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Earth-density effects in long baseline neutrino experiments

Tia Pandit ^* and Bipin Singh Koranga ^†

Department of Physics, Kirori Mal College, University of Delhi, Delhi-110007, India

^*Contact author: tiapandit777@outlook.com
^†Contact author: bskoranga@kmc.du.ac.in

Phys. Rev. D 113, 123046 – Published 17 June, 2026

DOI: https://doi.org/10.1103/8r1c-knd2

Abstract

The accurate modeling of Earth matter effects is a critical systematic consideration for precision measurements of the $C P$ -violating phase $δ_{C P}$ in long-baseline neutrino oscillation experiments. We investigate the extent to which constant and path-averaged density approximations are sufficient for reproducing the $ν_{μ} \to ν_{e}$ appearance probabilities predicted by the preliminary reference Earth model (PREM) across baselines ranging from $L = 1000 km$ to $L = 12000 km$ . Using a full three-flavor matrix exponentiation framework with spatially resolved PREM density profiles, we demonstrate that the constant density approximation introduces a negligible bias of less than 0.3° in the reconstructed $δ_{C P}$ for baselines up to $L \approx 5000 km$ , but undergoes a sharp increase beyond this threshold, reaching 17.8° at $L = 7000 km$ and 172.2° at $L = 12000 km$ . We show that this bias arises from energy-dependent distortions in the oscillation probability produced by the Earth’s internal density layering, which generate degeneracies between matter-induced and intrinsic $C P$ -violating contributions to the appearance channel that cannot be removed by marginalizing over a single effective density. These results demonstrate that the constant density approximation is not a conservative simplification but a source of fundamental systematic error at long baselines, and motivate the incorporation of spatially resolved Earth density treatments, such as PREM, in the analysis frameworks of next-generation long-baseline neutrino oscillation experiments.

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Earth-density effects in long baseline neutrino experiments

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