The impact of hierarchy upon the values of neutrino mixing parameters

TL;DR

This study analyzes how neutrino hierarchy affects the measurement of mixing parameters using detailed oscillation data, revealing hierarchy-dependent variations especially for , with the inverted hierarchy slightly favored but not significantly.

Contribution

It provides a detailed analysis of neutrino oscillation data incorporating all oscillation probabilities to assess hierarchy effects on mixing parameters.

Findings

Hierarchy influences the measured  and  parameters.

Inverted hierarchy slightly favored but not statistically significant.

Precise parameter values depend on hierarchy assumption.

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 $\Delta_{32} = 2.44^{+0.26}_{-0.20}$ and $2.48^{+0.25}_{-0.22}\times 10^{-3} {\rm eV}^2$, $\epsilon=\theta_{23}-\pi/4=0.06^{+0.06}_{-0.16}$ and $0.06^{+0.08}_{-0.17}$, and $\theta_{13}=-0.07^{+0.18}_{-0.11}$ and $-0.13^{+0.23}_{-0.16}$, for the normal and inverted hierarchy respectively. The inverted hierarchy is preferred at a statistically insignificant level of 0.3 $\sigma$.