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It has been recently shown that puzzling excess events observed by the LSNDand MiniBooNE neutrino experiments could be interpreted as a signal from theradiative decay of a heavy sterile neutrino ($\nu_h$) of the mass from 40 to 80MeV, with a muonic mixing strength $\mix \simeq 10^{-3} - 10^{-2}$, and thelifetime $10^{-11} < \tau_h < 10^{-9}$ s. We discuss bounds on $\mix$ obtainedfrom the recent precision measurements with muons and show that they areconsistent with the above limits. If the $\nu_h$ exists its admixture in theordinary muon or kaon decay would result in the decay chain $\muhd$ or $\khd$,respectively. We propose a new experiment for a sensitive search for theseprocesses in $\mu$ and $K$ decays at rest allowing to either definitivelyconfirm or exclude the existence of the $\nu_h$. To our knowledge, noexperiment has specifically searched for the signature of radiative decay ofmassive neutrinos from particles decays as proposed in this work. The search iscomplementary to the current experimental efforts to clarify the origin of theLSND and MiniBooNE anomalies.

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