The LSND/MiniBooNe excess events and heavy neutrino from muon and kaon decays

It has been recently shown that puzzling excess events observed by the LSND and MiniBooNE neutrino experiments could be interpreted as a signal from the radiative decay of a heavy sterile neutrino ($\nu_h$) of the mass from 40 to 80 MeV, with a muonic mixing strength $\mix \simeq 10^{-3} - 10^{-2}$, and the lifetime $10^{-11} < \tau_h < 10^{-9}$ s. We discuss bounds on $\mix$ obtained from the recent precision measurements with muons and show that they are consistent with the above limits. If the $\nu_h$ exists its admixture in the ordinary muon or kaon decay would result in the decay chain $\muhd$ or $\khd$, respectively. We propose a new experiment for a sensitive search for these processes in $\mu$ and $K$ decays at rest allowing to either definitively confirm or exclude the existence of the $\nu_h$. To our knowledge, no experiment has specifically searched for the signature of radiative decay of massive neutrinos from particles decays as proposed in this work. The search is complementary to the current experimental efforts to clarify the origin of the LSND and MiniBooNE anomalies.