On the decaying-sterile-neutrino solution to the electron (anti)neutrino appearance anomalies

We explore the hypothesis that the unexplained data from LSND and MiniBooNE are evidence for a new, heavy neutrino mass-eigenstate that mixes with the muon-type neutrino and decays into an electron-type neutrino and a new, very light scalar particle. We consider two different decay scenarios, one with Majorana neutrinos, one with Dirac neutrinos; both fit the data equally well. We find a reasonable, albeit not excellent, fit to the data of MiniBooNE and LSND. The decaying-sterile-neutrino hypothesis, however, cleanly evades constraints from disappearance searches and precision measurements of leptonic meson decays, as long as $1MeV\gtrsim m_4\gtrsim 10$~keV. The SBN program at Fermilab should be able to definitively test the decaying-sterile-neutrino hypothesis.