Abstract
The effects of $CP$-violating phases in active-sterile solar neutrino oscillations are discussed in a general scheme of $3+{N}_{s}$ mixing, without any constraint on the mixing between the three active and the ${N}_{s}$ sterile neutrinos, assuming only a realistic hierarchy of neutrino mass-squared differences. A generalized Parke formula describing the neutrino oscillation probabilities inside the Sun is calculated. The validity of the analytical calculation and the probability variation due to the unknown $CP$-violating phases are illustrated with a numerical calculation of the evolution equation in the case of $3+1$ neutrino mixing.
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