Neutrino oscillation in dense matter

Abstract

As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo ``vacuum-dominated,'' ``resonance,'' and ``matter-dominated'' three different stages successively. Neutrinos endure very different matter effects, and therefore present very different oscillation behaviors in these three different cases. In this paper, we focus on the less discussed matter-dominated case (i.e., $|{A}_{\mathrm{CC}}|\ensuremath{\gg}|\mathrm{\ensuremath{\Delta}}{m}_{31}^{2}|$), study the effective neutrino mass and mixing parameters as well as neutrino oscillation probabilities in dense matter using the perturbation theory. We find that as the matter parameter $|{A}_{\mathrm{CC}}|$ growing larger, the effective mixing matrix in matter $\stackrel{\texttildelow{}}{V}$ evolves approaching a fixed $3\ifmmode\times\else\texttimes\fi{}3$ constant real matrix which is free of $CP$ violation and can be described using only one simple mixing angle $\stackrel{\texttildelow{}}{\ensuremath{\theta}}$ which is independent of ${A}_{\mathrm{CC}}$. As for the neutrino oscillation behavior, ${\ensuremath{\nu}}_{e}$ decoupled in the matter-dominated case due to its intense charged-current interaction with electrons while a two-flavor oscillation are still presented between ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$. Numerical analysis are carried on to help understanding the salient features of neutrino oscillation in matter as well as testing the validity of those concise approximate formulas we obtained. At the end of this paper, we make a very bold comparison of the oscillation behaviors between neutrinos passing through the Earth and passing through a typical white dwarf to give some embryonic thoughts on under what circumstances these studies will be applied and put forward the interesting idea of possible ``neutrino lensing'' effect.