When CPT Violation Hides in Plain Sight: How CP Measurements Are Compromised and How to Fix Them

Abstract

The extraction of the leptonic charge-parity (CP)-violating phase $\hat{I}{´}_{\mathrm{CP}}$ from long-baseline neutrino oscillation experiments rests on the assumption of charge-parity-time (CPT) conservation. We show that CPT violation, parametrized as an asymmetry $\hat{I}´\hat{I}”m_{31}^2\equiv \hat{I}”{\bar{m}}_{31}^2-\hat{I}”m_{31}^2$ between neutrino and antineutrino mass splittings, induces an effective, energy-dependent phase shift $\ddot{I}{•}_{\mathrm{eff}}(E)$ that is functionally degenerate with $\hat{I}{´}_{\mathrm{CP}}$ in the appearance asymmetry $⟨\hat{I}”P⟩$. This has a profound implication for long-baseline experiments, where the tension between T2K and NO$\hat{I}½$A CPT-conserving best-fit $\hat{I}{´}_{\mathrm{CP}}$ values can be significantly alleviated by a CPT-violating truth; and a CPT-conserving fit can miss the true CP phase entirely for $|\hat{I}´\hat{I}”m_{31}^2|\gtrsim 0.3\times 10^{-3}{\text{eV}}^2$ for DUNE. We then demonstrate that atmospheric neutrino telescopes provide the natural tool to resolve this degeneracy: using existing data from IceCube-DeepCore (7.74 yr) and KM3NeT/ORCA-6 (433 kt-yr), we derive a world-leading constraint on CPT-violation at $|\hat{I}´\hat{I}”m_{31}^2|\le 0.57\times 10^{-3}{\text{eV}}^2$ at 90% CL. With the IceCube Upgrade and full ORCA detector, we can reach a $1\ddot{I}ƒ$ constraint at $10^{-4}{\text{eV}}^2$ within a decade, providing the independent CPT constraint needed to ensure that DUNE's $\hat{I}{´}_{\mathrm{CP}}$ measurement is unambiguous.