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 $\nu_{\mu}\rightarrow\nu_{e}$ appearance probability, but generates correlated biases across the $\nu_{\mu}\rightarrow\nu_{\tau}$ and $\nu_{\mu}\rightarrow\nu_{\mu}$ channels as dictated by PMNS unitarity. Our stochastic analysis reveals that the $\nu_{\mu}\rightarrow\nu_{\tau}$ channel is the most volatile carrier of the geophysical systematic. Across varying correlation lengths at baselines like $5000$ km and $7000$ km, the $\tau$-appearance channel consistently carries a larger mean bias and variance than the standard $\nu_{\mu}\rightarrow\nu_{e}$ appearance channel. These findings demonstrate that spatially resolved density treatments are a mathematical necessity for the analysis frameworks of future precision neutrino facilities.