Identifying neutrino mass hierarchy at extremely small theta13 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) < or approximately 10(-5), where long baseline neutrino experiments would be ineffectual.