Search for Axion Like Particles produced via the Primakoff process at COMPASS

This paper presents a reinterpretation of 2009 COMPASS data to search for Axion-Like Particles (ALPs) produced via the Primakoff process, deriving new exclusion limits on the ALP-photon coupling in the 0.2–600 MeV mass range by analyzing merged diphoton signatures that mimic Standard Model Compton scattering.

The Gist

The Big Picture: Hunting for Invisible Ghosts

Imagine the universe is a giant, bustling city. We know most of the "citizens" (particles like electrons and protons) because we can see them or feel their effects. But there's a huge part of the city we can't see: Dark Matter.

Physicists suspect that Dark Matter might be made of invisible "ghosts" called Axion-Like Particles (ALPs). These ghosts are tricky. They don't like to interact with us, but they might occasionally whisper to light (photons). If we can catch them whispering, we can prove they exist.

This paper is about a team of scientists who went back to an old set of data from a particle accelerator (called COMPASS) and asked a clever question: "Did we accidentally see these ghosts hiding in plain sight?"

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The Setup: The Particle Cannon

Think of the COMPASS experiment as a massive particle cannon.

1. The Ammo: They fired high-speed beams of pions (tiny particles) and muons (heavier cousins of electrons) at a block of Nickel.
2. The Goal: Originally, they weren't looking for ghosts. They were studying how these particles bounce off the nickel and emit a single flash of light (a photon). It's like shooting a bullet at a wall and watching the spark it makes.

The "Ghost" Trick: The Invisible Double-Flash

Here is where the physics gets interesting. The scientists hypothesized that if an ALP exists, it could be created in that collision.

• The ALP's Life: The ALP is born, zooms away, and then instantly decays (dies) into two flashes of light (two photons).
• The Problem: Because the cannon fires particles so fast, the ALP is moving at nearly the speed of light. This creates a "Lorentz boost" (a fancy way of saying it gets squished and sped up).
• The Result: The two flashes of light coming from the ALP are squeezed so tightly together that they look like one single flash.

The Analogy: Imagine two fireflies flying side-by-side at night. If they are far apart, you see two distinct dots of light. But if they are flying incredibly fast and very close together, your eye (or a camera) can't tell them apart. You just see one bright, blurry blob.

The ALP creates a "blurry blob" of light that looks exactly like the single spark the scientists were originally looking for.

The Detective Work: Finding the Clues

The scientists realized that the original data might be "contaminated." Some of the "single sparks" they recorded might actually be these "blurry blobs" (ALPs) masquerading as normal sparks.

They built a mathematical model to answer:

1. How many ALPs should we expect? (Based on how heavy they are and how strongly they talk to light).
2. How many would look like a single spark? (Based on the speed of the beam and the size of the detector's "pixels").
3. Did the data match the "Normal Spark" theory, or was there extra noise?

They compared the actual data from 2009 against their new model. They found that the data matched the "Normal Spark" theory perfectly well. There was no extra noise.

The Verdict: "Not Here" (But We Know Where to Look)

Since they didn't find any ALPs, they didn't discover the ghost. However, in science, a "no" is still a huge victory.

By not finding them, they were able to draw a map of where the ghosts cannot be.

• The Exclusion Zone: They proved that if ALPs exist with a mass between 0.2 and 600 MeV (a specific range of "heaviness"), they cannot be interacting with light as strongly as some theories suggested.
• The Bridge: This is important because previous experiments looked for very light ghosts (like a feather), and collider experiments looked for very heavy ghosts (like a boulder). This paper filled in the gap for the "medium-sized" ghosts.

Why This Paper is Cool

1. Recycling Old Data: They didn't need to build a new, expensive machine. They just used a clever new lens to look at old data they already had. It's like finding a hidden message in an old newspaper by using a new type of magnifying glass.
2. The "Charged" Advantage: Other experiments use beams of light (photons) to hunt for ALPs. But light is hard to track because it just keeps going. COMPASS used charged particles (pions/muons). When these particles bounce off the nickel, they leave a clear "footprint" (a track) that tells the scientists exactly where the interaction happened. This makes it much easier to spot the "ghost" signature against the background noise.
3. Future Proofing: The methods they developed here are now a blueprint. They can apply this same "ghost hunting" technique to future experiments (like the new AMBER experiment) and even look for ALPs that do split into two separate flashes of light, which they can't do with this specific dataset.

Summary

The scientists took a high-speed particle cannon, fired it at a nickel wall, and looked for a specific type of "ghost" (ALP) that hides by pretending to be a single spark of light. They didn't find the ghost, but they successfully proved that the ghost isn't hiding in that specific neighborhood. This narrows down the search for Dark Matter and gives future scientists a better map for where to look next.

Technical Summary

1. Problem Statement and Motivation

• Theoretical Context: The Standard Model (SM) faces the "strong CP problem," theoretically addressed by the Peccei-Quinn mechanism, which predicts the existence of the axion. Extensions of the SM predict a broader class of particles known as Axion-Like Particles (ALPs). ALPs are candidates for dark matter or mediators to the dark sector and couple to photons ($g_{a\gamma\gamma}$).
• Experimental Gap: While beam dump experiments constrain low-mass ALPs and high-energy colliders (like LEP/LHC) constrain higher masses, there is a need for independent constraints in the intermediate mass range (MeV to GeV).
• Specific Challenge: In high-energy fixed-target experiments, ALPs produced via the Primakoff process decay into two photons. Due to the high Lorentz boost of the incident beam (190 GeV), these decay photons are highly collimated. If the transverse separation is smaller than the detector's granularity, the two photons merge into a single electromagnetic cluster. This signature mimics the single-photon signal of Standard Model (SM) Primakoff Compton scattering, making ALP detection difficult as it gets buried in the SM background.

2. Methodology

The paper proposes a reinterpretation of the COMPASS 2009 dataset, which utilized 190 GeV $\pi^-$ and $\mu^-$ beams impinging on a fixed nickel (Ni) target.

• Signal Mechanism:
  • Production: ALPs are produced via the Primakoff effect ($\pi^-/\mu^- + Ni \to \pi^-/\mu^- + Ni + a$).
  • Decay: The ALP decays into a diphoton state ($a \to \gamma\gamma$).
  • Merging: Due to the high beam energy and the distance to the electromagnetic calorimeter (ECAL2, ~34 m), the decay photons often merge into a single reconstructed cluster if the opening angle is small or if the energy sharing is highly asymmetric (one photon falls below the detection threshold).
• Analysis Strategy:
  • The authors reinterpret the original COMPASS measurement of the ratio of observed events to the SM Monte Carlo prediction (Born term) for single-photon events.
  • They introduce a theoretical ratio $R_{theory}$ that includes the SM background (including pion polarizability effects for the pion beam) plus the ALP contribution.
  • Acceptance Modeling ($P_{acc}$): The probability of an ALP signal passing the single-photon selection is calculated as the product of three factors:
    1. Decay Probability ($P_{decay}$): Probability the ALP decays before reaching ECAL2.
    2. Merging Probability ($P_{merge}$): Calculated via two regimes:
       • Asymmetric Decay: One photon is soft ($<2$ GeV) and undetected.
       • Geometric Merging: Both photons are energetic but hit the same ECAL2 cell (3.8 cm granularity). This is modeled using a sigmoid function derived from a dedicated Monte Carlo simulation of the calorimeter geometry.
    3. Survival Probability ($P_{survive}$): Corrects for $e^+e^-$ pair conversion in the target and spectrometer material, accounting for the different path lengths of the SM photon vs. the ALP-decay photons.
• Statistical Framework: A profile likelihood approach is used to compare the observed data ratios ($R_{obs}$) with the theoretical predictions. Systematic uncertainties are handled via nuisance parameters. Exclusion limits are set at 95% Confidence Level (C.L.) using a $\Delta\chi^2 \geq 3.84$ criterion.

3. Key Contributions

• Novel Reinterpretation Framework: This work establishes a method to search for ALPs in datasets originally designed for SM precision measurements (pion polarizability) by exploiting the "merged cluster" signature.
• Analytical Merging Model: The authors develop a robust analytical model for the geometric merging probability of diphoton states in a calorimeter, avoiding the need for full GEANT4 simulations for every point in the parameter space scan.
• Topological Advantage: Unlike photoproduction experiments (e.g., PrimEx, GlueX) that struggle with beam backgrounds, the COMPASS charged-beam setup allows for a clean coincidence tag of the scattered charged particle, significantly suppressing beam-related backgrounds.
• Parameter Space Coverage: The analysis targets the intermediate mass range ($0.2 \lesssim m_a \lesssim 600$ MeV), bridging the gap between beam dump and collider experiments.

4. Results

• Exclusion Limits: The study derives 95% C.L. exclusion limits on the ALP-photon coupling $g_{a\gamma\gamma}$.
  • Coupling Limit: Couplings $g_{a\gamma\gamma} \gtrsim 10^{-1} \text{ GeV}^{-1}$ are excluded.
  • Mass Range: Sensitivity extends up to approximately 600 MeV.
• Beam Comparison:
  • Pion Beam: Yields significantly stronger limits than the muon beam. This is because the SM bremsstrahlung cross-section scales as $1/m^2$, meaning the heavier pion mass suppresses the SM background more effectively than the muon case, leading to a larger signal-to-background ratio.
  • High-Mass Tail: The pion beam limits show a distinct high-mass tail (up to 600 MeV) driven by the asymmetric decay mechanism, which remains visible even when geometric merging probability vanishes. The muon beam limits do not show this tail within the plotted range due to overwhelming SM background.
• Comparison: The results provide independent constraints that complement existing limits from LEP, beam dump experiments, and other Primakoff-based searches (PrimEx, GlueX).

5. Significance and Future Outlook

• Immediate Impact: The work demonstrates that existing high-statistics datasets from fixed-target experiments can be repurposed to search for new physics in unexplored kinematic regimes without new data taking.
• Future Applications:
  • COMPASS 2012 Dataset: The framework can be directly applied to the larger 2012 dataset collected with the same setup.
  • AMBER Experiment: The upcoming AMBER experiment (successor to COMPASS) plans to measure kaon polarizability using a 100 GeV $K^-$ beam. The heavier kaon mass will further suppress SM backgrounds, offering even greater sensitivity to ALPs using this merged-cluster technique.
  • Resolved Diphotons: The methodology serves as a baseline for future analyses focusing on resolved diphoton states (e.g., Primakoff $\pi^0$ production), where the merging constraint is relaxed, potentially extending sensitivity to higher masses.

In summary, this paper successfully reinterprets COMPASS data to place competitive constraints on ALP-photon couplings in the MeV-GeV range, highlighting the unique sensitivity of charged-beam fixed-target experiments to highly collimated diphoton signatures.