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, treating matter-induced extrinsic CPT violation and Earth density stratification as correlated systematics within a single $\ddot{I}{‡}^2$ framework. We study their joint impact on CP-phase reconstruction and mass-ordering dependence. Matter-induced extrinsic CPT violation produces a non-zero asymmetry $A_{\hat{I}¼e}^{\mathrm{CPT}}=(P_{\hat{I}¼e}-{\bar{P}}_{\hat{I}¼e})/(P_{\hat{I}¼e}+{\bar{P}}_{\hat{I}¼e})$, computed using exact three-flavour matrix exponentiation for T2K, NO$\hat{I}½$A, DUNE, and Hyper-Kamiokande. The asymmetry ranges from 0.022 to 0.180 at the respective peak energies and differs by up to $9\%$ between normal and inverted orderings. The surface $A_{\hat{I}¼e}^{\mathrm{CPT}}(E,\hat{I}{´}_{\mathrm{CP}})$ at DUNE reveals an interplay between extrinsic CPT and intrinsic CP violation in the high-$L/E$ regime requiring joint statistical treatment. We quantify the sensitivity of $A_{\hat{I}¼e}^{\mathrm{CPT}}$ to density uncertainties $\ddot{I}\to \ddot{I}(1+\epsilon )$ with $\epsilon =\pm 1\%,\pm 2\%,\pm 5\%$, finding that a $\pm 5\%$ uncertainty induces $|\hat{I}”A_{\mathrm{CPT}}|<0.008$ at DUNE. Replacing the PREM profile with a constant path-averaged density yields a $\hat{I}{´}_{\mathrm{CP}}$ reconstruction bias below $0.3^{\circ }$ for $L\le 5000$ km, increasing to $17.8^{\circ }$ at $7000$ km and $172.2^{\circ }$ at $12000$ km. Since both effects arise from the same matter Hamiltonian, they must be modelled jointly using a Poisson log-likelihood $\ddot{I}{‡}^2$ with nuisance-parameter pulls.

18 pages, 6 figures