New look at the degeneracies in the neutrino oscillation parameters, and their resolution by T2K, NO$\nu$A and ICAL

TL;DR

This paper analyzes the complex degeneracies in neutrino oscillation parameters and demonstrates how combined data from T2K, NOvA, and ICAL can resolve these ambiguities to accurately determine the neutrino mass hierarchy, octant, and CP phase.

Contribution

It introduces a comprehensive framework for understanding and classifying neutrino parameter degeneracies and shows how combined experimental data can resolve them.

Findings

Eight distinct solutions depending on hierarchy, octant, and CP phase.

Antineutrino data helps remove wrong-octant solutions.

Combined data resolves degeneracies at 2σ level.

Abstract

At present the three major unknowns in neutrino oscillation parameters are the mass hierarchy, the octant of $\theta_{23}$ and the CP phase $\delta_{CP}$. It is well known that the presence of hierarchy$-\delta_{CP}$ and octant degeneracies affects the unambiguous determination of these parameters. In this paper we show that a comprehensive way to study the remaining parameter degeneracies is in the form of a generalized hierarchy-$\theta_{23}$ - $\delta_{CP}$ degeneracy. We show that the wrong-hierarchy and/or wrong-octant solutions can be further classified into eight different solutions depending on whether they occur with the wrong or right value of $\delta_{CP}$. These eight solutions are different from the original eightfold degenerate solutions and can exist, in principle, even if $\theta_{13}$ is known. These multiple solutions, apart from affecting the determination of the true hierarchy and octant, also affect the accurate estimation of $\delta_{CP}$. We identify which of these eight different degenerate solutions can occur in the test ($\theta_{23} - \delta_{CP}$) parameter space, taking the long-baseline experiment NO$\nu$A running in the neutrino mode as an example. The inclusion of the NO$\nu$A antineutrino run removes the wrong-octant solutions appearing with both right and wrong hierarchy. Adding T2K data to this resolves the wrong hierarchy -- right octant solutions to a large extent. The remaining wrong hierarchy solutions can be removed by combining NO$\nu$A + T2K with atmospheric neutrino data. We demonstrate this using ICAL@INO as the prototype atmospheric neutrino detector. We find that the degeneracies can be resolved at the $2\sigma$ level by the combined data set, for the true parameter space considered in the study.