Identifying Neutrino Mass Hierarchy at Extremely Small ${\theta }_{13}$ through Earth Matter Effects in a Supernova Signal

Collective neutrino flavor transformations deep inside a supernova are sensitive to the neutrino mass hierarchy even at extremely small values of ${\theta }_{13}$. Exploiting this effect, we show that comparison of the antineutrino signals from a galactic supernova in two megaton class water Cherenkov detectors, one of which is shadowed by Earth, will enable us to distinguish between the hierarchies if ${sin}^2{\theta }_{13}\lesssim {10}^{-5}$, where long baseline neutrino experiments would be ineffectual.

Figure 1

Plot of the ratio $R$ defined in Eq. (7), as a function of the observable positron energy for normal hierarchy (left panel) and inverted hierarchy (right panel), with ${sin}^2{\theta }_{13}\lesssim {10}^{-5}$. For ${sin}^2{\theta }_{13}\gtrsim {10}^{-3}$, the ratio $R$ will be identical to the left panel for either hierarchy.