a function of temperature $T$ for two benchmark scenarios. The left panel corresponds to $m_{N_1}=7\,\mathrm{keV}$, where annihilation into fermionic final states is not very suppressed due to a relatively large value of the scalar mixing parameter $\alpha$. The right panel corresponds to $m_{N_1}=100\,\mathrm{keV}$, for which the Higgs channel dominates, and the other production channels are strongly suppressed because $\alpha$ is tiny.
• Figure 2: $N_1$ relic abundance $\Omega_{N_1} h^2$ as a function of the DM mass $M_{N_1}$ for different values of the scalar mixing parameter, $|\sin\alpha|$. All points satisfy the X-ray constraints. The observed relic abundance $\Omega_{N_1} h^2 = 0.12$ is shown as a reference by gray line. Each point corresponds to the numerical solution of the Boltzmann equation (Eq. \ref{['eq:Boltzmann_Y']}) accounting for all relevant dark-to-visible $2\!\to\!2$ annihilation channels.
• Figure 3: Fraction of the DM abundance contributed by $N_1$ as a function of $M_{N_1}$. The curves show the limits derived from Lyman-$\alpha$ forest constraints, using the equivalent thermal WDM masses $m_{\rm WDM} = 5.3\,\mathrm{keV}$ (red) and $m_{\rm WDM} = 1.9\,\mathrm{keV}$ (green). The region above each curve is excluded by Lyman-$\alpha$ observations.
• Figure 4: $N_1$ relic abundance for $M_{N_1}=7~\mathrm{keV}$. The color scale shows the corresponding values of the scalar mixing $|\sin\alpha|$. The gray line indicates the inferred DM abundance, $\Omega_{\rm DM}h^2\simeq 0.12$. Each point is obtained by solving the Boltzmann equation(Eq. \ref{['eq:Boltzmann_Y']}) with the thermally averaged annihilation rate including all relevant $2\to2$ production channels.
• Figure 5: $\sin^2 2\theta_{\rm eff}$ as a function of $M_{h_2}$ for parameter points satisfying $\Omega_{N_1}h^2\le 0.12$. The color scale indicates $\Gamma_{N_1}$, and the black stars mark points with $\Omega_{N_1}h^2=0.12\pm0.001$. The region between dashed lines corresponds to the range $\sin^2 2\theta_{\rm eff}\simeq (0.2{-}2)\times10^{-10}$ needed to produce a $3.5$ keV X-ray line via $N_1\to\nu\gamma$.