Neutrino phenomenology in a 3+1+1 framework

Evidence continues to grow in the MiniBooNE (MB) antineutrino mode supporting a low-energy excess compatible with the MB neutrino mode and possibly also confirming the results of the LSND experiment. At least one sterile neutrino is required to explain the anomalies consistent with the observations of other experiments. At the same time, there is a strong tension between the positive signals of LSND and MB and the null results of nu(e) and nu(mu) disappearance experiments. We explore a scenario, first proposed in [A. E. Nelson, Phys. Rev. D 84, 053001 (2011).], where the presence of an additional heavy sterile neutrino (with mass well above an eV) can alleviate tension between LSND, MB and the null results of disappearance experiments. We compare and contrast this 3 + 1 + 1 scenario with the more standard 3 + 1 scenario and carry out global fits to all oscillation data including new 2011 MB (nu) over bar data. We find that the tension can be somewhat alleviated and that a phenomenologically viable window for the heavy neutrino, consistent with rare decays and big bang nucleosynthesis constraints, can be found if the fifth neutrino has a mass of order 0.3-10 GeV. We also find, however, that the 2011 MB (nu) over bar data exacerbates the tension with null experiments in both the 3 + 1 and 3 + 1 + 1 models when the lowest energy bins are included, resulting in little improvement in the global fit. We also discuss the implications of an additional neutrino for the reactor and gallium anomalies, and show that an oscillation explanation of the anomalies is disfavored by cosmological considerations, direct searches, and precision electroweak tests.