Matter-Induced CPT Violation and Earth-Density Stratification Effects in Long-Baseline Neutrino Oscillation Experiments

Abstract

We present a unified analysis of two matter-potential systematics in long-baseline (LBL) neutrino oscillation experiments. Matter-induced extrinsic CPT violation produces a non-zero asymmetry $A_{μe}^{CPT} = (P_{μe} - P_{\barμ\bar{e}})/(P_{μe} + P_{\barμ\bar{e}})$, computed here with exact three-flavour matrix-exponentiation propagators for T2K, NO$ν$A, DUNE, and Hyper-Kamiokande; values range from 0.022 to 0.180 at the respective peak energies and differ by up to 9\% between normal and inverted mass orderings. The three-dimensional surface $A_{μe}^{CPT}(E, δ_{CP})$ at the DUNE baseline reveals an entanglement between extrinsic CPT violation and intrinsic CP violation in the high-$L/E$ regime that requires joint statistical treatment. Concurrently, replacing the Preliminary Reference Earth Model (PREM) with a constant path-averaged density introduces a $δ_{CP}$-reconstruction bias below $0.3^{\circ}$ for $L \leq 5000$ km but growing to $17.8^{\circ}$ at $L = 7000$ km and $172.2^{\circ}$ at $L = 12000$ km. Since both effects share the same matter-potential Hamiltonian they must be modelled jointly; a Poisson log-likelihood $χ^2$ statistic with nuisance-parameter pull terms is used to quantify the bias.