Signatures of heavy sterile neutrinos at long baseline experiments

Abstract

Sterile neutrinos with masses $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{eV}$ or higher, allowed with the current oscillation data, can potentially play an important role in astrophysics and cosmology. We explore possible signatures of such sterile neutrinos at long baseline experiments. We determine the neutrino conversion probabilities analytically in a 4-neutrino framework, including matter effects, treating the sterile mixing angles ${\ensuremath{\theta}}_{14}$, ${\ensuremath{\theta}}_{24}$, ${\ensuremath{\theta}}_{34}$, the deviation of ${\ensuremath{\theta}}_{23}$ from maximality, as well as ${\ensuremath{\theta}}_{13}$ and the ratio $\ensuremath{\Delta}{m}_{\ensuremath{\bigodot}}^{2}/\ensuremath{\Delta}{m}_{\mathrm{atm}}^{2}$ as small parameters for a perturbative expansion. This gives rise to analytically tractable expressions for flavor conversion probabilities from which effects of these parameters can be clearly understood. We numerically calculate the signals at a neutrino factory with near and far detectors that can identify the lepton charge, and point out observables that can discern the sterile mixing signals. We find that clean identification of sterile mixing would be possible for ${\ensuremath{\theta}}_{24}{\ensuremath{\theta}}_{34}\ensuremath{\gtrsim}0.005$ ($3\ensuremath{\sigma}$) and ${\ensuremath{\theta}}_{14}\ensuremath{\gtrsim}0.06\text{ }\text{ }\mathrm{rad}$ ($3\ensuremath{\sigma}$) with the current bound of ${\ensuremath{\theta}}_{13}<0.2\text{ }\text{ }\mathrm{rad}$; a better ${\ensuremath{\theta}}_{13}$ bound would allow probing smaller values of sterile mixing. We also generalize the formalism for any number of sterile neutrinos, and demonstrate that only certain combinations of sterile mixing parameters are relevant irrespective of the number of sterile neutrinos. This also leads to a stringent test of the scenario with multiple sterile neutrinos that currently is able to describe all the data from the short baseline experiments, including LSND and MiniBooNE.