Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments

TL;DR

This paper derives a simple identity linking neutrino oscillation parameters for different mass hierarchies, helping to clarify how combined long baseline experiments can resolve CP violation and mass hierarchy ambiguities.

Contribution

It introduces a novel identity relating solutions for different hierarchies in neutrino experiments, aiding in understanding how multiple experiments can exclude fake solutions.

Findings

Identity between solutions for normal and inverted hierarchies.

Application of the identity to T2K and NOνA experiments.

Enhanced understanding of experiment complementarity in resolving neutrino parameters.

Abstract

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for $\nu_\mu \to \nu_e$ appearance, we derive a simple identity between the solutions in the ($\sin^2 2\theta_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter $\sin^2 2\theta_{13}$ sets the scale of the $\nu_\mu \to \nu_e$ appearance probabilities at the atmospheric $\delta m^2_{atm} \approx 2.4 \times 10^{-3}$ eV$^2$ whereas $\sin \delta $ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{\sin^2 2\theta_{13}}$ divided by the {\it critical} value of $\sqrt{\sin^2 2\theta_{13}}$. We apply this identity to the two proposed long baseline experiments, T2K and NO$\nu$A, and we show how it can be used to provide a simple understanding of when and why fake solutions are excluded when two or more experiments are combined. The identity demonstrates the true complimentarity of T2K and NO$\nu$A.