Exploring the Neutrino Mass Hierarchy from Isotopic Ratios of Supernova Nucleosynthesis Products in Presolar Grains

We study the nucleosynthesis in a core-collapse supernova model including newly calculated neutrino-induced reaction rates with both collective and Mikheyev-Smirnov-Wolfenstein (MSW) neutrino-flavor oscillations considered. We show that the measurement of a pair of $^{11}$B/$^{10}$B and $^{138}$La/$^{139}$La or $^6$Li/$^7$Li and $^{138}$La/$^{139}$La in presolar grains that are inferred to have originated from core-collapse supernovae could constrain the neutrino mass hierarchy. The new shell-model and the model of quasi-particle random phase approximation in the estimate of three important neutrino-induced reactions, $\nu+^{16}$O, $\nu+^{20}$Ne, and $\nu+^{138}$Ba are applied in our reaction network. The new rates decrease the calculated $^{7}$Li/$^{6}$Li ratio by a factor of five compared with the previous study. More interestingly, these new rates result in a clear separation of the isotopic ratio of $^{11}$B/$^{10}$B between normal and inverted mass hierarchies in the O/Ne, O/C, and C/He layers where $^{138}$La abundance depends strongly on the mass hierarchy. In these layers, the sensitivity of the calculated abundances of $^{10,11}$B and $^{6,7}$Li to the nuclear reaction uncertainties is also tiny. Therefore, we propose that the $^{11}$B/$^{10}$B vs. $^{138}$La/$^{139}$La and $^6$Li/$^7$Li vs. $^{138}$La/$^{139}$La in type X silicon carbide grains sampled material from C/He layer can be used as a new probe to constrain the neutrino mass hierarchy.