# Muon Capture Constraints on Sterile Neutrino Properties

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We show that ordinary and radiative muon capture impose stringent constraints on sterile neutrino properties. In particular, we consider a sterile neutrino with a mass between $40$ and $80~{\rm MeV}$ that has a large mixing with the muon neutrino and decays predominantly into a photon and light neutrinos due to a large transition magnetic moment. Such a model was suggested as a possible resolution to the puzzle presented by the results of the LSND, KARMEN, and MiniBooNE experiments. We find that the scenario with the radiative decay to massless neutrinos is ruled out by measurements of the radiative muon capture rates at TRIUMF in the relevant mass range by a factor of a few in the squared mixing angle. These constraints are complementary to those imposed by the process of electromagnetic upscattering and de-excitation of beam neutrinos inside the neutrino detectors induced by a large transition magnetic moment. The latter provide stringent constraints on the size of the transitional magnetic moment between muon, electron neutrinos and $N$. We also show that further extension of the model with another massive neutrino in the final state of the radiative decay may be used to bypass the constraints derived in this work.