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 \cite{Nelson:2010hz},
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 anti-nu 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 BBN 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 anti-nu 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.
