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We investigate the feasibility of probing the neutrino mass hierarchy and themixing angle $\phi_{13}$ with the neutrino burst from a future supernova. Aninverse power-law density $\rho \sim r^{n} $ with varying $n$ is adopted in theanalysis as the density profile of a typical core-collapse supernova. Thesurvival probabilities of $\nu_{e}$ and $\bar{\nu}_{e}$ are shown to reduce totwo-dimensional functions of $n$ and $\phi_{13}$. It is found that in the$n-\sin^{2} \phi_{13}$ parameter space, the 3D plots of the probabilityfunctions exhibit highly non-trivial structures that are sensitive to the masshierarchy, the mixing angle $\phi_{13}$, and the value of $n$. The conditionsthat lead to observable differences in the 3D plots are established. With theuncertainty of $n$ considered, a qualitative analysis of the Earth mattereffect is also included.Comment: 16 pages, 3 figures. Ref [11] added, and some typos correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Probing neutrino mass hierarchies and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>13</mml:mn></mml:msub></mml:math>with supernova neutrinos

Probing neutrino mass hierarchies andϕ13with supernova neutrinos