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Multiple Axions in Laboratory Experiments

This paper develops general formulas for axion-photon oscillations involving multiple axion species, demonstrating that their interference and coherence effects can qualitatively alter, enhance, or suppress experimental signals in light-shining-through-a-wall, helioscope, and haloscope searches, thereby offering new avenues to identify and characterize axion multiplicity.

Original authors: Arturo de Giorgi, Joerg Jaeckel, Sebastian Monath, Volodymyr Takhistov

Published 2026-09-23

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CC BY 4.0

Original authors: Arturo de Giorgi, Joerg Jaeckel, Sebastian Monath, Volodymyr Takhistov

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

Deep within the fabric of our universe, physicists suspect there may be more to the story of light and matter than the standard model of particle physics currently tells. For decades, the discovery of the Higgs boson confirmed that invisible fields can give particles their mass, but it also left open the door for other, lighter fields that might be hiding in plain sight. One of the most compelling candidates for these hidden fields is the axion, a ghostly particle originally proposed to solve a puzzle about why the strong nuclear force behaves the way it does. While the standard story imagines just one type of axion, many modern theories, particularly those involving extra dimensions or the vast landscape of string theory, suggest that nature might be far more crowded. These theories predict not a single axion, but a whole spectrum of them, a family of particles with slightly different masses and strengths of interaction, all waiting to be found.

The question of whether these particles exist singly or in a crowd is not just a matter of counting; it fundamentally changes how we look for them. If only one axion exists, the search is a straightforward hunt for a specific signal. But if a whole family exists, they can interact with each other in ways that are impossible for a single particle. They can reinforce each other's signals, making them easier to spot, or they can cancel each other out, hiding the evidence entirely. This is the core mystery that a new study by researchers from Durham University, Heidelberg University, and the High Energy Accelerator Research Organization in Japan sets out to solve. They have developed a new way of thinking about how these particles behave in the lab, showing that the presence of multiple axions can completely alter the outcome of experiments designed to find them.

To understand the researchers' approach, imagine trying to hear a single voice in a quiet room versus trying to hear a choir. In a standard search for axions, scientists act like they are listening for a soloist. They shine a powerful laser beam through a strong magnetic field. If axions exist, some of the light should turn into these invisible particles and pass through a solid wall that blocks the light. On the other side of the wall, a second magnetic field should turn the axions back into light, which detectors can then see. This is known as a "light-shining-through-a-wall" experiment. If there is only one axion, the amount of light that reappears depends on how long the magnetic fields are and how strong the axion's connection to light is.

However, the new study reveals that if there are many axions, the process becomes a complex interplay of waves. When the laser light converts into axions, it doesn't just turn into one type; it creates a mixture of all the different axion species at once. As these axions travel through the wall, they continue to move and evolve. Because each axion in the family has a slightly different mass, they travel at slightly different speeds. This causes them to drift out of step with one another, a phenomenon known as decoherence. If the wall is thin or the axions are very light, they stay in step, and their effects add up together, potentially making the signal much brighter than expected. But if the wall is thick or the axions have different masses, they can fall out of step and interfere with each other, sometimes canceling the signal out completely. The researchers found that this interference can be destructive, meaning that having more axions could actually make an experiment less sensitive, causing a signal to vanish where a single axion would have been visible.

The team tested these ideas using computer models based on specific theories, such as those inspired by string theory and extra dimensions. They simulated experiments with different numbers of axions, ranging from just one to a hundred. Their calculations showed that in some scenarios, the signal could be boosted by the square of the number of axions, a massive increase. In others, the signal would only grow linearly, or it would be suppressed entirely due to the chaotic interference of the different masses. Crucially, they demonstrated that this behavior is not random noise but a predictable pattern. By carefully adjusting the length of the magnetic fields or the thickness of the wall, scientists could change the interference pattern. This means that if a signal is found, researchers could potentially distinguish whether it comes from a single axion or a whole family by seeing how the signal changes when the experimental setup is tweaked.

The study also looked at other ways of hunting for these particles, such as helioscopes, which look for axions coming from the Sun, and haloscopes, which search for axions that make up the dark matter surrounding our galaxy. In the case of solar axions, the researchers found that the Sun acts like a massive production factory, sending out a continuous stream of axions. If multiple axions exist, their different masses would create a complex pattern in the energy of the light they produce when converted back in a detector. By using a buffer gas to change the properties of the light inside the detector, scientists could tune the experiment to resonate with specific axion masses, revealing a spectrum of peaks rather than a single line. For dark matter searches, the presence of multiple axions would mean that the dark matter in our neighborhood is not a single uniform substance but a mixture of different types, each vibrating at its own frequency.

The implications of this work are significant for the future of particle physics. It suggests that the search for axions cannot rely on a single, static strategy. Instead, experiments must be designed to be flexible, capable of scanning across different parameters to map out the underlying structure of the axion sector. If nature has chosen to populate the universe with a diverse family of axions, the new formulas provide the tools to decode that diversity. The researchers emphasize that while a single axion might be easier to find in a simple setup, the presence of multiple axions offers a richer, albeit more complicated, signature. By understanding how these particles interfere and cooperate, scientists can turn a potential dead end into a diagnostic tool, using the very act of interference to count the number of axions and measure their properties. This shifts the goal from simply finding a particle to understanding the architecture of the hidden sector of the universe, turning laboratory experiments into powerful spectroscopes for the invisible world.

Technical Summary: Multiple Axions in Laboratory Experiments

Problem Statement
Axions and axion-like particles (ALPs) are well-motivated extensions of the Standard Model, often arising as pseudo-Goldstone bosons in theories such as the string theory "axiverse" or extra-dimensional models. While experimental searches typically assume the existence of a single axion species, theoretical frameworks generically predict a spectrum of multiple axion fields with correlated masses and couplings. The implications of this multiplicity for laboratory-based searches—specifically Light-Shining-Through-a-Wall (LSW) experiments, helioscopes, and haloscopes—remain underexplored. A critical question is whether the presence of multiple axions qualitatively alters observational signatures compared to single-axion scenarios, and if experimental parameters can be tuned to distinguish between these possibilities.

Methodology
The authors develop a general formalism for axion-photon oscillations in the presence of an arbitrary number of axion fields ( $N$ ) coupled to the electromagnetic field. Starting from an effective Lagrangian describing $N$ axions with masses $m_n$ and relative coupling coefficients $c_n$ , they derive the equations of motion for photon-axion propagation in external magnetic fields.

Key methodological steps include:

Eigenstate Analysis: The authors diagonalize the mixing matrix in the presence of a background magnetic field to determine the propagation eigenstates. They account for medium effects, including photon refraction (effective mass $m_\gamma$ ) and absorption (damping $\Gamma$ ).
Conversion Probability Derivation: Using an eikonal approximation and plane-wave ansatz, they derive the probability for photon regeneration ( $P_{\gamma \to X \to \gamma}$ ) in LSW setups and axion-to-photon conversion in helioscopes. The derivation explicitly tracks the interference terms arising from the superposition of different axion mass eigenstates.
Benchmark Models: To illustrate the phenomenology, the authors analyze three representative scenarios:
- Stringy Axions: A log-normal mass distribution inspired by the string axiverse.
- KK Maxions: Kaluza-Klein (KK) modes with a tree-level mass and specific coupling patterns.
- KK ALPs: KK modes with a tree-level mass but no instanton-induced mixing.
Experimental Scenarios: The formalism is applied to specific experimental configurations, including the ALPS II LSW experiment, the proposed IAXO helioscope, and generic haloscope searches (e.g., ADMX, CAPP).

Key Contributions and Results

Coherence and Interference Effects: The central finding is that axion multiplicity can qualitatively alter experimental signals through coherence and interference.
- Coherent Regime: For sufficiently light axions where the mass splittings are small compared to the experimental resolution (specifically, when the phase difference accumulated over the baseline is negligible), the conversion probability can be enhanced by a factor of $\sim N^2$ relative to a single axion.
- Incoherent Regime: As mass splittings increase or experimental baselines lengthen, decoherence occurs. The signal scales linearly with $N$ ( $\sim N$ ) or, in specific interference configurations, can be suppressed.
- Destructive Interference: The authors demonstrate that multiple axions do not guarantee signal enhancement. In certain parameter regimes (e.g., specific wall thicknesses or magnetic field lengths), destructive interference between axion modes can suppress the regenerated photon signal, potentially reducing experimental sensitivity compared to single-axion expectations.
Light-Shining-Through-a-Wall (LSW):
- The wall thickness ( $L_w$ ) plays a non-trivial role in multi-axion systems. Even without a magnetic field, axions propagate across the wall, accumulating relative phases.
- The regeneration probability contains interference terms dependent on $L_w$ and the mass differences $(m_n^2 - m_k^2)$ .
- Fourier Analysis: The authors propose using Fourier analysis of the signal as a function of experimental parameters (magnetic region length $L$ and wall thickness $L_w$ ) to reconstruct the axion mass spectrum. The interference terms generate distinct peaks in the Fourier domain corresponding to mass splittings, allowing for the identification of axion multiplicity.
Helioscopes:
- Solar axion fluxes are broad in energy. The authors show that while energy integration can wash out oscillatory features, spectral analysis remains sensitive to multiplicity.
- Buffer Gas: Varying the pressure of a buffer gas in the regeneration region allows for tuning the effective photon mass. This can induce resonant conversion for specific axion masses. In multi-axion scenarios, this results in a series of resonance peaks (or a broadened feature for nearly degenerate spectra), providing a diagnostic tool to distinguish single vs. multiple axion origins.
Haloscopes:
- Haloscopes detect dark matter axions via resonant conversion. In multi-axion scenarios, this manifests as multiple distinct resonance lines if mass splittings exceed the experimental linewidth.
- If mass splittings are small, resonances overlap, potentially appearing as a single broadened peak. The signal strength depends on the local dark matter density distribution among the species, which is model-dependent.

Significance and Claims
The paper claims that the presence of multiple axions is not merely a quantitative scaling of single-axion signals but introduces qualitative changes in observational signatures.

Non-Monotonic Sensitivity: The authors emphasize that increasing the number of axion fields does not generically enhance sensitivity; destructive interference can suppress signals in fixed experimental configurations.
Diagnostic Power: By varying experimental parameters (such as magnetic field lengths, wall thickness, or buffer gas pressure), laboratory experiments can act as spectroscopic probes. These variations allow researchers to distinguish between single and multi-axion scenarios and extract information about mass splittings and coupling structures.
Complementarity: The work highlights the complementarity between LSW, helioscope, and haloscope searches. LSW experiments offer full control over production and detection parameters to probe interference, helioscopes provide high-statistics fluxes sensitive to spectral features, and haloscopes offer high mass resolution for dark matter detection.

The authors conclude that existing and near-future experiments possess the diagnostic power to probe axion multiplicity, thereby transforming laboratory searches into tools for exploring the underlying structure of the axion sector beyond the minimal single-field paradigm.

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