Collective neutrino oscillations in matter and CP violation

We explore CP violation effects on the neutrino propagation in dense environments, such as in core-collapse supernovae, where the neutrino self-interaction induces nonlinear evolution equations. We demonstrate that the electron (anti)neutrino fluxes are not sensitive to the CP violating phase if the muon and tau neutrinos interact similarly with matter. On the other hand, we numerically show that new features arise, because of the nonlinearity and the flux dependence of the evolution equations, when the muon and tau neutrinos have different fluxes at the neutrinosphere (due to loop corrections or physics beyond the standard model). In particular, the electron (anti)neutrino probabilities and fluxes depend upon the CP violating phase. We also discuss the CP effects induced by radiative corrections to the neutrino refractive index.