Revisiting quantum decoherence for neutrino oscillations in matter with constant density

Abstract

We reexamine the matter neutrino oscillation probabilities considering the decoherence phenomenon as a subleading effect. In this paper we point out the relevance of having the correct interpretation of the decoherence matrix in the different quantum bases, within the framework of neutrino oscillation probabilities in matter. Based on this treatment we develop an analytical formula for matter neutrino oscillation probabilities for three generations, with a range of application up to the decoherence parameter $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{GeV}$. We observe that, due to decoherence, the amplitudes of the neutrino/antineutrino oscillation probabilities increase in an energy independent way. We also find that decoherence can reduce the absolute value of the $CP$ asymmetry, relative to its value at the pure oscillation case. As a side effect we have found a degeneracy between the decoherence parameter $\mathrm{\ensuremath{\Gamma}}$ and the $CP$ violation phase $\ensuremath{\delta}$.