Exploring the Neutrino Mass Hierarchy Probability with Meteoritic Supernova Material, {ν}-Process Nucleosynthesis, and {θ}13 Mixing

There is recent evidence that some SiC X grains from the Murchison meteorite may contain supernova-produced {\nu}-process 11B and or 7Li encapsulated in the grains. The synthesis of 11B and 7Li via neutrino-induced nucleon emission (the {\nu} -process) in supernovae is sensitive to the neutrino mass hierarchy for finite sin^2(2{\theta}13) > 0.001}. This sensitivity arises because, when there is 13 mixing, the average electron neutrino energy for charged-current neutrino reactions is larger for a normal mass hierarchy than for an inverted hierarchy. Recent constraints on {\theta}13 from the Daya Bay, Double Chooz, MINOS, RENO and T2K collaborations all suggest that indeed sin^2(2{\theta}13) > 0.001}. We examine the possible implications of these new results based upon a Bayesian analysis of the uncertainties in the measured meteoritic material and the associated supernova nucleosynthesis models. We show that although the uncertainties are large, they hint at a marginal preference for an inverted neutrino mass hierarchy. We discuss the possibility that an analysis of more X grains enriched in Li and B along with a better understanding of the relevant stellar nuclear and neutrino reactions could eventually reveal the neutrino mass hierarchy.