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.

The NA62 experiment will begin taking data in 2015. Its primary purpose is a 10% measurement of the branching ratio of the ultrarare kaon decay $K^+ \to \pi^+ \nu \bar{ \nu }$, using the decay in flight of kaons in an unseparated beam with momentum 75 GeV/c.The detector and analysis technique are described here.

The NA48/2 Collaboration at CERN has accumulated and analysed unprecedented statistics of rare kaon decays in the K_e4 modes: K_e4(+-) (K^±→π^+ π^- e^±ν) and K_e4(00) (K^±→π^0 π^0 e^±ν) with nearly one percent background contamination. It leads to the improved measurement of branching fractions and detailed form factor studies. New final results from the analysis of 381 K^±→π^±γγ rare decay candidates collected by the NA48/2 and NA62 experiments at CERN are presented. The results include a decay rate measurement and fits to Chiral Perturbation Theory (ChPT) description.

With the use of the general variational principle of selforganization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the control over the evolution of systems of many particles. The geometric nature of this principle is analyzed. On the basis of the de Broglie-Bohm representation of the Schrodinger equation, we establish a connection of the nonlocality and the coherence of the systems of many particles with mass entropic forces. The defining role of a coherent acceleration and a space-time curvature in the control over the synthesis of new structures in systems with varying constraints is demonstrated. The basic criteria for electromagnetic fields to initiate the processes of self-organizing synthesis and for the quantum properties of a nonlocality on macroscopic scales, which are necessary for the self-organizing synthesis, are formulated.

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).

The rare decay K L 0 → π 0 ν ṽ branching ratio measurement is one of the clearest Standard Model test. Calculations based on the SM predict Br( K L 0 → π 0 ν ṽ ) ≈ 2.8 × 10 −11 , but the most accurate experimental value Br( K L 0 → π 0 ν ṽ ) < 6.7 × 10 −8 (90

The projected KLOD facility is intended for finding and investigating the ultrarare decay K L 0 → π0ν\(\bar \nu \); its branching ratio predicted by the Standard Model is Br = (3.0 ± 0.6) × 10−11. Designing and testing the prototype of the decay-volume veto system and beam veto calorimeter, which are the most important detectors of the facility, are considered. It is shown that the proposed beam veto calorimeter is able to detect γ rays with a high efficiency at the neutron flux of 300 MHz.

The rare decay K L 0 → π0ν\(\tilde v\) branching ratio measurement is one of the clearest Standard Model test. Calculations based on the SM predict Br(K L 0 → π0ν\(\tilde v\)) ≈ 2.8 × 10−11, but the most accurate experimental value Br(K L 0 → π0ν\(\tilde v\)) < 6.7 × 10−8 (90% C.L.). We present design of a new experimental setup KLOD (U-70 accelerator, IHEP, Protvino) for K L 0 → π0ν\(\tilde v\) branching ratio measurement. Sensitivity of the KLOD experiment will be enough for registration of 2.4 events K L 0 → π0ν\(\tilde v\) for every 10 days of the data taking (according to SM predictions).

The future investigations of rare decays of elementary particles demand the creation of new-generation setups which can perform much greater statistics and precise experimental data. The proposed new setups at CERN, NA62 (NA48/3 (P326SPS)), and at IHEP, OKA, are planned to obtain experimental data at the level of 10−10–10−12 branching ratio. The main goals of both experimental programs are connected with the study of ultrarare kaon decays, but beams of these experiments contain 95% (NA48) and 50% (OKA) of pions. It is natural to use the pion part of these beams for study of rare pion decays. The pion program may be performed simultaneously or consecutively with the main tasks. Such problems as search for tensor interaction, measurements of branching ratio and form factors of some pion decays, effects of polarization, and search for new particles are included in this program.

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.

Using data collected with the ISTRA+ spectrometer during the 2001 run of the U-70 proton synchrotron in Protvino, the first observation of the radiative kaon decay K − → µ−π0γν is reported. The ratio Br(K µ3γ, 5 < E*γ < 30 MeV)/Br(K µ3) is found to be [0.270 ± 0.029(stat.) ± 0.026(syst.)]% and the ratio Br(K µ3γ, 30 < E*γ < 60 MeV)/Br(K µ3) = [0.0448 ± 0.0068(stat.) ± 0.0099(syst.)]%. These ratios are consistent with the theoretical predictions 0.21 and 0.047%, respectively. The measured angular distribution asymmetry for the region 5 < E*γ < 30 MeV, A(cos ϑ*µγ) = 0.093 ± 0.141, is two standard deviations away from the theoretical prediction of 0.354. The measured asymmetry in the T-odd variable ξ = pγ · (pµ × pπ)/m K 3 is −0.03 ± 0.13.

Results of study of the K^ - →π ^0 e^ - νγ decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be R = Br(K^ - →π ^0 e^ - ν_e γ )/Br(K^ - →π ^0 e^ - ν_e ) = (1.81±0.03(stat.)±0.07(syst.)) × 10 −2 for E * γ > 10 MeV and θ * eγ > 10°. For comparison with the previous experiment the branching ratio with cuts E * γ > 10 MeV, 0.6 < cos θ * eγ < 0.9 is calculated: R = Br(K^ - →π ^0 e^ - ν_e γ )/Br(K^ - →π ^0 e^ - ν_e ) = (0.47±0.02(stat.) ± 0.03(syst.)) × 10 −2 . For the cuts E * γ > 30 MeV and θ * eγ > 20°, used in most theoretical papers, Br = (3.06 ± 0.09(stat.) ± 0.14(syst.)) × 10 −4 . For the asymmetry we get A ξ = −0.015 ± 0.021. At present it is the best estimate of this asymmetry.

Using data collected with the ISTRA+ spectrometer during the 2001 run of the U-70 proton synchrotron in Protvino, the first observation of the radiative kaon decay K- --> mu(-) pi(0) gamma nu is reported. The ratio Br(K-mu 3 gamma, 5 < E-gamma* < 30 MeV)/ Br(K-mu 3) is found to be [0.270 +/- 0.029(stat.) +/- 0.026( syst.)]% and the ratio Br(K-mu 3 gamma, 30 < E-gamma* < 60 MeV)/ Br(K-mu 3) = [0.0448 +/- 0.0068( stat.) +/- 0.0099( syst.)]%. These ratios are consistent with the theoretical predictions 0.21 and 0.047%, respectively. The measured angular distribution asymmetry for the region 5 < E-gamma* < 30 MeV, A(cos theta*(mu gamma)) = 0.093 +/- 0.141, is two standard deviations away from the theoretical prediction of 0.354. The measured asymmetry in the T - odd variable xi = p(gamma) . (p(mu) x p(pi))/m(K)(3) is - 0.03 +/- 0.13.

Results of study of the \(K^ - \to \pi ^0 e^ - \overline \nu \gamma \) decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be \(R = \frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}\) = (1.81±0.03(stat.)±0.07(syst.)) × 10−2 for E*γ > 10 MeV and θ*eγ > 10°. For comparison with the previous experiment the branching ratio with cuts E*γ > 10 MeV, 0.6 < cos θ*eγ < 0.9 is calculated: R = \(\frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}\) = (0.47±0.02(stat.) ± 0.03(syst.)) × 10−2. For the cuts E*γ > 30 MeV and θ*eγ > 20°, used in most theoretical papers, Br = (3.06 ± 0.09(stat.) ± 0.14(syst.)) × 10−4. For the asymmetry we get A ξ = −0.015 ± 0.021. At present it is the best estimate of this asymmetry.

Results of study of the K- -> pi(0)e(-)(v) over bar gamma decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be R = Br(K- -> pi(0)e(-)(v) over bar (e)gamma)/Br(K- -> pi(0)e(-)(v) over bar (e)) = (1.81 +/- 0.03(stat.) +/- 0.07(syst.)) x 10(-2) for E-gamma* > 10 MeV, 0.6 < cos theta(e gamma)* < 0.9 is calculated: R = Br(K- -> pi(0)e(-)(v) over bar (e)gamma)/Br(K- -> pi(0)e(-)(v) over bar (e)) = (0.47 +/- 0.02(stat.) +/- 0.03 (syst.)) x 10(-2). For the cuts E-gamma* > 30 MeV and theta(e gamma)* > 20 degrees, used in most theoretical papers, Br = (3.06 +/- 0.09(stat.) +/- 0.14(syst.)) x 10(-4). For the asymmetry we get A(xi) = -0.015 +/- 0.021. At present it is the best estimate of this asymmetry.