⚛️ phenomenology

Warm fermionic dark matter from freeze-in at stronger coupling

This paper investigates warm fermionic dark matter produced via freeze-in in a minimal Higgs portal scenario with low reheating temperatures, finding that velocity-suppressed production necessitates higher reheating temperatures than scalar models and results in a non-thermal momentum distribution that excludes fermion masses below approximately 100–180 keV via Lyman- $\alpha$ constraints.

Original authors: Duarte Feiteira, Vinícius Oliveira

Published 2026-06-23

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Duarte Feiteira, Vinícius Oliveira

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 Big Picture: A New Kind of Dark Matter

Imagine the universe is a giant, bustling party. For a long time, scientists thought the mysterious "Dark Matter" that holds galaxies together was like a shy guest who arrived early, mingled with everyone, and then left quietly (this is the standard "WIMP" theory). But we haven't found this guest yet.

This paper proposes a different story: Dark Matter is a late-night guest who arrived after the party was mostly over. Because they arrived late, they never really got to mingle with the other guests (the Standard Model particles). They are "warm" (moving relatively fast) rather than "cold" (moving slowly), and they arrived through a mechanism called "freeze-in."

The Setup: The "Higgs Portal"

The authors imagine a secret door connecting our visible world to the dark world. This door is the Higgs boson (the particle that gives other particles mass).

The Door: The Higgs boson acts as a bridge.
The Guests: The Dark Matter is a type of fermion (a particle like an electron, but invisible).
The Catch: Usually, if the door is open wide (strong coupling), the Dark Matter would have mixed with the party guests and we would have seen it by now. But, the authors suggest the party started at a very low temperature.

The "Low Temperature" Twist

Think of the early universe as a cooling soup.

Standard Scenario: The soup is boiling hot. If you open the door, Dark Matter rushes in and mixes perfectly.
This Paper's Scenario: The soup is barely warm. Even if the door is wide open, the "heat" isn't strong enough to push the Dark Matter into the soup. The Dark Matter trickles in slowly, one by one, never reaching a crowd.

Because the temperature is low, the Dark Matter stays "out of equilibrium." This is a loophole: it allows the connection between the Higgs and Dark Matter to be strong (making it easier to detect) without the Dark Matter becoming too abundant or thermalized.

The Production Line: "Freeze-In"

How does the Dark Matter get made?
Imagine the hot soup contains heavy particles (like quarks and leptons). Occasionally, two of these heavy particles collide and, through the Higgs "door," turn into a pair of Dark Matter particles.

The Problem: This process is like trying to bake a cake in a cold oven. It's very slow.
The Velocity Suppression: The paper finds that for fermionic Dark Matter, this "baking" is even harder than for scalar (non-fermionic) Dark Matter. The particles need to be moving fast to collide effectively. If the "oven" (the universe) is too cold, the production stops.
The Result: To get enough Dark Matter to fill the universe today, the universe had to be slightly hotter (reheating temperature) than previously thought for similar models.

The "Warm" Problem: The Lyman-Alpha Constraint

This is the most critical part of the paper.

Cold Dark Matter is like a slow-moving turtle; it clumps together easily to form small structures (like dwarf galaxies).
Warm Dark Matter is like a fast-moving rabbit; it zooms around so much that it smears out small structures.

The authors calculate that because the Dark Matter was produced in this specific "low-temperature" way, it has a very strange speed distribution. It's not a smooth curve; it's a jagged, non-thermal shape.

The Constraint: Astronomers look at the "Lyman-alpha forest" (a pattern of gas clouds in the early universe) to see how much small-scale structure exists. If Dark Matter is too "warm" (too fast), it wipes out these small structures.
The Finding: The paper calculates that if this Dark Matter is lighter than about 100–180 keV (a very small mass, but heavy for a sub-atomic particle), it would be too fast and would have erased the small structures we see today. Therefore, the Dark Matter must be heavier than this limit.

The "Oscillating" Bound

One of the most interesting findings is that the limit on how light the Dark Matter can be isn't a straight line. It wiggles up and down.

The Analogy: Imagine the universe has different "production lines" for Dark Matter, each using a different heavy ingredient (Charm quarks, Tau leptons, Bottom quarks).
As the temperature of the universe changes, different ingredients become available.
- At one temperature, the "Charm" line is open, making fast Dark Matter.
- At a slightly higher temperature, the "Tau" line opens, making even faster Dark Matter.
- At an even higher temperature, the "Bottom" line opens.
Because these lines turn on and off at different temperatures, the "warmth" of the Dark Matter fluctuates. This creates a wavy, non-monotonic constraint on the mass, which is different from previous models where the limit just got steadily weaker as things got hotter.

Can We Detect It?

Yes! This is the good news.
Because the connection (coupling) between the Higgs and Dark Matter can be stronger than in other theories (thanks to the low-temperature loophole), we might actually be able to see it.

The Test: If the Higgs boson decays into invisible Dark Matter particles, we would see "missing energy" in particle colliders like the Large Hadron Collider (LHC).
The Prediction: The authors say that if this theory is right, future upgrades to the LHC (HL-LHC) or future colliders (FCC) might be able to spot these invisible decays.

Summary

The Theory: Dark Matter is a fermion that arrived late to the universe's party via a strong connection to the Higgs boson, but the party was too cold for it to mix in.
The Speed: This method produces Dark Matter that is "warm" (fast), which puts strict limits on how light it can be (must be > ~100 keV) so it doesn't destroy small galaxies.
The Quirk: The speed limit wiggles because different heavy particles start contributing to the production at different temperatures.
The Hope: Because the connection is strong, we might be able to catch this Dark Matter in the act of being created at particle colliders soon.

Technical Summary: Warm Fermionic Dark Matter from Freeze-in at Stronger Coupling

Problem Statement
The nature of Dark Matter (DM) remains an open question. While the standard Weakly Interacting Massive Particle (WIMP) paradigm relies on thermal freeze-out, the lack of experimental confirmation has motivated non-thermal alternatives, specifically the freeze-in mechanism. In standard freeze-in, DM is produced via feeble couplings, rendering the scenario experimentally inaccessible. However, in a low-reheating temperature ( $T_R$ ) scenario, DM production is Boltzmann-suppressed, allowing for sizeable couplings to the Standard Model (SM) without thermalizing the dark sector. This opens the possibility of observable signatures, such as invisible Higgs decays.

Previous work has explored this regime for scalar DM, finding that sub-MeV DM produced via low-temperature freeze-in is "warm" (possessing large comoving momentum), leading to strong constraints from Lyman- $\alpha$ forest data. This paper extends that analysis to fermionic DM within the minimal Higgs portal scenario, investigating how the distinct kinematic and dynamic properties of fermions alter the relic abundance, momentum distribution, and observational constraints compared to the scalar case.

Theoretical Setup and Methodology
The authors consider a minimal Higgs portal where a singlet Majorana fermion $\chi$ (mass $m_\chi$ ) couples to the SM Higgs doublet $H$ . The interactions are described by effective field theory operators (CP-even and CP-odd) suppressed by scales $\Lambda$ and $\Lambda_5$ . Below the Higgs mass ( $m_h \approx 125$ GeV), these interactions are integrated out to yield effective four-fermion operators mediating DM production from SM fermion annihilation ( $f\bar{f} \to \chi\bar{\chi}$ ).

The study focuses on the "stronger coupling" regime with reheating temperatures $T_R < 800$ MeV. Two thermal histories are analyzed:

Instant Reheating: The SM temperature rises abruptly to $T_R$ , and production begins immediately.
Flat Temperature Profile: The SM bath maintains a constant temperature $T_R$ during a pre-reheating epoch, followed by the standard radiation-dominated era.

The authors solve the Boltzmann equation for the DM yield $Y_\chi$ and the phase-space distribution $f_\chi(p, T)$ , accounting for both pre- and post-reheating contributions. They compute the cross-sections for $f\bar{f} \to \chi\bar{\chi}$ , noting a specific dependence on the Mandelstam variable $s$ that differs from the scalar case.

Key Contributions and Results

Velocity Suppression and Relic Abundance:
The fermionic production cross-section is strongly velocity-suppressed near the kinematic threshold ( $s \approx 4m_f^2$ ). Unlike scalar DM, where production can be efficient at lower temperatures, the fermionic scenario requires larger reheating temperatures to reproduce the observed relic abundance. Specifically, the production rate is suppressed by factors of $e^{-2m_f/T}$ when $T_R < m_f$ . Consequently, to match the relic density, the model favors $T_R$ values above the QCD phase transition scale ( $T_R \gtrsim 150$ MeV), where heavier fermions (charm, tau, bottom) dominate the production channels.
Non-Thermal Momentum Distribution:
The resulting DM momentum distribution is highly non-thermal and cannot be captured by the standard $\alpha\beta\gamma$ -parametrization used for thermal or standard freeze-in DM.
- Instant Reheating: The distribution is exponentially suppressed at low momenta ( $q \ll m_f/T_R$ ) because production is cut off at $T_R$ , preventing particles from redshifting to low comoving momenta. The spectrum peaks at $q \sim m_f/T_R \gg 1$ .
- Flat Temperature Profile: The pre-reheating epoch fills the infrared region, replacing the exponential suppression with a power-law behavior ( $f(q) \propto q^2$ ) at low momenta. This results in a "softer" spectrum compared to the instant case, allowing for lighter DM masses to satisfy structure formation bounds.
Parameter Space and Constraints:
The authors map the parameter space ( $m_\chi$ vs. $\Lambda^{-1}$ ) against three primary constraints:
1. LHC Invisible Higgs Decays: Current limits ( $BR_{inv} \lesssim 10\%$ ) and projected sensitivities (HL-LHC, FCC) constrain the effective scales $\Lambda$ and $\Lambda_5$ .
2. Lyman- $\alpha$ Forest: This is the dominant constraint for sub-MeV warm DM. Using the CLASS tool and mapping thermal WDM bounds ( $m_{WDM} > 5.3$ $m_{W D M} > 5.3$ keV) to the non-thermal distribution, the authors find:
  - For Instant Reheating, DM masses below 120–177 keV are excluded, depending on $T_R$ .
  - For Flat Temperature Profile, the bound is slightly weaker, excluding masses below 95–140 keV.
3. Non-Monotonic Lyman- $\alpha$ Bound: A distinct feature of the fermionic case is the oscillatory behavior of the Lyman- $\alpha$ bound as a function of $T_R$ . As $T_R$ increases, different production channels (muon, charm, tau, bottom) "switch on." Heavier channels inject DM with higher comoving momentum ( $q \sim m_f/T_R$ ), temporarily hardening the spectrum and tightening the mass bound before the overall softening of the spectrum at higher $T_R$ relaxes it again. This contrasts with the scalar case, where the bound monotonically weakens with $T_R$ .

Significance and Claims
The paper claims that fermionic warm DM produced via freeze-in at stronger coupling is a viable scenario that is potentially testable at colliders, unlike standard high-temperature freeze-in. The key findings are:

Collider Accessibility: The requirement for $T_R \gtrsim 0.2$ GeV (to overcome velocity suppression) pushes the model into a regime where invisible Higgs decays provide competitive constraints, potentially reachable by the HL-LHC and FCC.
Stricter Mass Bounds: The Lyman- $\alpha$ constraints are tighter for fermionic DM than for scalar DM produced via the same mechanism. This is due to the dominance of heavier production channels (e.g., charm quarks) which generate a harder momentum spectrum ( $q \sim m_c/T_R$ ) compared to the pion/muon channels dominant in the scalar case.
Distinctive Signatures: The non-monotonic behavior of the Lyman- $\alpha$ bound and the inability to describe the momentum distribution with standard parametrizations serve as unique signatures distinguishing this fermionic scenario from scalar or thermal alternatives.

The authors conclude that the effective scale $\Lambda$ required to reproduce the relic abundance lies between $3 \times 10^5$ and $10^6$ GeV, a range partially accessible to future collider experiments, thereby bringing fermionic non-thermal dark matter within experimental reach.