Effects of Cosmic Muons on $\mu$eV-to-meV Scale Axion Dark Matter Searches

This paper evaluates cosmic muon-induced synchrotron radiation as a potential background for axion dark matter searches, concluding that while high-resolution $\mu$eV-scale experiments are currently protected by their quality factors, future broadband detectors without sufficient energy resolution will be vulnerable to this noise source.

The Gist

Imagine the universe is filled with a ghostly substance called Dark Matter. Scientists have a strong hunch that a tiny, invisible particle called the Axion makes up most of this stuff. Finding an axion would be like discovering the missing piece of the universe's puzzle, solving two huge mysteries at once: what dark matter is and why the laws of physics behave the way they do.

To catch these ghosts, scientists built giant, super-sensitive "traps" called Haloscopes. Think of these as giant, hollow copper drums placed inside incredibly strong magnets (like the ones in MRI machines, but much stronger).

The Setup: The Silent Symphony

The theory goes like this: If an axion flies through this strong magnetic field, it should magically transform into a tiny spark of light (a photon). Because the axion has a specific "weight" (energy), this light should hum at a very specific, pure musical note.

The scientists tune their copper drum to listen for that exact note. If they hear a hum that matches the axion's predicted weight, they've found dark matter!

The Problem: The Cosmic Noise

However, the universe is noisy. While the scientists are trying to hear that faint axion whisper, there are other things making noise. One of the biggest culprits is Cosmic Muons.

Think of cosmic muons as raindrops made of high-speed particles constantly raining down on Earth from space. They are everywhere, passing through walls, people, and our detectors.

When these "muon raindrops" hit the strong magnetic field inside the detector, they don't just pass through silently. They get forced to spin in tight circles (like a car skidding on ice). As they spin, they emit their own tiny sparks of light. This is called Synchrotron Radiation.

The Paper's Mission: Is the Rain Drowning Out the Whisper?

The authors of this paper asked a critical question: "Is the light emitted by these spinning cosmic muons so loud that it drowns out the axion signal?"

They ran massive computer simulations (like a video game for physics) to track millions of these muons as they flew through a simulated detector. They calculated exactly how much "noise" light these muons would create across different energy levels.

The Findings: Good News and a Warning

1. The Good News for Current Detectors:
For the experiments running right now (like the famous ADMX experiment), the answer is no, the muons are not a problem.

• The Analogy: Imagine you are trying to hear a single violin playing a perfect note in a quiet concert hall. The cosmic muons are like a few people in the back of the hall whispering. Because the current detectors are so high-quality (they have a high "Q factor," which is like having a super-sharp ear that only listens to one specific note), the whispering doesn't matter. The violin (axion) is still clearly audible.

2. The Warning for Future Detectors:
The paper warns that for future experiments that want to listen to a wider range of notes at once (broadband searches), the muons could become a major problem.

• The Analogy: Imagine you want to listen to an entire orchestra playing many different songs at once, but you have a microphone that isn't very good at distinguishing between different sounds (low energy resolution). In this scenario, the background whispering of the muons (the noise) might get so loud that it covers up the music entirely. If the future detectors don't have a way to filter out this "muon rain," they might miss the axion signal.

The Bottom Line

The authors did a deep dive to make sure scientists aren't wasting time or getting false alarms. They concluded:

• Current experiments are safe: The "quality" of their detectors is high enough to ignore the cosmic muon noise.
• Future experiments need to be careful: If they build detectors that scan a wide range of energies without very sharp resolution, the cosmic muons could create enough noise to hide the dark matter signal.

In short, the universe is full of cosmic "rain," but for now, our axion detectors are wearing raincoats that work perfectly. Just make sure the next generation of raincoats is even better!

Technical Summary

1. Problem Statement

The search for QCD axion dark matter using Sikivie haloscopes (resonant cavities in strong magnetic fields) is currently limited by Johnson noise and electronic readout noise in the radio-to-microwave frequency range (µeV scale). While natural radioactivity is traditionally ignored, this paper investigates a specific, often overlooked background source: synchrotron radiation emitted by cosmic muons traversing the strong magnetic fields (typically 8 T) of axion detectors.

The core concern is that charged particles moving through a magnetic field emit radiation. Since the power of this synchrotron radiation scales with $B^2$ (similar to the axion-to-photon conversion signal), high-flux cosmic muons could potentially generate a noise floor that mimics or obscures the axion signal, particularly in future broadband experiments that may lack the high quality factors ($Q$) or fine energy resolution of current resonant cavity experiments.

2. Methodology

The authors employed a hybrid approach combining Monte Carlo simulations with analytical physics calculations to estimate the background noise.

• Muon Generation and Tracking (GEANT4):

  • Used the GEANT4 software package to simulate cosmic muon trajectories entering a cylindrical copper cavity (1 m length, 0.2 m radius) within an 8 T solenoid magnetic field.
  • Simulated muon fluxes based on sea-level data: ~17 muons/s entering from the top and ~40 muons/s entering from the side walls.
  • Recorded key parameters for each muon: entry/exit timestamps, pitch angle ($\alpha$) relative to the magnetic field, and Lorentz factor ($\gamma$).
  • Note: The standard GEANT4 synchrotron radiation package was deemed insufficient because a significant portion of cosmic muons have moderate Lorentz factors ($\gamma < 10$) and non-vertical pitch angles, requiring a more precise treatment.

• Analytical Synchrotron Radiation Integration:

  • Developed a custom analytical framework based on Liénard's formula and the theory of synchrotron radiation harmonics (Ref. [44]).
  • Calculated the angular-frequency-differential synchrotron radiation power spectra ($dP/d\omega$).
  • Hybrid Calculation Strategy:
    • For high harmonics ($n \gg 1$), the discrete harmonic number $n$ was replaced with continuous angular frequency $\omega$ for integration.
    • For low harmonics (small $\gamma$), a hybrid loop was implemented to sum discrete harmonics $n$ and integrate over the corresponding polar angles $\theta$ to avoid errors arising from treating discrete harmonics as continuous.
  • The total power was normalized based on the flux and distribution of $\alpha$ and $\gamma$ obtained from the GEANT4 simulation.

3. Key Contributions

• First Quantitative Estimate: This is the first publication to estimate the effects of natural radioactivities and cosmic rays specifically on axion dark matter haloscopes.
• Analytical Framework: The authors developed a robust method to calculate synchrotron radiation spectra for particles with a wide range of Lorentz factors and pitch angles, addressing the limitations of standard simulation packages for low-energy, non-relativistic, or moderately relativistic regimes.
• Noise Temperature Conversion: The study converts the calculated radiation power into an equivalent noise temperature ($T$), allowing for direct comparison with the sensitivity limits of axion detectors.

4. Results

• Muon Characteristics: The simulation confirmed that muons entering the cavity have a broad distribution of Lorentz factors ($\gamma$) and pitch angles ($\alpha$). Side-wall muons contribute more significantly to the total background due to higher flux (40/s vs. 17/s).
• Radiation Spectrum: The synchrotron radiation from these muons creates a broad spectrum spanning from $\mu$eV to meV.
• Comparison with Current Experiments (ADMX, CAPP):
  • For current experiments operating at the $\mu$eV scale (e.g., ADMX at 1 GHz), the muon synchrotron noise is negligible.
  • This is due to the extremely high quality factor ($Q \approx 50,000$) of copper cavities and the fine energy resolution of the readout systems, which effectively filter out the broadband muon noise.
  • Even with a low energy resolution assumption ($\Delta E/E = 10\%$), the muon noise only becomes comparable to the signal of a DFSZ axion if the quality factor drops to $Q \approx 10$.
• Implications for Future Experiments (BREAD, MADMAX):
  • Future broadband axion experiments often utilize photon counters or lower-$Q$ designs to cover wider frequency ranges.
  • If these experiments lack sufficient energy resolution or signal enhancement (high $Q$), the synchrotron radiation from cosmic muons could become a dominant noise source, potentially limiting sensitivity.

5. Significance and Conclusion

The paper concludes that while cosmic muons are not a threat to current high-$Q$ resonant cavity axion searches, they represent a critical design constraint for the next generation of broadband axion detectors.

• Design Guidance: Future experiments utilizing photon counters or broadband detection strategies must account for cosmic muon backgrounds. This may necessitate:
  • Improved energy resolution in readout systems.
  • Active muon vetoes or shielding.
  • Careful optimization of the quality factor ($Q$) to ensure signal enhancement outweighs the broadband noise.
• Broader Application: The methodology developed is also applicable to other high-field experiments, such as high-frequency gravitational wave searches and beta-decay measurements using cyclotron radiation emission spectroscopy.

In summary, the authors provide a rigorous framework to ensure that as axion searches expand into broader frequency bands, they do not inadvertently become limited by the synchrotron radiation of the very cosmic rays they must traverse.