Searches for the light invisible axion-like particle in K⁺ → π ⁺π ⁰ a decay

A high-statistics data sample of the K⁺ K + decays is recorded by the OKA collaboration. A missing mass analysis is performed to search for a light invisible pseudoscalar axion-like particle (ALP) a in the decay K⁺ → π ⁺ π ⁰ a K + → π + π 0 a . No signal is observed, and the upper limits for the branching ratio of the decay are calculated. The $$90%$$ 90 % confidence level upper limit changes from 2.5· 10⁻⁶ 2.5 · 10 - 6 to 2· 10⁻⁷ 2 · 10 - 7 for the ALP mass from 0 to 200 MeV/ c² c 2 , except for the region of π ⁰ π 0 mass, where the upper limit is 4.4· 10⁻⁶ 4.4 · 10 - 6 .