Natural SUSY with mixed axion/axino dark matter

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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

Imagine the universe is a giant, complex machine. For decades, physicists have been trying to figure out why this machine works the way it does, specifically why some parts are incredibly heavy and others are incredibly light. This puzzle is called the "Hierarchy Problem."

To fix this, scientists proposed a theory called Supersymmetry (SUSY). Think of SUSY as a "shadow world" where every known particle has a heavier, invisible twin. For a long time, we hoped to find these twins at the Large Hadron Collider (LHC), but so far, we haven't found them. This has created a new puzzle: if these twins exist, why are they hiding at such high energy levels? This is the "Little Hierarchy Problem."

This paper explores a clever way to solve both the "Big" and "Little" problems while also explaining Dark Matter—the invisible stuff that holds galaxies together.

Here is the story in simple terms:

1. The Two Problems We Need to Solve

The Big Problem (Hierarchy): Why is the force of gravity so weak compared to the other forces? SUSY fixes this by adding those "shadow twins."
The Strong CP Problem: There's a weird glitch in the laws of physics regarding how particles behave (specifically, why they don't seem to care about "left" vs. "right" in certain interactions). To fix this, physicists invented a mechanism called the Peccei-Quinn (PQ) solution, which introduces a new, ghostly particle called the Axion.

2. The New Cast of Characters

In this "Natural SUSY" scenario, we aren't just looking for the usual shadow twins. Because of the Axion solution, we get a whole new family of particles:

The Axion: A super-light, ghostly particle that is a great candidate for Dark Matter.
The Saxion: A heavy, boring particle (like a rock).
The Axino: The "shadow twin" of the Axion. It's the star of this show.

3. The Mystery of the Missing Dark Matter

Usually, scientists thought the "Lightest Supersymmetric Particle" (LSP) was a Neutralino (a heavy shadow twin). They thought these Neutralinos were the main ingredient of Dark Matter.

The Problem: We've built giant detectors (like tanks of liquid xenon) to catch these Neutralinos. But they haven't shown up. It's like setting a trap for a mouse and finding nothing.
The Twist: What if the Neutralino isn't the main Dark Matter? What if the Axino is the boss?

4. The "Mixed Diet" Solution

The authors propose a "Mixed Axion-Axino" diet for the universe's Dark Matter. Think of it like a smoothie:

The Ice (Axions): These are the cold, heavy chunks that make up most of the smoothie. They are "Cold Dark Matter."
The Liquid (Axinos): These are the lighter, warmer liquid that fills in the gaps. They are "Warm Dark Matter."

In this scenario, the heavy Neutralino (the mouse we were trying to catch) is actually unstable. It's like a ticking time bomb that eventually decays (explodes) into an Axino.

The Catch: Because the Neutralino decays into the Axino, the Axino inherits the Neutralino's "abundance."
The Result: Even though the Neutralinos are rare (because they decay), the Axinos they turn into can make up the perfect amount of Dark Matter we see in the universe today.

5. The Two Sweet Spots

The authors did the math and found two specific "recipes" where this works perfectly:

Recipe A (The Warm Soup): If the "PQ Scale" (a measure of how heavy the Axion family is) is around $10^{11}$ GeV, the Dark Matter is mostly made of Axinos. These are "warm," meaning they move a bit faster. This works if the Axino is very light (about the weight of a virus).
Recipe B (The Cold Ice): If the PQ Scale is higher (around $3 \times 10^{12}$ GeV), the Dark Matter is mostly Axions (Cold), with just a tiny splash of Axinos. This is the more popular solution because "Cold Dark Matter" fits our current understanding of how galaxies form better.

6. How to Catch Them?

Since the heavy Neutralinos decay into Axinos, they might hang around for a split second before exploding.

The Signature: If we look at particle colliders (like the LHC) or specialized "Long-Lived Particle" detectors, we might see a Neutralino traveling a short distance and then suddenly vanishing into an Axino and a photon or a Z-boson.
The Difference: In older theories, if a Neutralino decayed, it would break the rules of "R-parity" (a conservation law). In this new theory, it decays without breaking those rules, just changing its identity. This gives us a unique way to tell this theory apart from others.

The Bottom Line

This paper suggests that the universe's Dark Matter isn't just one thing. It's a mixture of ghostly Axions and their lighter, warmer cousins, the Axinos. This idea saves "Natural SUSY" from being ruled out by the lack of WIMP detections, offering a new path to understanding why the universe is the way it is.

In a nutshell: The universe isn't just filled with heavy, invisible mice (Neutralinos). Instead, the mice are actually just delivery trucks that drop off a cargo of invisible, ghostly dust (Axions) and warm mist (Axinos), which together make up the Dark Matter holding our galaxies together.

1. Problem Statement

The paper addresses the intersection of three major challenges in particle physics and cosmology:

The Little Hierarchy Problem (LHP): While Supersymmetry (SUSY) solves the gauge hierarchy problem, the lack of superpartners at the LHC has created a tension between the weak scale and the superpartner mass scale. "Natural SUSY" models (characterized by low fine-tuning, $\Delta_{EW} \lesssim 30$ ) are required to resolve this.
The Strong CP Problem: The Standard Model (SM) cannot explain why the QCD vacuum angle $\theta$ is so small. The Peccei-Quinn (PQ) mechanism and the resulting axion are the standard solution.
Dark Matter (DM) Exclusion: Multi-ton noble liquid detectors (e.g., LZ) have placed severe limits on Weakly Interacting Massive Particles (WIMPs). In Natural SUSY, the Lightest Supersymmetric Particle (LSP) is typically a higgsino-like neutralino ( $\tilde{\chi}^0_1$ ). If this neutralino constitutes all DM, it is now largely excluded by direct detection limits. Even if its abundance is depleted, limits remain tight.

The Core Question: Can a Natural SUSY framework incorporating the PQ mechanism accommodate a viable Dark Matter candidate that evades current WIMP limits? The authors propose that the axino ( $\tilde{a}$ ), the fermionic superpartner of the axion, serves as the LSP, leading to a mixed axion-axino dark matter scenario.

2. Methodology

The authors employ a phenomenological approach combining Natural SUSY benchmark points with axion cosmology.

Model Framework:
- Natural SUSY Benchmark: They utilize the NUHM3 benchmark point (from the string landscape), featuring heavy first/second generation scalars ($30$ TeV) to solve flavor/CP problems, but light third-generation scalars ($6$ TeV) and gauginos ($2.2$ TeV) to ensure naturalness ( $\Delta_{EW} \approx 25$ ). The lightest neutralino is higgsino-like with mass $m_{\tilde{\chi}^0_1} \sim 200$ GeV.
- PQ Models: They analyze two specific SUSY axion models:
  1. DFSZ (Dine-Fischler-Srednicki-Zhitnitsky): Involves two Higgs doublets coupled to a PQ singlet.
  2. KSVZ (Kim-Shifman-Vainshtein-Zakharov): Involves heavy quarks coupled to a PQ singlet.
- LSP Assumption: The axino ( $\tilde{a}$ ) is the LSP, while the higgsino-like neutralino ( $\tilde{\chi}^0_1$ ) is the Next-to-Lightest SUSY Particle (NLSP).
Production Mechanisms Calculated:
The total relic density $\Omega_{a\tilde{a}}h^2$ is calculated by summing contributions from:
1. Coherent Oscillations (CO): Standard cold axion production ( $\Omega_a^{CO}$ ).
2. Non-Thermal Production (NTP): Decays of the NLSP neutralino ( $\tilde{\chi}^0_1 \to \tilde{a} + Z/h$ ) which inherit the neutralino abundance.
3. Thermal Production (TP): Freeze-in production of axinos from the thermal bath.
  - DFSZ: TP is independent of the reheating temperature ( $T_R$ ) due to direct Higgs/axino couplings.
  - KSVZ: TP depends linearly on $T_R$ via gluon-gluino couplings.
4. Gravitino Decay: Cascade decays of thermally produced gravitinos into axinos.
5. Saxion Decays: Ignored in the primary analysis due to constraints on dark radiation ( $N_{eff}$ ), assuming saxions decay early or are heavy.
Constraints Applied:
- BBN Safety: The neutralino lifetime ( $\tau_{\tilde{\chi}}$ ) must be short enough ( $\lesssim 100$ s, effectively $T_D \lesssim 3-5$ MeV) to avoid disrupting Big Bang Nucleosynthesis.
- Relic Density: The sum of axion and axino densities must match the observed value $\Omega_{DM}h^2 \approx 0.12$ .
- Direct Detection: The model must satisfy LZ limits, which is naturally achieved if the WIMP (neutralino) abundance is suppressed.

3. Key Contributions

Viable Natural SUSY LSP: The paper demonstrates that in Natural SUSY, the axino can be the LSP, evading the "neutrino floor" of WIMP direct detection experiments that rule out higgsino-like neutralinos as the sole DM component.
Decay Constraints: They explicitly map the decay temperature of the higgsino-like neutralino ( $\tilde{\chi}^0_1 \to \tilde{a}Z, \tilde{a}h$ ) against the PQ scale ( $f_a$ ) and axino mass ( $m_{\tilde{a}}$ ). They show that for $f_a \gtrsim 10^{15}$ GeV, decays occur too late for BBN, excluding that region.
DFSZ vs. KSVZ Comparison: They provide a comparative analysis of thermal axino production in both models, highlighting that DFSZ production is $T_R$ -independent, whereas KSVZ is linearly dependent on $T_R$ .
Mixed DM Scenarios: They identify specific regions in the $(f_a, m_{\tilde{a}})$ parameter space where the mixed axion-axino density matches observations, distinguishing between "warm" axino-dominated and "cold" axion-dominated regimes.

4. Key Results

The authors mapped the viable parameter space for the mixed dark matter scenario:

DFSZ Model Results:
- Region 1 (Axino-Dominated): For $f_a \sim 10^{11}$ GeV and $m_{\tilde{a}} \sim 100$ keV, the axino constitutes the bulk of DM. These axinos are Warm Dark Matter (WDM). The axion contribution is minor ( $\sim 2-3\%$ ).
- Region 2 (Axion-Dominated): For higher scales $f_a \sim 3 \times 10^{12}$ GeV, thermal axino production is suppressed. Here, the DM is primarily Cold Axions, with a tiny axino contribution ( $\sim 0.1\%$ ). This is considered the more "engaging" solution as it preserves the cold DM paradigm.
- Overproduction: For $f_a \sim 10^9$ GeV or $f_a \sim 10^{13}$ GeV (with standard initial misalignment angle $\theta_i=1$ ), the model predicts overclosure (too much DM).
KSVZ Model Results:
- Similar viable regions exist. For $f_a \sim 10^{11}$ GeV, axinos dominate (WDM). For $f_a \sim 5 \times 10^{11}$ GeV, axions dominate (CDM), with axinos making up only $\sim 3\%$ .
- The KSVZ thermal production is sensitive to $T_R$ , allowing for tuning of the axino abundance.
Neutralino Decay Signatures:
- For the viable parameter space, the neutralino decays occur in the MeV–GeV range.
- Lifetimes range from $10^{-12}$ to $1$ second.
- Crucially, for $f_a \lesssim 10^{15}$ GeV, the decays happen before BBN, satisfying cosmological constraints.
- Experimental Signature: These decays could manifest as Long-Lived Particles (LLPs) at colliders (ATLAS, CMS, FASER, MATHUSLA), specifically looking for displaced vertices from $\tilde{\chi}^0_1 \to \tilde{a}Z$ or $\tilde{a}h$ .

5. Significance

Resolving the WIMP Crisis: This work offers a robust solution to the tension between Natural SUSY (which predicts light higgsinos) and the null results of WIMP direct detection. By shifting the LSP to the axino, the model remains "natural" while evading current exclusion limits.
Phenomenological Predictions: Unlike "all-axion" models where the neutralino is stable or decays via R-parity violation (RPV), this model predicts specific two-body decays ( $\tilde{\chi}^0_1 \to \tilde{a}Z/h$ ). This provides a distinct experimental signature for LLP searches at the LHC and future colliders.
Cosmological Viability: It demonstrates that mixed axion-axino dark matter is not only possible but preferred in Natural SUSY contexts, particularly in the DFSZ framework where thermal production is naturally suppressed at high $f_a$ , favoring a cold axion-dominated universe.
Model Discrimination: The paper distinguishes between DFSZ and KSVZ scenarios based on the dependence of thermal production on the reheating temperature, providing a roadmap for future cosmological and collider constraints.

In summary, the paper establishes that Natural SUSY with a mixed axion-axino dark matter sector is a viable, testable, and theoretically motivated framework that resolves the hierarchy problem, the strong CP problem, and the dark matter detection crisis simultaneously.