# Hierarchy independent sensitivity to leptonic {\delta}_CP with atmospheric neutrinos

## TL;DR

This paper investigates how low energy atmospheric neutrino events can be used to measure the leptonic CP phase {\delta}_CP without hierarchy ambiguity, showing promising sensitivity at sub-GeV energies.

## Contribution

It demonstrates that atmospheric neutrinos at sub-GeV energies can distinguish {\delta}_CP values independently of mass hierarchy, with a preliminary sensitivity analysis assuming an ideal detector.

## Key findings

- Sub-GeV atmospheric neutrinos can differentiate {\delta}_CP values.
- No hierarchy sensitivity at these energies.
- Preliminary  analysis indicates potential for {\delta}_CP measurement.

## Abstract

The Dirac leptonic CP phase {\delta}_CP is one of the crucial unknown parameters in neutrino oscillation physics. In this paper we explore the possibility of using low energy atmospheric neutrino events to probe {\delta}_CP . We show that at sub GeV energies, when the events are binned as a function of the energy and direction of the final state leptons, a consistent distinction between various true {\delta}_CP values is obtained. We also show that at these energies there is no sensitivity to the mass ordering/hierarchy, so that {\delta}_CP can be measured without hierarchy ambiguity. In addition a preliminary \c{hi}^2 analysis of the sensitivity to {\delta}_CP using atmospheric neutrinos assuming a generic detector with perfect separation between charged current {\nu}_{\mu} , \bar{{\nu}}_{\mu} , {\nu}_e and \bar{{\nu}}_e events is given.