  We consider searching for light sterile fermions and new forces by using long
baseline oscillations of neutrinos and antineutrinos. A new light sterile state
and/or a new force can lead to apparent CPT violation in muon neutrino and
antineutrino oscillations. As an example, we present an economical model of
neutrino masses containing a sterile neutrino. The potential from the Standard
Model neutral current gives rise to a difference between the disappearance
probabilities of neutrinos and antineutrinos, when mixing with a light sterile
neutrino is considered. The addition of a B-L interaction adds coherently to
the neutrino current potential and increases the difference between neutrino
and antineutrino disappearance. We find that this model can improve the fit to
the results of MINOS for both neutrinos and antineutrinos, without any CPT
violation, and that the regions of parameter space which improve the fit are
within experimental constraints.
