A Fourth Neutrino and its Consequences on CP Asymmetries
A general analysis of the consequences of including a fourth neutrino in the standard model matter content, on CP violating observables at neutrino oscillation experiments, is presented. Neutrino oscillations in vacuum and with matter effects are studied. For the former we update and generalize previous studies on CP asymmetries with an additional active neutrino using an updated fit of the PMNS mixing matrix. We study the values of the new CP violating phases which maximize the different CP asymmetries in T2K and MINOS-like setups aiming to elucidate if the new phases yield measurable effects in the most favorable case. We show that due to a combined effect of kinematics and unitarity it is possible to obtain an observable asymmetry in the survival channels without violating CPT. For the MINOS-like setup, we find maximum asymmetries in vacuum of the order of 2% and 4% for the $\nu_\mu \to \nu_e$ and $\nu_e \to \nu_\tau$ channels respectively. For the T2K-like setup we obtain maximum asymmetries of the order of 6% in the survival $\nu_\mu \to \nu_\mu$ channel. Tree level matter effects enhance the former reaching asymmetries of the order of 10% for the $\nu_\mu \to \nu_e$ and $\nu_e \to \nu_\tau$ channels, while the $\nu_\mu \to \nu_\mu$ survival channel changes slightly depending on the mass hierarchy. Box diagrams with the fourth mass eigenstate as a virtual particle were also considered, the corrections to the scattering amplitude being negligible.