Comments on arXiv:1011.3046 "Muon Capture Constraints on Sterile Neutrino Properties"

It has been very recently reported (McKeen, Pospelov, arXive:1011.3046) that the parameter region suggested for an explanation of the neutrino oscillation results from the LSND, KARMEN and MiniBooNE experiments in terms of the production and radiative decay of a heavy neutrino ($\nu_h$) can be ruled out based on the measurements of the radiative muon capture (RMC) on hydrogen. We calculate limits on mixing strength between the $\nu_h$ and $\nu_\mu$ by using results of this experiment, and find out that they essentially disagree with the reported bounds. For the $\nu_h$ with mass 60 MeV our limit is worse by a factor of 5, while for 90 MeV it is worse by about two orders of magnitude. We also noticed the wrong behavior of the reported limit curve in the low mass region. The importance of accurate Monte Carlo simulations of the $\nu_h$ signal in the RMC experiment is stressed. Our conclusion is that the whole LSND-MiniBooNE parameter region cannot be ruled out by the RMC measurements.