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

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.

32 pages, 6 figures, 4 tables, version accepted for publication in Phys. Rev. D

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