Unsterile-Active Neutrino Mixing

We consider a sterile neutrino to be an unparticle, namely an "unsterile" neutrino, and study its mixing with a canonical active neutrino via a see-saw mass matrix. There is no unitary transformation that diagonalizes the mixed propagator and a field redefinition is required. The unsterile-like propagating mode features a resonance for anomalous dimension between 0 and 1/3, but the complex pole disappears when the anomalous dimension is larger than 1/3. The active-like propagating mode is described by a stable pole, but inherits a non-vanishing spectral density above the unparticle threshold. We also find that the radiative decay width of the unsterile neutrino into the active neutrino (and a photon) via charged current loops is suppressed, and this suppression weakens the bound from the X-ray or soft gamma-ray background when one considers the unsterile neutrino to be a dark matter candidate.