# Disentangling genuine from matter-induced CP violation in neutrino oscillations

## TL;DR

This paper decomposes neutrino oscillation CP asymmetries into matter-induced and genuine components, providing a method to distinguish and measure intrinsic CP violation and neutrino mass hierarchy effects in experiments.

## Contribution

It demonstrates that CP asymmetries in neutrino oscillations can be separated into matter-induced and genuine CP violation parts, with explicit formulas for different baseline regimes.

## Key findings

- CPT-odd component is small at medium baselines and nearly δ-independent.
- At long baselines, hierarchy-odd CPT-odd term dominates above the first oscillation node.
- Near the second oscillation maximum, the CPT-odd term vanishes, highlighting regions to measure genuine CP violation.

## Abstract

We prove that, in any flavor transition, neutrino oscillation CP violating asymmetries in matter have two disentangled components: (a) a CPT-odd T-invariant term, non-vanishing iff there are interactions with matter; (b) a T-odd CPT-invariant term, non-vanishing iff there is genuine CP violation. As function of the baseline, these two terms are distinct L-even and L-odd observables, respectively. In the experimental region of terrestrial accelerator neutrinos, we calculate their approximate expressions from which we prove that, at medium baselines, the CPT-odd component is small and nearly $\delta$-independent, so it can be subtracted from the experimental CP asymmetry as a theoretical background, provided the hierarchy is known. At long baselines, on the other hand, we find that (i) a Hierarchy-odd term in the CPT-odd component dominates the CP asymmetry for energies above the first oscillation node, and (ii) the CPT-odd term vanishes, independent of the CP phase $\delta$, at E = 0.92 GeV(L/1300 km) near the second oscillation maximum, where the T-odd term is almost maximal and proportional to $\sin\delta$. A measurement of the CP asymmetry in these energy regions would thus provide separate information on (i) the neutrino mass ordering, and (ii) direct evidence of genuine CP violation in the lepton sector.