Prospect of measuring the neutrino mass hierarchy at θ 13 → 0 via a supernova neutrino signal

Collective neutrino flavor transformations deep inside a supernova are sensitive to the neutrino mass hierarchy even at extremely small values of θ 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 the Earth, will enable us to distinguish between the hierarchies if sin 2 θ 13 10 −5 , where long baseline neutrino experiments would be ineffectual.