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Heavy neutrino nu_h with m_h < 300MeV/c^2 can be effectively searched for in kaon decays. We put upper limits on mixing matrix element |U_mu_h}|^2 for radiatively decaying nu_h from K->mu nu_h (nu_h -> nu gamma) decay chain in the following parameter region: 30MeV/c^2 < m_h < 80MeV/c^2; 10^{-11}sec < tau_h < 10^{-9}sec. For the whole region |U_{mu h}|^2 < 5 x 10^{-5} for Majorana type of nu_h and | U_{mu h}|^2 < 8 x 10^{-5} for the Dirac case.
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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.
The radiative decay K->mu nu gamma has been studied at ISTRA+ setup in a new kinematical region. About 22K events of K^- -> mu^- nu_mu gamma have been observed. The sign and value of Fv-Fa have been measured for the first time. The result is Fv-Fa=0.21(4)(4).
The recent progress in search for T-violating transverse muon polarization in the decays K^+ --> pi^0 mu^+ nu and K^+ --> mu^+ nu gamma in the on-going experiment E246 at KEK is reported. Future prospects in polarization measurements are also discussed.
A high statistics data sample of the $K^{+}tomu^{+} u_{mu}$ decay was accumulated by the OKA experiment in 2012. The missing mass analysis was performed to search for the decay channel $K^{+}tomu^{+} u_{H}$ with a hypothetic stable heavy neutrino in the final state. The obtained missing mass spectrum does not show peaks which could be attributed to existence of stable heavy neutrinos in the mass range (220 $< m_{ u_{H}} <$ 375) MeV$/c^{2}$. As a result, we obtain upper limits on the branching ratio and on the value of the mixing element $|U_{mu H}|^{2}$.
High statistics data for the K+ -> mu+ nu gamma decay can allow the precision determination of the kaon structure dependent form factors and the kaon polarizability. This study is possible at the proposed FNAL CKM experiment. CKM (Charged Kaons at the Main injector) is a decay-in-flight spectrometer with two RICH, and designed to run at the main injector with a high kaon flux. The radiative decay data will be taken complementary to the primary CKM effort to study the rare kaon decay (K to pi nu nubar) for which CKM was primarily designed. We summarize here the underlying physics of K ->mu nu gamma, the experimental status, and how the CKM spectrometer will be adapted for this study.
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