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A high-statistics data sample of the 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 . No signal is observed, and the upper limits for the branching ratio of the decay are calculated. The 90 % confidence level upper limit changes from 2.5 · 10 - 6 to 2 · 10 - 7 for the ALP mass from 0 to 200 MeV/ c 2 , except for the region of π 0 mass, where the upper limit is 4.4 · 10 - 6 .

The K + → π + π 0 π 0 γ decay is observed by the OKA collaboration. About 60 events of the decay observed with signal:noise ≈ 1 . The branching ratio obtained by normalization to K + → π + π 0 π 0 is measured to be ( 3.7 ± 0.9 ( s t a t ) ± 0.3 ( s y s t ) ) × 10 - 6 for E γ ∗ > 10 MeV . The branching ratio, γ energy spectrum and angular distribution are consistent with ChPT prediction.

— The OKA Collaboration has obtained a new upper limit on the K + → π 0 π 0 π 0 e + ν decay probability which is 65 times lower than the one currently listed by PDG. However it is still about 10 4  times worse than the theoretical prediction. It was suggested that production of pionium A 2π in the final state of the semileptonic K + decay with subsequent A 2π → π 0 π 0 decay will increase the value of theoretical branching ratio due to the absence of five-particle phase space suppression. We demonstrate that despite the gain in the phase space the decay K + → A 2π π 0 e + ν appears to be strongly suppressed because of the smallness of the pionium wave function at zero π mesons separation.

Results of a study of the K+→π0e+νγ decay at OKA setup are presented. More than 32,000 events of this decay are observed. The differential spectra over the photon energy and the photon–electron opening angle in kaon rest frame are presented. The branching ratios, normalized to that of Ke3 decay are calculated for different cuts on Eγ∗ and cosΘeγ∗. In particular, the branching ratio for Eγ∗>30 MeV and Θeγ∗>20∘ is measured R = Br(K+→π0e+νeγ)Br(K+→π0e+νe) = = (0.587±0.010(stat.)±0.015(syst.))×10-2, which is in a good agreement with ChPT O(p4) calculations.

A data acquisition system of the OKA experiment on studying rare kaon decays on the U-70 accelerator is described. The basis of the blocked data acquisition system was the high-speed multichannel information system MISS with autonomous controllers that read out the front-end electronics in the sequential data reading mode and buffering data during the accelerator burst. Data stored in the buffer memory are read out and processed at the end of the accelerator burst. The DATE package builds subevents from event fragments and events from subevents via the event building network. The event building network with the star topology is made with 1GbE-interfaces and 24 × 1 Gb E-switch. The GlusterFS cluster file system underlies the distributed storage system.

The$$K^{+} \\rightarrow \\pi ^{+}\\pi ^{0}\\pi ^{0}\\gamma $$K + → π + π 0 π 0 γ decay is observed by the OKA collaboration. About 60 events of the decay observed with signal:noise$$\\approx 1$$≈ 1 . The branching ratio obtained by normalization to$$K^{+} \\rightarrow \\pi ^{+}\\pi ^{0}\\pi ^{0}$$K + → π + π 0 π 0 is measured to be$$(3.7 \\pm 0.9(stat) \\pm 0.3(syst))\\times 10^{-6}$$( 3.7 ± 0.9 ( s t a t ) ± 0.3 ( s y s t ) ) × 10 - 6 for$$E_{\\gamma }^*>10\\,\\textrm{MeV}$$E γ ∗ > 10 MeV . The branching ratio,$$\\gamma $$γ energy spectrum and angular distribution are consistent with ChPT prediction.

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$$K^{+} \\rightarrow \\pi ^{+} \\pi ^{0} a$$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$$2.5\\cdot 10^{-6}$$2.5 · 10 - 6 to$$2\\cdot 10^{-7}$$2 · 10 - 7 for the ALP mass from 0 to 200 MeV/$$c^{2}$$c 2 , except for the region of$$\\pi ^{0}$$π 0 mass, where the upper limit is$$4.4\\cdot 10^{-6}$$4.4 · 10 - 6 .

A precise measurement of the vector and axial-vector form factors difference \\[F_V-F_A\\] in the \\[K^+ ^+ _ \\] decay is presented. About 95K events of \\[K^+ ^+ _ \\] are selected in the OKA experiment. The result is \\[F_V-F_A=0.134 0.021(stat) 0.027(syst)\\]. Both errors are smaller than in the previous \\[F_V-F_A\\] measurements.

A high statistics data sample of the decays of \\[K^+\\] mesons to three charged particles was accumulated by the OKA experiment in 2012 and 2013. This allowed to select a clean sample of about 450 events with \\[K^+ ^+ ^- ^+ \\] decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the \\[K^+ ^+ ^- ^+ \\], with \\[E_ ^* > 30\\ MeV\\] is equal to \\[(0.71 0.05) 10^-5\\]. The measured differential branching fraction over photon energy is compared with the prediction of the chiral perturbation theory to \\[ O(p^4)\\]. A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.

The paper presents a measurement of the T-odd correlation in radiation decay \\(K^+ ^0 e^+ _e \\) performed on the installation of the 101200 candidate events of the investigated decay were identified. Measured correlation \\(_ e \\) -is a mixed product of moments \\(e^+\\), \\(^0\\), \\(\\) in the kaon rest system, normalized by \\(M^3_K\\). To assess the asymmetry of the distribution by \\(_ e \\) the value used is \\(A_= N_+-N_- N_++N_-\\), where \\(N_+(-)\\) is the number of events with \\(\\) greater than (less than) zero. For the \\(A_\\) asymmetry, the value is obtained \\(A_ = (+0.1 3.9(\\)stat.\\() 1.7(\\)syst.\\())10^-3\\) or \\(|A_| < 5.410^-3 (90\\%~ CL)\\)