⚛️ phenomenology

Freeze-in and Freeze-out in a Right-Handed Neutrino Extended MSSM with a Seesaw Mechanism

This paper investigates a scenario where light Higgsinos and right-handed sneutrinos contribute to dark matter via freeze-out and freeze-in mechanisms, respectively, but ultimately rules it out because the resulting over-abundant sterile neutrinos have lifetimes exceeding the age of the universe.

Original authors: Tushar Gupta, Matti Heikinheimo, Katri Huitu, Harri Waltari

Published 2026-02-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tushar Gupta, Matti Heikinheimo, Katri Huitu, Harri Waltari

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: Two Ways to Fill the Dark Matter Tank

Imagine the universe is a giant bathtub, and Dark Matter is the water we need to fill it up to a specific level to make the universe work correctly. Scientists have been trying to figure out how this water got there.

For decades, the leading theory was "Freeze-out."

The Analogy: Imagine a crowded party (the early universe). Everyone is bumping into each other, dancing, and interacting. Eventually, the party gets so cold that people stop dancing and leave the room. The people who stay behind are the "Dark Matter." They were once part of the crowd but got "frozen out" when things cooled down.
The Problem: In the world of Supersymmetry (a popular theory about hidden particles), the most likely candidate for this "party-goer" is a particle called a Higgsino. However, recent experiments (like the LZ experiment) have looked for these Higgsinos and found nothing. It's like looking for a specific guest at a party and realizing they aren't there. If they were there, they would have been easy to spot.

So, the authors of this paper asked: What if we try a different way to fill the bathtub?

The New Idea: The "Freeze-in" Leak

Instead of a crowded party where people leave, imagine a slow leak in the bathtub.

The Analogy: The "Freeze-in" mechanism suggests that Dark Matter particles are so shy and weakly connected to the rest of the universe that they never join the party. Instead, they slowly drip in from a faucet over billions of years. Because they interact so weakly, they never reach a "thermal equilibrium" (they never get warm enough to mix with the hot water).
The Candidate: The authors looked at a specific type of particle called a Right-Handed Sneutrino. Think of this as a "ghostly cousin" of the neutrino (a tiny, ghostly particle we already know exists). These ghosts are so shy they barely touch anything else, making them perfect candidates for a slow drip (freeze-in).

The Setup: The "Seesaw" and the "Naturalness" Problem

The paper mixes two big ideas:

Naturalness: Physicists hate "fine-tuning." It's like balancing a pencil on its tip; it's possible, but it feels unnatural. They prefer theories where things just "fall into place" naturally. This suggests that the Higgsino should be light (around the size of a proton, but heavier).
The Seesaw Mechanism: This is a theory explaining why neutrinos are so light. Imagine a seesaw. If one side (the heavy "Right-Handed Neutrino") goes down, the other side (the light "Left-Handed Neutrino") goes up. The heavier the right side, the lighter the left side.

The authors tried to combine these: A light Higgsino (for naturalness) that provides some Dark Matter via "Freeze-out," plus a ghostly Sneutrino that provides the rest via "Freeze-in."

The Twist: The "Zombie" Problem

Here is where the plot thickens. The authors ran the numbers to see if this "Two-Source" plan (Freeze-out + Freeze-in) works.

They found a major problem with the Right-Handed Neutrinos (the heavy side of the seesaw).

The Scenario: To get the right amount of Dark Matter from the "Freeze-in" leak, the Right-Handed Neutrinos have to be incredibly light and incredibly shy.
The Consequence: Because they are so light and shy, they become cosmologically stable. In other words, they don't die. They live forever.
The Zombie Metaphor: Imagine these neutrinos are zombies. They are produced in the early universe, but because they are so shy, they don't interact with anything. They just float around, accumulating over billions of years.
The Disaster: The paper calculates that if you have enough of these "zombie" neutrinos to make the Sneutrino freeze-in work, you end up with too many zombies. They would contribute so much mass to the universe that the total Dark Matter would be way too high. It's like trying to fill a bathtub with a slow drip, but you accidentally opened the main firehose at the same time. The tub overflows.

The Verdict: Ruling Out the Plan

The authors tested this idea across three different versions of the "Seesaw" theory (Type-I, Linear, and Inverse).

The Result: In all three cases, the "Zombie Neutrinos" produced too much Dark Matter. The universe would be too heavy, and the math breaks.
The Exception: The only version that might work is the Dirac Neutrino model. In this specific model, the "Zombies" don't exist as separate particles, so there is no overflow. However, this is a very specific and restrictive case.

The Conclusion in Plain English

The authors set out to see if we could save the "Natural" light Higgsino theory by adding a "Freeze-in" Sneutrino to the mix.

They discovered that while the math for the Sneutrino looks good, it forces the existence of "Ghost Neutrinos" that live forever. These ghosts pile up and create too much Dark Matter, violating the rules of our universe.

The Takeaway:
You can't have your cake and eat it too. You can't have a light, natural Higgsino and a freeze-in Sneutrino working together in these specific models, because the "byproduct" (the sterile neutrinos) ruins the whole recipe by overfilling the Dark Matter tank. The universe simply doesn't allow for this specific combination of particles.

1. Problem Statement

The paper addresses the tension between Naturalness in the Minimal Supersymmetric Standard Model (MSSM) and current experimental constraints on Dark Matter (DM).

Naturalness: The discovery of a 125 GeV Higgs boson and the lack of superpartners at the LHC suggest that colored superpartners are heavy (multi-TeV). However, naturalness arguments favor a light Higgsino mass ( $|\mu| \sim$ electroweak scale) to avoid fine-tuning in the electroweak symmetry-breaking condition.
The Conflict: A light Higgsino acts as a Weakly Interacting Massive Particle (WIMP). However, direct detection experiments (LZ, PandaX, XENONnT) have severely constrained the spin-independent scattering cross-section of WIMPs. Pure Higgsino DM is only viable if the gaugino masses ( $M_1, M_2$ ) are extremely heavy ( $\sim 15$ TeV) to suppress Z-boson couplings, which reintroduces fine-tuning.
Proposed Alternative: The authors investigate a hybrid scenario where the MSSM is extended with right-handed neutrino superfields (Seesaw mechanism). This introduces Right-Handed Sneutrinos ( $\tilde{\nu}_R$ ) as a second DM candidate produced via the Freeze-in mechanism (Feebly Interacting Massive Particles, or FIMPs). The goal is to see if a combination of Freeze-out (Higgsinos) and Freeze-in (Sneutrinos) can saturate the observed relic density while evading direct detection limits.

2. Methodology

The authors perform a comprehensive phenomenological study of MSSM extended with various Seesaw mechanisms (Type-I, Linear, and Inverse).

Model Framework:
- MSSM Extension: Adds right-handed neutrino superfields ( $N^c$ ) and, for Linear/Inverse seesaws, sterile neutrino superfields ( $S$ ).
- Seesaw Scales: They focus on a low seesaw scale ( $M_N \ll M_W$ ) to generate small neutrino masses via tiny Yukawa couplings ( $y_\nu \sim 10^{-10} - 10^{-13}$ ), ensuring the $\tilde{\nu}_R$ remains out of thermal equilibrium.
- Mass Spectrum: Assumes light Higgsinos ( $\mu \sim 330$ GeV) and heavy gauginos to satisfy naturalness and direct detection bounds.
Numerical Tools:
- Model Generation: SARAH v4.14.5.
- Spectrum Calculation: SPheno v4.0.5.
- Relic Density: micrOMEGAs v5.3.41.
- Procedure: They manually implemented freeze-in processes (approx. 700 dominant $2 \to 2$ scattering processes per generation) involving Higgs/Higgsino mediators, as the standard module had limitations. They scanned parameter space (Yukawa couplings, mass matrices) to match the Planck relic density ( $\Omega h^2 \approx 0.12$ ).
Benchmark Points (BP): Two specific points (BP1, BP2) were analyzed where the Lightest Supersymmetric Particle (LSP) is a sneutrino, with Higgsinos acting as the Next-to-Lightest Supersymmetric Particle (NLSP).

3. Key Contributions & Analysis

A. The Hybrid Freeze-out/Freeze-in Scenario

The study confirms that a light Higgsino can coexist with a freeze-in sneutrino.

Mechanism: Higgsinos annihilate via the W-boson portal (Freeze-out), while $\tilde{\nu}_R$ are produced via decays and scatterings of thermal bath particles mediated by Higgs/Higgsinos (Freeze-in).
Decoupling: Due to the feeble couplings ( $y_\nu$ ), the two sectors are effectively decoupled. The heavier species (NLSP) decays into the lighter one (LSP) with a delay ( $\sim 0.12$ seconds), which is safe for Big Bang Nucleosynthesis (BBN) as the decay products thermalize before BBN.

B. Direct Detection Constraints

Higgsino DM: The study reiterates that light Higgsinos are excluded as the sole DM candidate by LZ/PandaX constraints unless gauginos are $\sim 15$ TeV (unnatural).
Sneutrino DM: If the sneutrino is the LSP, the spin-independent nucleon cross-section is negligible ( $\sim 10^{-90}$ cm $^2$ ), evading all direct detection limits.

C. The Sterile Neutrino Constraint (The Critical Finding)

The paper's most significant contribution is the rigorous analysis of the sterile neutrino component ( $\nu_R$ ) associated with the sneutrino.

Dodelson-Widrow (DW) Mechanism: Even if the sneutrino is produced via freeze-in, the corresponding fermionic sterile neutrino is produced via oscillations (DW mechanism) in the early universe.
Lifetime Issue: To achieve the correct sneutrino relic density via freeze-in, the Yukawa couplings must be extremely small ( $y_\nu \sim 10^{-12}$ ). This implies the sterile neutrino mass is very low ( $m_N \sim 5-20$ eV) and its lifetime is extremely long ( $\tau \sim 10^{10}$ years), exceeding the age of the universe.
Overabundance: These long-lived sterile neutrinos act as a separate DM component. Using the DW formula, the authors calculate that for the parameter space required to satisfy the sneutrino freeze-in, the sterile neutrino contribution to the relic density is massively overabundant ( $\Omega_{\nu_R} h^2 \gg 0.12$ , often $>3$ ).
Seesaw Specifics:
- Type-I Seesaw: Fails completely. The mixing angle required for the correct neutrino mass spectrum leads to DW overproduction.
- Linear/Inverse Seesaw: Attempting to suppress the mixing by increasing the sterile mass requires large parameters ( $\mu_S$ ) that either reintroduce large couplings (ruining freeze-in) or effectively reduce the model back to a Type-I scenario where overproduction persists.
- Dirac Neutrinos: The only surviving scenario. In the Dirac case, there are no Majorana mass terms, meaning no sterile mass eigenstates exist to oscillate and overproduce via the DW mechanism.

4. Results

Ruling Out Hybrid Scenarios: The authors conclude that the hybrid "Freeze-out Higgsino + Freeze-in Sneutrino" scenario is ruled out for Type-I, Linear, and Inverse Seesaw models.
Reason: The parameter space that yields the correct sneutrino abundance inevitably produces sterile neutrinos that overclose the universe via the Dodelson-Widrow mechanism.
Surviving Model: The scenario is only viable in the Dirac neutrino extension of the MSSM, where sterile neutrino mass eigenstates are absent, thus avoiding the DW overproduction constraint.

5. Significance

Naturalness vs. Cosmology: The paper demonstrates that even if one attempts to solve the naturalness problem with light Higgsinos and the DM problem with freeze-in sneutrinos, the neutrino sector imposes a fatal cosmological constraint.
Constraint on Seesaw Models: It provides a strong theoretical argument against low-scale Type-I, Linear, and Inverse Seesaw models in the context of FIMP dark matter, as they cannot simultaneously satisfy neutrino mass requirements, freeze-in production, and relic density bounds.
Future Directions: The work highlights that if such a hybrid scenario exists, it must rely on Dirac neutrinos, shifting the focus of model building away from Majorana mass terms in the low-scale seesaw regime.

In summary, while the combination of freeze-out and freeze-in is theoretically attractive for natural SUSY, the Dodelson-Widrow overproduction of sterile neutrinos acts as a "cosmological veto" for all standard seesaw extensions, leaving only the Dirac neutrino model as a viable candidate.