Cosmic rays hitting the atmosphere make many short-lived particles. This paper looks for hypothetical particles called axions that might be produced when a charged kaon decays into a charged pion and an axion. If the axion lives long enough, it can travel down to large underground detectors and then decay into two photons. The authors use data from Super‑Kamiokande and IceCube to set limits on the axion’s interaction strength for masses up to about 350 MeV (mega–electron volts).

Axions are light particles originally proposed to solve a puzzle in the strong force of nature. More generally, axion‑like particles can appear in many theories beyond the Standard Model. The strength of an axion’s interactions is usually expressed by a number called the decay constant, f_a: larger f_a means weaker interactions. In this work the authors focus on axions produced in the rare kaon decay K+ → π+ a and detected via the two‑photon decay a → γγ (γ denotes a photon).

To estimate how many axions reach detectors, the authors model how many charged kaons are made when cosmic rays strike the air. They use a numerical cascade code (MCEq) together with a standard model of the cosmic‑ray spectrum and a hadronic interaction model called SIBYLL‑2.3c. They then fold in the kaon decay probability into axions and the chance that an axion survives the trip to a detector and decays inside it. The study considers two example coupling patterns: one where axions couple mainly to gluons (the carriers of the strong force) and another where gluon and electroweak couplings are similar.

Using the expected signal shapes and the real data from Super‑Kamiokande and IceCube, the authors derive constraints on f_a for axion masses up to about 350 MeV — nearly the maximum mass allowed by the kaon decay kinematics. These atmospheric searches probe axion parameters in a way that is complementary to laboratory beam‑dump and accelerator experiments. The technique exploits the continuous, wide‑energy cosmic‑ray flux and very large detector volumes to look for rare decays.