⚛️ phenomenology

FIMP dark matter in the scotogenic model at low-reheating temperatures

This paper investigates the phenomenology of singlet fermion dark matter produced via the freeze-in mechanism in the scotogenic model under low-reheating temperature scenarios, demonstrating that such conditions significantly reshape the viable parameter space while remaining consistent with lepton flavor violation and direct detection constraints.

Original authors: Robinson Longas, Andrés Rivera, David Suarez

Published 2026-09-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Robinson Longas, Andrés Rivera, David Suarez

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with invisible matter that holds galaxies together, yet we have never seen a single particle of it. This "dark matter" makes up most of the material in the cosmos, but it refuses to interact with light or ordinary matter in any way we can easily detect. For decades, scientists have hunted for it by looking for heavy particles that might bump into atomic nuclei, but their searches have come up empty. This silence has forced researchers to reconsider how these particles might have formed in the first place. Instead of being born in a hot, crowded early universe where they constantly collided and settled into a balance, perhaps they were created slowly and quietly, like raindrops forming on a cold windowpane, never reaching a state of thermal equilibrium. This idea, known as "freeze-in," suggests that dark matter particles interact so weakly with the rest of the universe that they were never truly part of the hot soup of the early cosmos.

At the same time, scientists are trying to solve a different puzzle: why neutrinos, the ghostly particles that stream through us by the trillions, have mass at all. The standard model of physics, which explains how the known universe works, cannot account for this. One popular theory, called the scotogenic model, proposes that neutrinos get their mass through a specific loop of interactions involving new, unseen particles. In this framework, the same new particles that give neutrinos their mass also happen to be the perfect candidate for dark matter. A team of researchers has now explored a specific version of this theory where the universe reheated to a surprisingly low temperature after its initial expansion. They found that this cooler history changes everything about how we might find dark matter, turning a nearly invisible candidate into something that future experiments could actually detect.

The researchers focused on a specific type of dark matter particle, a heavy fermion that is the lightest of a new family of particles. In the standard version of this theory, where the early universe was extremely hot, the interactions required to create the right amount of dark matter would be so incredibly weak that detecting them would be impossible. The particles would be too shy to ever leave a trace in our detectors. However, the team investigated what happens if the universe cooled down much faster and reached a lower maximum temperature than previously assumed. In this "low-reheating" scenario, the production of dark matter is suppressed because the universe never gets hot enough to create them easily. To compensate for this shortage and still end up with the amount of dark matter we observe today, the particles must interact with ordinary matter much more strongly than in the hot universe scenario.

This shift in temperature fundamentally alters the landscape of the theory. The researchers calculated that if the universe's maximum temperature was between 5 and 50 billion degrees, the dark matter particles would need to have a much stronger connection to the visible world. This stronger connection means they are no longer hiding in the shadows. Instead, they could potentially scatter off electrons or atomic nuclei in a way that current and upcoming detectors are sensitive enough to see. The team mapped out the specific conditions under which this works, looking at the mass of the dark matter particle and the mass of the other new particles in the theory. They found that for dark matter particles with masses between 60 and 700 billion electron volts, and for specific relationships between the masses of the new particles, the model becomes highly testable.

The study also had to ensure that this new, more detectable version of the theory did not break other rules of physics. The researchers checked that the model remained consistent with the known behavior of neutrinos and did not produce signals that have already been ruled out by experiments looking for rare decays of muons. They found that by carefully adjusting the properties of the new particles, the model could satisfy all these strict constraints while still allowing for the stronger interactions needed for detection. In particular, they showed that the mass difference between two specific types of new particles plays a critical role. If this difference is kept very small, the model allows for the larger interactions required by the low-temperature scenario without violating the limits set by other experiments.

The results suggest that the next generation of dark matter detectors, which are designed to be incredibly sensitive to tiny energy deposits, could finally catch a glimpse of these particles. The researchers highlighted that experiments like LUX-ZEPLIN, which is already taking data, and future projects like DARWIN, which aims to be even more sensitive, could probe a significant portion of this newly viable space. If the universe did indeed reheat to these lower temperatures, the dark matter we are looking for might not be the ghostly, undetectable entity we have been chasing for decades, but a particle that is just within reach of our best instruments. This work does not prove that the universe was cool or that this specific model is correct, but it demonstrates that if these conditions are met, the long-sought dark matter could be right in front of us, waiting to be found by the right kind of experiment.

Technical Summary: FIMP Dark Matter in the Scotogenic Model at Low-Reheating Temperatures

Problem Statement
The Standard Model (SM) fails to explain neutrino masses, the baryon asymmetry of the universe, and the nature of dark matter (DM). While Weakly Interacting Massive Particles (WIMPs) have been the dominant DM paradigm, the lack of conclusive signals has motivated the exploration of Feebly Interacting Massive Particles (FIMPs) produced via the freeze-in mechanism. The scotogenic model offers a unified framework generating neutrino masses radiatively while providing a stable DM candidate. However, standard FIMP studies within this model typically assume high-reheating temperatures ( $T_{rh} \gg m_{DM}$ ), resulting in extremely small Yukawa couplings ( $y \sim 10^{-13}$ ) that render the model experimentally inaccessible. This work investigates the phenomenology of singlet fermion DM ( $N_1$ ) in the scotogenic model under the assumption of instantaneous, low-reheating temperatures ( $T_{rh} \lesssim m_{DM}$ ), exploring whether this scenario can enhance testability while satisfying cosmological and experimental constraints.

Methodology
The authors analyze the minimal scotogenic model, which extends the SM with an inert scalar doublet ( $\eta$ ) and three right-handed Majorana neutrinos ( $N_i$ ) under a discrete $Z_2$ symmetry. The lightest $Z_2$ -odd fermion, $N_1$ , is identified as the DM candidate.

Theoretical Framework: The study utilizes the Lagrangian defined by Yukawa couplings ( $y_{\alpha i}$ ) and the scalar potential parameters ( $\lambda_{1-5}$ ). Neutrino masses are generated at the one-loop level, proportional to the parameter $\lambda_5$ .
Constraints: The parameter space is constrained by:
- Theoretical: Vacuum stability, perturbativity, perturbative unitarity, and the requirement that the inert vacuum is the global minimum.
- Phenomenological: Charged Lepton Flavor Violation (CLFV), specifically the branching ratio $B(\mu \to e\gamma) < 1.5 \times 10^{-13}$ ; Big Bang Nucleosynthesis (BBN) limits on the lifetimes of unstable species; and collider bounds on scalar masses (LEP and LHC).
- Cosmological: The observed DM relic density ( $\Omega_{DM}h^2 \approx 0.12$ ) and oblique parameters ( $S, T, U$ ).
Production Mechanisms:
- Freeze-in: The DM yield is calculated by integrating the Boltzmann equation from the reheating temperature $T_{rh}$ down to the present. The production is dominated by the two-body decays of heavy scalars ( $H^0, A^0, H^\pm$ ) into $N_1$ and SM leptons. The authors derive analytical approximations for both high- $T_{rh}$ and low- $T_{rh}$ regimes.
- SuperWIMP: A secondary mechanism where a heavier $Z_2$ -odd particle (specifically $N_2$ ) freezes out and subsequently decays into $N_1$ . This requires specific bounds on the product of Yukawa couplings $y_1 y_2$ to ensure decay occurs before BBN but after freeze-out.
Numerical Analysis: The authors perform a scan over the DM mass ( $1 \text{ GeV} \le m_N \le 10^4 \text{ GeV}$ ) and reheating temperatures, fixing the scalar mass hierarchy via the ratio $n = m_{A^0}/m_N$ and a small splitting $\delta$ between CP-even and CP-odd scalars. They utilize tools like SARAH, SPheno, and micrOMEGAs for the superWIMP thermal calculations.

Key Contributions and Results
The primary finding is that low-reheating scenarios significantly alter the viable parameter space for FIMP DM in the scotogenic model:

Enhanced Yukawa Couplings: In the low- $T_{rh}$ regime ( $T_{rh} < m_{\chi}$ ), the production of DM is Boltzmann-suppressed. To compensate and reproduce the observed relic density, the required Yukawa couplings ( $y_1$ ) must be orders of magnitude larger than in the standard high- $T_{rh}$ scenario. The paper demonstrates that $y_1$ can reach values of $\mathcal{O}(0.1)$ while maintaining the freeze-in condition (preventing thermalization).
Direct Detection Prospects: The enhanced couplings directly impact the scattering cross-sections.
- Nuclear Recoils: The spin-independent (SI) scattering cross-section, typically loop-suppressed, is significantly increased. The authors show that for mass hierarchies $n=3$ and $n=4$ , and reheating temperatures $5 \text{ GeV} \lesssim T_{rh} \lesssim 50 \text{ GeV}$ , the parameter space becomes accessible to current (LUX-ZEPLIN) and future (DARWIN) direct detection experiments.
- Electron Scattering: For larger hierarchies ( $n=4$ ), DM-electron scattering mediated by charged scalars also provides complementary sensitivity.
Role of Mass Hierarchy: The ratio $n = m_{A^0}/m_N$ is critical. For mild hierarchies ( $n=2.1$ ), couplings remain too small for detection. As $n$ increases, the Boltzmann suppression of the heavier scalars reduces the production rate, necessitating larger $y_1$ to match the relic density, thereby opening the window for experimental tests.
CLFV and BBN Compatibility: The study confirms that the enlarged parameter space remains consistent with CLFV bounds ( $\mu \to e\gamma$ ) provided the other Yukawa couplings (specifically $y_2$ in the superWIMP context) are appropriately tuned. The superWIMP mechanism is shown to be viable for compressed spectra ( $n \approx 1.1$ ) to ensure cold DM, with $y_1 y_2$ bounded between $\sim 10^{-12}$ (BBN) and $\sim 10^{-6}$ (freeze-out/decay timing).

Significance
The paper claims that low-reheating temperatures reconcile the freeze-in paradigm with experimentally testable signatures within the scotogenic model. By shifting the viable region to larger Yukawa couplings, the model moves from being "untestable" to being within the reach of next-generation direct detection experiments. The work highlights that the interplay between the reheating temperature and the dark sector mass hierarchy is a decisive factor in the phenomenological viability of FIMP dark matter, offering a predictive region of the scotogenic parameter space that can be extensively explored by upcoming experiments like DARWIN and Oscura.

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