The impact of hierarchy upon the values of neutrino mixing parameters

Abstract

A neutrino-oscillation analysis is performed of the more finely binned Super-K atmospheric, MINOS, and CHOOZ data in order to examine the impact of neutrino hierarchy in this data set upon the value of ${\theta }_{13}$ and the deviation of ${\theta }_{23}$ from maximal mixing. Exact oscillation probabilities are used, thus incorporating all powers of ${\theta }_{13}$ and $\epsilon :={\theta }_{23}-\pi /4$. The extracted oscillation parameters are found to be dependent on the hierarchy, particularly for ${\theta }_{13}$. We find at 90% CL are ${\Delta }_{32}=2.44_{-0.20}^{+0.26}$ and $2.48_{-0.22}^{+0.25}\times 10^{-3}{\mathrm{eV}}^2$, $\epsilon ={\theta }_{23}-\pi /4=0.06_{-0.16}^{+0.06}$ and $0.06_{-0.17}^{+0.08}$, and ${\theta }_{13}=-0.07_{-0.11}^{+0.18}$ and $-0.13_{-0.16}^{+0.23}$, for the normal and inverted hierarchy respectively. The inverted hierarchy is preferred at a statistically insignificant level of 0.3 $\sigma$.

4 pages, 2 figure

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