Unsterile-active neutrino mixing: Consequences on radiative decay and bounds from the x-ray background

Abstract

We consider a sterile neutrino to be an unparticle, namely, an unsterile neutrino, with anomalous dimension $\ensuremath{\eta}$ and study its mixing with a canonical active neutrino via a seesaw mass matrix. We show that there is no unitary transformation that diagonalizes the mixed propagator and a field redefinition is required. The propagating or ``mass'' states correspond to an unsterilelike and activelike mode. The unsterile mode features a complex pole or resonance for $0\ensuremath{\le}\ensuremath{\eta}l1/3$ with an ``invisible width'' which is the result of the decay of the unsterile mode into the active mode and the massless particles of the hidden conformal sector. For $\ensuremath{\eta}\ensuremath{\ge}1/3$, the complex pole disappears, merging with the unparticle threshold. The active mode is described by a stable pole, but ``inherits'' a nonvanishing spectral density above the unparticle threshold as a consequence of the mixing. We find that the radiative decay width of the unsterile neutrino into the active neutrino (and a photon) via charged current loops, is suppressed by a factor $\ensuremath{\sim}[2{sin}^{2}({\ensuremath{\theta}}_{0})\frac{{M}^{2}}{{\ensuremath{\Lambda}}^{2}}{]}^{\ensuremath{\eta}/(1\ensuremath{-}\ensuremath{\eta})}$, where ${\ensuremath{\theta}}_{0}$ is the mixing angle for $\ensuremath{\eta}=0$, $M$ is approximately the mass of the unsterile neutrino, and $\ensuremath{\Lambda}\ensuremath{\gg}M$ is the unparticle scale. The suppression of the radiative (visible) decay width of the sterile neutrino weakens the bound on the mass and mixing angle from the x-ray or soft gamma-ray background.