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 $K^{+} \to \pi^{+} \pi^{0} a$. No signal is observed, the upper limits for the branching ratio of the decay are calculated. The $90\%$ confidence level upper limit is changing from $2.5\cdot10^{-6}$ to $2\cdot10^{-7}$ for the ALP mass from 0 to 200 MeV/$c^{2}$, except for the region of $\pi^{0}$ mass, where the upper limit is $4.4\cdot10^{-6}$.

Abstract 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 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 .

The T -odd correlation ξ_π eγ , which is the mixed product of the momenta of e^ + , π^0 , and γ in the system of rest of the kaon divided by M_K^3 , has been measured in the K + → π 0 e + ν e γ radiative decay among 101 200 candidate events detected at the OKA setup. The asymmetry of the distribution in ξ_π eγ is characterized by the ratio A_ξ = N_ + - N_ - /N_ + + N_ - , where N_ + ( - ) is the number of events with positive (negative) ξ. The value A_ξ = (+0.1 ± 3.9(stat.) ± 1.7(syst.)) × 10 –3 or |A_ξ| < 5.4 ×10^ - 3 (90

The paper presents a measurement of the T-odd correlation in radiation decay K^+ →π^0 e^+ν_eγ performed on the installation of the 101200 candidate events of the investigated decay were identified. Measured correlation ξ_π e γ -is a mixed product of moments e^+, π^0, γ in the kaon rest system, normalized by M^3_K. To assess the asymmetry of the distribution by ξ_π e γ the value used is A_ξ= N_+-N_-/N_++N_-, where N_+(-) is the number of events with ξ greater than (less than) zero. For the A_ξ asymmetry, the value is obtained A_ξ = (+0.1 ± 3.9(stat.) ±1.7(syst.))×10^-3 or |A_ξ| < 5.4×10^-3 (90% CL)

On the statistics of ~1.7 × 108 interactions of positively charged kaons on copper nuclei, coherent events of the K+π0 system production are selected. The cross sections for the Coulomb and coherent strong components and their interference in the region of the K*(892) meson are measured. The partial width for the decay K*(892) → K+γ is determined. When studying the mass spectrum of the K+π0 system, an effect which can be interpreted as the interference of the chiral anomaly and the K*(892) s-channel amplitudes is found. This gives an estimate for the ratio of the observed amplitude of the chiral anomaly to the theoretical one: Aexp/Ath = 0.9 ± 0.24(stat.) ± 0.3(syst.).

Results of a study of the K^+ →π ^0 e^+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 K_e3 decay are calculated for different cuts on E^*_γ and cosΘ ^*_eγ . In particular, the branching ratio for E^*_γ>30 MeV and Θ ^*_e γ>20^∘ is measured R = Br(K^+ →π ^0 e^+ν _eγ ) /Br(K^+ →π ^0 e^+ν _e) = = (0.587±0.010( stat .)±0.015( syst .)) × 10^-2 , which is in a good agreement with ChPT O(p^4) calculations.

Results of a study of the $$K^+ \rightarrow \pi ^{0} e^{+} \nu \gamma $$ 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 $$K_{e3}$$ decay are calculated for different cuts on $$E^*_\gamma $$ and $$cos\Theta ^{*}_{e\gamma }$$ . In particular, the branching ratio for $$E^{*}_{\gamma }>30$$ MeV and $$\Theta ^{*}_{e \gamma }>20^{\circ }$$ is measured R = $$\frac{Br(K^+ \rightarrow \pi ^{0} e^{+} \nu _{e} \gamma ) }{Br(K^+ \rightarrow \pi ^{0} e^{+} \nu _{e})} $$ = = (0.587±0.010(stat.)±0.015(syst.)) $$\times 10^{-2}$$ , which is in a good agreement with ChPT $$O(p^{4})$$ calculations.

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 $$K^{+}\rightarrow \pi ^{+}\pi ^{-}\pi ^{+}\gamma $$ decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the $$K^{+}\rightarrow \pi ^{+}\pi ^{-}\pi ^{+}\gamma $$ , with $$E_{\gamma }^{*} > 30\ \hbox {MeV}$$ is equal to $$(0.71 \pm 0.05) \times 10^{-5}$$ . The measured differential branching fraction over photon energy is compared with the prediction of the chiral perturbation theory to $${\mathcal {O}}(p^{4})$$ . A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.

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

A high statistics data sample of the \(K^{+}\rightarrow \mu ^{+}\nu _{\mu }\) decay was accumulated by the OKA experiment in 2012. The missing mass analysis was performed to search for the decay channel \(K^{+}\rightarrow \mu ^{+}\nu _{H}\) with a hypothetic stable heavy neutrino in the final state. The obtained missing mass spectrum does not show peaks that could be attributed to existence of stable heavy neutrinos in the mass range \((270< m_{\nu _{H}} < 375)\) MeV\(/c^{2}\). As a result, upper limits on the branching ratio and on the value of the mixing element \(|U_{\mu H}|^{2}\) are obtained.

Recent results from OKA setup concerning form factor studies in K e 3 decay are presented. About 5.25 M events obtained for decays of 17.7 GeV/ c K + are selected for the analysis. The linear and quadratic slopes for the decay form factor f + ( t ) are measured: λ' + = 2.95 ± 0.022 ± 0.018 × 10 -2 for the linear slope fit and λ + = 2.611 ± 0.035 ± 0.028 × 10 -2 , λ" + = 1.91 ± 0.19 ± 0.14 × 10 -3 for the quadratic one. The scalar and tensor contributions are compatible with zero. Several alternative parametrizations are tried: the Pole fit parameter is found to be M V = 891 ± 3 MeV; the parameter of the dispersive parametrization is measured to be Λ + = 2.458 ± 0.018 × 10 -2 .

The ratio of branching fractions for K^ - → e^ - ν̅_e π ^0 and K − → π − π 0 decays has been measured using the ISTRA+ spectrometer. The result of our measurement is the following: ℛ_Ke_3 /K_2π = 0.2423 ± 0.0015(stat.) ± 0.0037(syst.). Using the current PDG value for the K 2π branching fraction, this result leads to the measured K e 3 branching fraction of Br( K e 3 ) = 0.0501 ± 0.0009 and to the value of | V us | f + (0) = 0.2115 ± 0.0021.

Heavy neutrino νh with mh≲300MeV/c2 can be effectively searched for in kaon decays. We put upper limits on a mixing matrix element |Uμh|2 for radiatively decaying νh from K−→μ−νh(νh→νγ) decay chain in the following parameter region: 30MeV/c2⩽mh⩽80MeV/c2; 10−11s⩽τh⩽10−9s. For the whole region |Uμh|2≲5⋅10−5 for Majorana type of νh and |Uμh|2≲8⋅10−5 for the Dirac case.

The radiative decay K−→μ−νμγ has been studied at ISTRA+ setup in a new kinematic region. About 22K events of K−→μ−νμγ have been observed. The sign and value of FV−FA have been measured for the first time. The result is FV−FA=0.21±0.04(stat)±0.04(syst).

Results of study of the radiative kaon decay K-->pi0 e nu gamma at ISTRA+ setup are presented. 4476 events of this decay have been observed. The branching ratio is measured.

Results of the study of the K− → π0e−νγ decay at ISTRA+ setup are presented. 4476 events of this decay have been observed. The ratio of branching rati os (R), R = Br(K −→π0e−νeγ) Br(K−→π0e−νe) = (1.81± 0.03(stat.)± 0.07(syst.))× 10−2, has been obtained for E∗ γ > 10 MeV andθ ∗ eγ > 10◦. For comparison with previous experiments, the branching ra tio with cutsE∗ γ > 10 MeV, 0.6 < cosθ ∗ eγ < 0.9 is calculated,R = Br(K−→π0e−νeγ) Br(K−→π0e−νe) = (0.47± 0.02(stat.) ± 0.03(syst.)) × 10 −2. For the cutsE∗(γ) > 30 MeV andθ ∗ eγ > 20◦, used in most theoretical papers, we have obtained Br(K− → π0e−νeγ) = (3.13± 0.09± 0.14) × 10−4. For the asymmetryAξ we get Aξ = −0.015±0.021. At present it is the best estimate of this asymmetry.