There is recent evidence that some SiC $X$ grains from the Murchison meteorite may contain supernova-produced $\nu$-process ${}^{11}\mathrm{B}$ and or ${}^7\mathrm{Li}$ encapsulated in the grains. The synthesis of ${}^{11}\mathrm{B}$ and ${}^7\mathrm{Li}$ via neutrino-induced nucleon emission (the $\nu$ process) in supernovas 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 $\mathrm{Li}$ and $\mathrm{B}$ along with a better understanding of the relevant stellar nuclear and neutrino reactions could eventually reveal the neutrino mass hierarchy.

• Received 1 August 2011

DOI:https://doi.org/10.1103/PhysRevD.85.105023