Probing neutrino mass hierarchies and $ϕ_{13}$ with supernova neutrinos

Abstract

We investigate the feasibility of probing the neutrino mass hierarchy and the mixing angle $ϕ_{13}$ with the neutrino burst from a future supernova. An inverse power-law density $ρ\sim r^{n} $ with varying $n$ is adopted in the analysis as the density profile of a typical core-collapse supernova. The survival probabilities of $ν_{e}$ and $\barν_{e}$ are shown to reduce to two-dimensional functions of $n$ and $ϕ_{13}$. It is found that in the $n-\sin^{2} ϕ_{13}$ parameter space, the 3D plots of the probability functions exhibit highly non-trivial structures that are sensitive to the mass hierarchy, the mixing angle $ϕ_{13}$, and the value of $n$. The conditions that lead to observable differences in the 3D plots are established. With the uncertainty of $n$ considered, a qualitative analysis of the Earth matter effect is also included.