A search for the massless dark photon in the decay K^+→ π^+π^0 γ is performed with the OKA detector exposed to 17.7 GeV/c RF separated secondary beam of the U70 Proton Synchrotron. A high-statistics data sample of the K^+ decays is used for a missing mass search of the stable massless invisible dark photon () in the final state. In the absence of a statistically valuable signal the upper limit on the branching ratio of the decay Br<2.0×10^-6 is obtained with a 90

Results of study of the K^+→π^0e^+νγ decay at OKA setup are presented. More than 150K candidates for this decay have been selected. The branching ratios, normalized to that of K_e3 decay are calculated for different cuts on E^*_γ and Θ^*_eγ . In particular, the branching ratio for E^*_γ>30 MeV and Θ^*_eγ>20^∘ is measured R=Br(K^+→π^0e^+ν_eγ)/Br(K^+→π^0e^+ν_e)=(0.610± 0.007(stat.)± 0.011(syst.))× 10^-2 , which is in a good agreement with ChPT O(p^6) calculations.

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 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.

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 search for the K+ → π0π0π0e+ν decay is performed by the OKA collaboration. The search is based on 3.65 × 109 K+ decays. No signal is observed. The upper limit set is BR(K+ → π0π0π0e+ν) < 5.4 × 10–8 90

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.

The K (+) -> pi (+) pi( 0) pi (0) gamma decay is observed by the OKA collaboration. About 60 events of the decay observed with signal:noise approximate to 1. The branching ratio obtained by nor-malization to K (+) -> pi (+) pi( 0) pi (0) gamma is measured to be (3.7 +/- 0.9(stat)+/- 0.3(syst))x10(-6)for E-gamma(& lowast;)>10 MeV. The branching ratio,gamma energy spectrum and angular distribution are consistent with ChPT prediction

The K^+→π ^+π ^0π ^0γ 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 ^0π ^0 is measured to be (3.7 ± 0.9(stat) ± 0.3(syst))× 10^-6 for E_γ^*>10 MeV . The branching ratio, 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 .

The $K^{+} \to \pi^{+}\pi^{0}\pi^{0}\gamma$ decay is observed by the OKA collaboration. The branching ratio is measured to be $(4.1 \pm 0.9(stat) \pm 0.4(syst))\times 10^{-6}$. The branching ratio and $\gamma$ energy spectrum are consistent with ChPT prediction.

The K^+→π^+π^0π^0γ decay is observed by the OKA collaboration. The branching ratio is measured to be (4.1 ± 0.9(stat) ± 0.4(syst))× 10^-6. The branching ratio and γ energy spectrum are consistent with ChPT prediction.

On the statistics of $$\sim 1.7\times 10^{8}$$ interactions of positively charged kaons on copper nuclei coherent events of the $$K^{+}\pi^{0}$$ -system production are selected. Cross sections for the Coulomb, coherent strong components and their interference in the region of $$K^{*}(892)$$ -meson are measured. When studying the mass spectrum of the $$K^{+}\pi^{0}$$ -system, an effect is found, which can be interpreted as the interference of the chiral anomaly and the $$K^{*}(892)$$ s-channel amplitudes. This gives an estimate for the ratio of the observed amplitude of the chiral anomaly to the theoretical one: $$A_{\textrm{exp}}/A_{\textrm{th}}=0.90\pm 0.24\textrm{(stat.)}\pm 0.3$$ (syst.).

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.