Octant Degeneracy and Plots of Parameter Degeneracy in Neutrino Oscillations Revisited

TL;DR

This paper analyzes the octant degeneracy in neutrino oscillation parameters, visualizes it on a specific parameter plane, and discusses how future experiments can resolve this degeneracy using energy spectra near the first oscillation maximum.

Contribution

It provides an analytical study of the octant degeneracy in neutrino oscillations and evaluates the effectiveness of future experiments in resolving it.

Findings

Energy spectra near the first oscillation maximum help resolve the octant degeneracy.

Spectra near the second oscillation maximum are less effective for resolving degeneracy.

The octant degeneracy persists in certain experimental conditions, but can be mitigated with specific spectral analyses.

Abstract

The three kinds of parameter degeneracy in neutrino oscillation, the intrinsic, sign and octant degeneracy, form an eight-fold degeneracy. The nature of this eight-fold degeneracy can be visualized on the ($\sin^22\theta_{13}$, $1/\sin^2\theta_{23}$)-plane, through quadratic curves defined by $P(\nu_\mu\to\nu_e)=$ const. and $P(\bar{\nu}_\mu\to\bar{\nu}_e)=$ const., along with a straight line $P(\nu_\mu\to\nu_\mu)=$ const. After $\theta_{13}$ was determined by reactor neutrino experiments, the intrinsic degeneracy in $\theta_{13}$ transforms into an alternative octant degeneracy in $\theta_{23}$, which can potentially be resolved by incorporating the value of $P(\nu_\mu\to\nu_\mu)$. In this paper, we analytically discuss whether this octant parameter degeneracy is resolved or persists in the future long baseline accelerator neutrino experiments, such as T2HK, DUNE, T2HKK and ESS$\nu$SB. It is found that the energy spectra near the first oscillation maximum are effective in resolving the octant degeneracy, whereas those near the second oscillation maximum are not.