Bridging the divide: axion searches and axino phenomenology at colliders

This paper presents a phenomenological study demonstrating that the Large Hadron Collider can probe supersymmetric DFSZ axion models with higgsino masses below 1 TeV and axion decay constants under $10^{11}$ GeV by analyzing displaced decays of neutralinos into axinos using Monte Carlo simulations and detector sensitivity estimates.

The Gist

The Big Picture: Two Worlds of Physics

Imagine the universe has two main detective teams trying to solve the same mystery: What is Dark Matter?

1. The "Quiet" Team (Direct Detection & Astrophysics): These scientists are like people whispering in a library. They use giant, sensitive microphones (like radio telescopes or underground tanks) to listen for the faintest "whisper" of a dark matter particle interacting with normal matter. They are looking for a specific type of particle called an Axion.
2. The "Loud" Team (Colliders): These scientists are like rock stars at a mosh pit. They smash particles together at the Large Hadron Collider (LHC) with incredible force, creating a chaotic explosion of new particles. They look for the debris of these crashes to see if anything strange pops out.

The Problem: For a long time, these two teams haven't been talking to each other. The "Quiet" team has been looking for Axions, but they might be looking in the wrong place if the universe is actually made of a "supersymmetric" version of the Axion.

The Characters: The Axion, The Axino, and The Higgsino

To understand this paper, we need to meet the cast of characters:

• The Axion: The original suspect. It's a ghostly particle proposed to solve a puzzle about why the universe doesn't violate certain symmetry rules (the "Strong CP problem"). It's very light and interacts very weakly with everything else.
• The Axino: The Axion's "supersymmetric twin." In the world of Supersymmetry (SUSY), every particle has a heavier, "super" partner. The Axino is the super-partner of the Axion.
• The Higgsino: A heavy, unstable particle related to the Higgs boson. In this story, the Higgsino is the "older brother" who is about to die and pass the torch to the Axino.

The Plot: A Disappearing Act

The paper proposes a specific scenario:

1. The Setup: In the early universe, heavy Higgsinos were created.
2. The Decay: These heavy Higgsinos are unstable. They want to decay into the lightest, most stable particle available, which is the Axino (our Dark Matter candidate).
3. The Twist: Usually, particles decay instantly. But because the Axino is so "ghostly" (it interacts very weakly), the Higgsino takes a long time to decay.
   • Analogy: Imagine a firework that is supposed to explode immediately. But because the fuse is made of a special, slow-burning material, it takes a few seconds to burn down.
4. The Signature: When the Higgsino finally explodes (decays), it happens away from the collision point. It leaves a "displaced vertex"—a second explosion happening a few millimeters or centimeters away from where the crash started.
   • Analogy: Imagine two cars crashing. Usually, the airbags pop instantly. But in this scenario, the airbag pops a few feet away from the crash site, floating in mid-air before inflating. That's a "displaced vertex."

The Challenge: The "Supersymmetric" Blind Spot

Here is the tricky part. The "Quiet" Team (direct detection) relies on the Axion interacting with photons (light).

• In a normal universe, the Axion talks to light quite well.
• But in a Supersymmetric universe (DFSZ model), the Axion's "voice" is muffled. The math shows that the Axion's interaction with light is suppressed by a factor of 20 or even completely cancelled out.
• Analogy: The "Quiet" Team is trying to hear a whisper, but the Axion has been given a mute button. They can't hear it, so they might conclude, "Axions don't exist!" But they are wrong; the Axion is just too quiet for their microphones.

The Solution: The Collider as a Flashlight

This is where the paper shines. The "Loud" Team (the LHC) doesn't need the Axion to talk to light. They just need to see the Higgsino decay into the Axino.

• The paper calculates that if the Higgsino is light enough (under 1,000 GeV) and the "Axion decay constant" (a measure of how weakly it interacts) is below a certain limit, the LHC can spot these delayed explosions (displaced vertices).
• They ran computer simulations (using tools like MadGraph and MadAnalysis) to see if the ATLAS detector at the LHC could catch this.
• The Result: Yes! If the Higgsino is light enough, the LHC can see these delayed decays. This allows them to probe a range of Axion properties that the "Quiet" Team cannot see because the Axion is too quiet for them.

The Takeaway: Bridging the Divide

This paper is a bridge. It says:

"Hey, the 'Quiet' Team might be missing the Axion because it's too shy to talk to light. But the 'Loud' Team at the LHC can catch it in the act of its brother (the Higgsino) dying. We need both teams to look at the same data to solve the mystery."

In simple terms:
If you are looking for a ghost that refuses to make a sound, you can't just listen for it. You have to watch the house it lives in. If you see a door open and close slowly in a room where no one is supposed to be, you know the ghost is there. The LHC is watching the doors; the direct detection experiments are just listening for whispers. This paper shows that watching the doors (collider searches) is the best way to find this specific type of ghost.

Why It Matters

• It saves the theory: It proves that even if the Axion is "supersymmetric" and hard to detect with traditional methods, it's not impossible to find.
• It guides the future: It tells experimentalists at the LHC exactly what to look for (delayed decays) and tells theorists that they need to keep looking at these specific models.
• It connects the dots: It shows that particle physics (colliders) and astrophysics (stars and galaxies) are two sides of the same coin, and we need to combine their results to understand the Dark Matter universe.

Technical Summary

1. Problem Statement

The paper addresses two major theoretical challenges in particle physics and cosmology:

• The Strong CP Problem: The Standard Model (SM) Lagrangian allows for a CP-violating $\theta$-term in QCD, which implies a large neutron electric dipole moment (EDM) inconsistent with experimental bounds. The Peccei-Quinn (PQ) mechanism introduces a global $U(1)_{PQ}$ symmetry, the breaking of which generates the axion, dynamically canceling the $\theta$-term.
• The Electroweak Hierarchy Problem: The Higgs mass is unstable against quantum corrections, requiring fine-tuning to remain at the electroweak scale. Supersymmetry (SUSY) stabilizes this mass.
• The Detection Gap: While the axion is a prime dark matter candidate, its couplings to SM particles are suppressed by the axion decay constant $f_a$. In the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model, the axion-photon coupling is a primary target for direct detection (e.g., ADMX, HAYSTAC). However, in a supersymmetric DFSZ (DFSZ-PQMSSM) scenario, the presence of higgsinos alters the electromagnetic anomaly, potentially suppressing the axion-photon coupling by a factor of $\sim 20$ or even causing it to vanish. This renders traditional axion searches insensitive to these well-motivated models.

Core Question: How can we probe supersymmetric DFSZ axion models where the axion-photon coupling is suppressed, rendering direct detection and astrophysical searches ineffective?

2. Methodology

The authors propose a collider-based approach focusing on the axino (the fermionic superpartner of the axion) as the Lightest Supersymmetric Particle (LSP).

• Model Construction:

  • They extend the Minimal Supersymmetric Standard Model (MSSM) with a gauge-singlet PQ-charged field $S$ (Kim-Nilles mechanism) to generate the $\mu$-term dynamically.
  • The model assumes R-parity conservation, making the axino stable.
  • The Next-to-Lightest Supersymmetric Particle (NLSP) is assumed to be a higgsino-like neutralino ($\tilde{\chi}^0_1$), which is required to be light ($< 1$ TeV) to solve the hierarchy problem naturally.
  • The axino mixes with neutralinos, allowing the higgsino NLSP to decay into the axino LSP and a Higgs ($h$) or Z boson.

• Phenomenological Analysis:

  • Decay Dynamics: The decay $\tilde{\chi}^0_1 \to \tilde{a} + h/Z$ is suppressed by $1/f_a$. This results in a displaced vertex signature if $f_a$ is in a specific range ($10^9 - 10^{11}$ GeV).
  • Simulation:
    • The model was implemented in SARAH and exported to UFO format.
    • MadGraph 2.9.16 was used to generate Monte Carlo (MC) events for proton-proton collisions ($\sqrt{s}=13$ TeV) producing higgsino pairs ($\tilde{\chi}^0_2\tilde{\chi}^0_1$, $\tilde{\chi}^0_1\tilde{\chi}^0_1$, etc.).
    • PYTHIA handled parton showering and hadronization.
    • MadAnalysis5 was used for fast detector simulation (based on ATLAS) and event selection.

• Selection Criteria:

  • Signal: Pair production of higgsinos $\to$ prompt decay of heavier states $\to$ displaced decay of the NLSP ($\tilde{\chi}^0_1$) into an axino ($\tilde{a}$) and a boson ($h/Z$).
  • Kinematics: The $h/Z$ decays hadronically (specifically $h \to b\bar{b}$). The axino escapes, creating Missing Transverse Momentum ($E_T^{miss}$).
  • Cuts:
    • Displaced Vertex (DV): Mass $m_{DV} > 10$ GeV, tracks $N_{track} \ge 5$, radial displacement $4 \text{ mm} < R < 300 \text{ mm}$.
    • $E_T^{miss} > 150$ GeV.

3. Key Contributions

1. Identification of a "Blind Spot": The paper demonstrates that in SUSY DFSZ models, the axion-photon coupling can be significantly suppressed, creating a parameter space where direct detection experiments lose sensitivity.
2. Collider Sensitivity to Axinos: It establishes that the axino in these models can be probed via displaced vertices at the LHC. The lifetime of the higgsino NLSP scales as $c\tau \propto f_a^2 / m_{\tilde{\chi}}^3$, making it ideal for LLP searches.
3. Complementarity: The study provides a rigorous framework showing how collider searches complement direct detection and astrophysical bounds, specifically covering the region where $f_a < 10^{11}$ GeV and $m_{\tilde{\chi}} < 1$ TeV.
4. Quantitative Projections: The authors provide exclusion contours for the $f_a$ vs. $m_{\tilde{\chi}}$ and $m_{\tilde{a}}$ parameter spaces based on 140 fb$^{-1}$ of LHC Run 2 data.

4. Results

• Displaced Vertex Sensitivity:

  • For higgsino masses below 1 TeV and axion decay constants $f_a < 10^{11}$ GeV, the LHC (with 140 fb$^{-1}$) can effectively probe the model.
  • Figure 7 & 8: Show 95% CL exclusion contours in the $(m_{\tilde{\chi}^0_1}, m_{\tilde{a}})$ and $(m_{\tilde{\chi}^0_1}, f_a)$ planes.
  • Kinematic Thresholds: A kinematic cutoff exists where $m_{\tilde{\chi}^0_1} < m_{\tilde{a}} + m_h$, below which the decay is forbidden.
  • Lifetime Constraints:
    • If $f_a$ is too small, the decay is prompt (no displaced vertex).
    • If $f_a$ is too large, the decay occurs outside the tracker volume (no signal).
    • The "sweet spot" for detection is roughly $f_a \sim 10^9 - 10^{11}$ GeV.

• Comparison with Other Searches (Figure 10):

  • Photon Coupling: The paper shows that for SUSY DFSZ models ($E/N = 2$), the axion-photon coupling is suppressed compared to non-SUSY DFSZ ($E/N = 8/3$). Direct detection limits (ADMX, etc.) are significantly weaker or non-existent for these models.
  • Astrophysical Bounds: Constraints from black hole spins and stellar cooling (proton/neutron/electron couplings) are shown. The collider search fills a gap where astrophysical bounds are weak or model-dependent.
  • Gravitino Distinction: The authors note that while light gravitinos can mimic axino signals, measuring the NLSP lifetime allows for the determination of $f_a$. If this $f_a$ matches constraints from axion searches, it confirms the axino hypothesis.

5. Significance

• Bridging the Divide: This work successfully connects the fields of axion dark matter and collider SUSY phenomenology. It proves that even if the axion is "invisible" to photon-coupling experiments due to SUSY suppression, its superpartner (the axino) leaves a distinct, detectable signature at the LHC.
• Model-Dependent Sensitivity: It highlights that while generic ALP searches are robust, specific UV-complete models (like SUSY DFSZ) require tailored search strategies. The displaced vertex channel is the unique probe for these specific scenarios.
• Experimental Impact: The paper notes that this theoretical work has already inspired an experimental search by the ATLAS collaboration (Ref [244]), demonstrating the immediate practical impact of the study.
• Future Directions: The authors suggest that High-Luminosity LHC (HL-LHC) could probe higher $f_a$ values, and searches for R-parity violation or wino-like NLSPs could further expand the reach.

In summary, the paper provides a critical roadmap for discovering supersymmetric axion models that are otherwise hidden from traditional dark matter detection methods, utilizing the unique capability of the LHC to detect long-lived particles.