Matter effects and CP violating neutrino oscillations with nondecoupling heavy neutrinos

The evolution equation for active and sterile neutrinos propagating in a general anisotropic or polarized background environment is found and solved for a special case when heavy neutrinos do not decouple, resulting in nonunitary mixing among light neutrino states. Then new $\mathrm{CP}$ violating neutrino oscillation effects appear. In contrast with the standard unitary neutrino oscillations these effects can be visible even for two flavor neutrino transitions and even if one of the elements of the neutrino mixing matrix is equal to zero. They do not necessarily vanish with $\ensuremath{\delta}{m}^{2}\ensuremath{\rightarrow}0$ and they are different for various pairs of flavor neutrino transitions $({\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}),$ $({\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}),$ $({\ensuremath{\nu}}_{\ensuremath{\tau}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}).$ Neutrino oscillations in vacuum and Earth's matter are calculated for some fixed baseline experiments and a comparison between unitary and nonunitary oscillations are presented. It is shown, taking into account the present experimental constraints, that heavy neutrino states can affect $\mathrm{CP}$ and T asymmetries. This is especially true in the case of ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ oscillations.