Correlated Matter Induced Biases in Long-Baseline Neutrino Oscillation Measurements

Abstract

We demonstrate that treating Earth matter effects via a constant-density approximation introduces a fundamental systematic error in long-baseline neutrino oscillation analyses. Using exact numerical propagation through realistic PREM profiles, we show that matter-profile mismodeling does not merely affect the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_e$ appearance probability, but generates correlated biases across the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\ddot{I}}„$ and $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\hat{I}}¼$ channels as dictated by PMNS unitarity. Our stochastic analysis reveals that the $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_{\ddot{I}}„$ channel is the most volatile carrier of the geophysical systematic. Across varying correlation lengths at baselines like $5000$ km and $7000$ km, the $\ddot{I}„$-appearance channel consistently carries a larger mean bias and variance than the standard $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_e$ appearance channel. These findings demonstrate that spatially resolved density treatments are a mathematical necessity for the analysis frameworks of future precision neutrino facilities.

7 pages, 3 figures