Earth-Density Stratification and Quantum Gravity Corrections in Long-Baseline Neutrino Oscillation Experiments

Abstract

We present the first unified study of Earth matter-density stratification and Planck-scale quantum-gravity effects in long-baseline neutrino oscillations, treating both as correlated systematic uncertainties within a full three-flavor framework. Neutrino propagation is computed using matrix exponentiation with spatially resolved Preliminary Reference Earth Model (PREM) density profiles, allowing a quantitative assessment of matter-profile effects beyond the constant-density approximation. We find that the resulting bias in the reconstructed CP-violating phase remains below 0.3{\deg} for baselines (L \lesssim 5000) km, but increases to 17.8{\deg} at (L=7000) km and 172.2{\deg} at (L=12000) km, leading to a potential sign reversal of the inferred CP violation. We further incorporate Planck-scale corrections through the unique gauge-invariant dimension-5 operator of the Standard Model effective field theory. For quasi-degenerate neutrino masses ((m \sim 2) eV), the solar mass-squared splitting receives a correction of order ((1.0 \pm 0.5)\times10^{-5},\mathrm{eV}^2), while the atmospheric splitting remains essentially unchanged. Most importantly, we identify a previously unexplored degeneracy regime in which Planck-scale perturbations can partially compensate matter-induced biases. Around (L\approx7000) km, specific Majorana phases reduce the combined bias by about 30%, demonstrating that the two effects cannot be treated independently. These results highlight the necessity of propagating both Earth-density and quantum-gravity uncertainties as correlated systematics in precision measurements of leptonic CP violation.