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Searching for Axions from Atmospheric Kaon Decays

This paper proposes a novel search for axions produced by atmospheric kaon decays ( $K^{+}\rightarrow\pi^{+}a$ ) that subsequently decay into photon pairs within large underground detectors like Super-Kamiokande and IceCube, using existing data to derive new constraints on the axion decay constant for masses up to approximately 350 MeV.

Original authors: Tousif Raza

Published 2026-09-21

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CC BY 4.0

Original authors: Tousif Raza

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

The universe is filled with invisible particles that constantly rain down on Earth, created when high-energy cosmic rays from deep space collide with the upper atmosphere. These collisions act like a natural particle factory, churning out a shower of secondary particles, including a type of matter called mesons. Among these, a specific particle known as the charged kaon is of particular interest to physicists because it can occasionally transform into other, rarer particles. One such hypothetical particle is the axion, a ghostly, lightweight particle proposed to solve a deep mystery in physics regarding why the universe behaves the way it does under the strong nuclear force. While the existence of axions remains unproven, their potential properties suggest they could be produced in these atmospheric collisions and, if they live long enough, travel deep underground to be detected by massive sensors hidden beneath mountains or ice.

A researcher has turned their attention to this natural laboratory, investigating whether axions are being created in the Earth's atmosphere through the decay of charged kaons. Instead of building a machine to smash particles together, they looked at the data collected by two of the world's largest underground observatories: Super-Kamiokande in Japan and IceCube in Antarctica. These facilities are designed to catch neutrinos, but they are also sensitive enough to spot the faint signature of an axion decaying into two flashes of light. The researcher calculated how many axions should be produced by the constant bombardment of cosmic rays, how many would survive the journey through the atmosphere and rock to reach the detectors, and what their decay would look like inside the instrumented volumes. They focused on axions with masses up to about 350 million electron volts, a range that is kinematically possible for the kaon decays occurring in the sky above.

The study reveals that while no axions were found, the absence of a signal allows scientists to set strict limits on how these particles could behave. By comparing their predictions against the actual data recorded by Super-Kamiokande and IceCube, the researcher determined which combinations of axion mass and interaction strength are ruled out. They found that for axions in the mass range they studied, the detectors would have seen a clear signal if the particles interacted with light or matter more strongly than a certain threshold. Specifically, the data excludes a wide range of possibilities for the axion decay constant, a value that dictates how easily the particle interacts with the rest of the universe. The analysis showed that Super-Kamiokande provided the strongest constraints for lower-energy axions, while IceCube, with its ability to detect higher-energy events, offered complementary limits for heavier axions that travel further before decaying.

This work demonstrates that the Earth's atmosphere serves as a powerful, continuous source for searching for new physics, offering a unique perspective that complements traditional laboratory experiments. The researcher showed that the flux of cosmic rays creates a steady stream of potential axions, and that large underground detectors can effectively act as traps for these elusive particles. Although the study did not discover the axion, it successfully narrowed the search space, proving that atmospheric kaon decays provide a novel and effective way to probe the properties of these hypothetical particles. The findings suggest that future, even larger detectors could push these limits further, potentially uncovering the axion or definitively closing the door on certain versions of this particle.

Technical Summary: Searching for Axions from Atmospheric Kaon Decays

Problem and Motivation
The strong CP problem in Quantum Chromodynamics (QCD) necessitates an explanation for the vanishingly small effective vacuum angle ( $|\bar{\theta}| \lesssim 10^{-10}$ ). The Peccei-Quinn mechanism addresses this by introducing a global $U(1)_{PQ}$ symmetry, the spontaneous breaking of which yields the axion, a pseudo-Nambu-Goldstone boson. More broadly, axion-like particles (ALPs) appear in various Standard Model extensions and string compactifications, potentially serving as dark matter or driving inflation. While extensive searches exist via accelerator-based beam-dump experiments, this work investigates a distinct production mechanism: the rare flavor-changing neutral-current (FCNC) decay of charged kaons ( $K^+ \to \pi^+ a$ ) occurring naturally in the Earth's atmosphere. Cosmic-ray interactions with atmospheric nuclei generate a continuous, isotropic flux of secondary mesons, including charged kaons, creating a natural fixed-target environment for producing weakly coupled light particles.

Methodology
The author employs an Effective Field Theory (EFT) framework to describe axion interactions with Standard Model gauge fields, considering two benchmark scenarios: "gluon-dominance" (coupling primarily to gluons) and "co-dominance" (coupling equally to gluons and electroweak bosons).

Flux Modeling: The atmospheric production of axions is modeled using the Matrix Cascade Equations (MCEq) numerical code. The simulation incorporates the Hillas–Gaisser model for primary cosmic rays, the NRLMSISE-00 atmospheric model, and the SIBYLL-2.3c hadronic interaction model. The differential axion flux is calculated by integrating the parent charged-kaon flux over the atmospheric production height, accounting for the kinematics of the two-body decay $K^+ \to \pi^+ a$ and the survival probability of axions propagating to underground detectors.
Detector Analysis: The study utilizes data from two large underground neutrino detectors: Super-Kamiokande and IceCube. The analysis focuses on the diphoton decay channel ( $a \to \gamma\gamma$ $a \to γ γ$ ), which reconstructs as electron-like events.
- Super-Kamiokande: Analyzes the zenith-angle distribution of events (0 to 1) over a 5326-day interval, covering an axion energy range of approximately 1–90 GeV.
- IceCube: Analyzes the reconstructed energy distribution for reconstructed zenith angles in the range $0.2 \le \cos \theta \le 1$ over a 641-day interval, covering a much higher energy range (562 GeV to 446 TeV).
Statistical Framework: Constraints are derived using a binned Poisson likelihood-ratio test statistic ( $\chi^2$ ) comparing observed data against the sum of expected background and signal. The analysis treats the inverse axion decay constant ( $1/f_a$ ) as the parameter of interest for fixed axion masses ( $m_a$ ). Additionally, a model-independent analysis constrains the product of branching ratios $BR(K^+ \to \pi^+ a) \times BR(a \to \text{visible})$ as a function of the axion proper decay length ( $c\tau_a$ ).

Key Contributions and Results

Novel Production Channel: The paper establishes atmospheric kaon decays as a viable probe for axions, covering the mass range $m_a \lesssim 350$ MeV, which is kinematically accessible in $K^+ \to \pi^+ a$ .
Constraints on $f_a$ : Using Super-Kamiokande and IceCube data, the author derives 90% confidence level (C.L.) exclusion limits on the axion decay constant $f_a$ $f_{a}$ .
- Super-Kamiokande provides the strongest constraints over most of the mass range, reaching $1/f_a \sim 10^{-5} \text{ GeV}^{-1}$ . This sensitivity is attributed to the larger atmospheric kaon flux at lower energies (1–90 GeV).
- IceCube yields weaker constraints on $f_a$ (reaching $\sim 10^{-4} \text{ GeV}^{-1}$ ) due to the lower flux of high-energy parent kaons. However, the high Lorentz boosts of axions in the IceCube energy range extend their decay lengths, allowing sensitivity to larger values of $1/f_a$ (weaker couplings) for which lower-energy axions would predominantly decay before reaching Super-Kamiokande.
Complementarity: The two experiments probe complementary regions of the axion parameter space. Super-Kamiokande is sensitive to lower masses and longer lifetimes relative to the detector distance, while IceCube's high-energy reach allows it to probe comparatively larger values of $1/f_a$ via time-dilation effects.
Model-Independent Limits: The study sets 90% C.L. upper limits on the branching ratio product $BR(K^+ \to \pi^+ a) \times BR(a \to \text{visible})$ down to $\sim 10^{-10}$ . These limits are most sensitive for proper decay lengths of $c\tau_a \sim 1\text{--}3$ km (Super-K) and $c\tau_a \sim 10^{-3}\text{--}10^{-2}$ km (IceCube).

Significance and Claims
The paper claims that atmospheric kaon decays offer a "novel probe" of axion parameter space that is complementary to existing terrestrial bounds from beam-dump experiments (e.g., NA62, E949, CHARM) and astrophysical constraints (e.g., SN1987A). While the derived constraints do not exceed the strongest existing beam-dump limits, the atmospheric approach provides a distinct experimental signature characterized by a broad energy spectrum, an extended production region, and different propagation baselines compared to accelerator-based experiments. The author concludes that large underground neutrino detectors offer independent and complementary sensitivity to long-lived particles produced in atmospheric meson decays, with future facilities like Hyper-Kamiokande and IceCube-Gen2 poised to further extend this sensitivity.

Technical Summary: Searching for Axions from Atmospheric Kaon Decays

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