Earth-Density Effects in LBL Experiments: A Comprehensive Review of Theory, Observations, and Future Directions

TL;DR

The paper addresses how uncertainties in Earth's density influence three-flavour neutrino oscillations and CP-violation measurements in long-baseline experiments, notably through the phase $δ_{\rm CP}$. It analyzes MSW effects and quantifies density-induced uncertainties using the Cervera–Freund perturbative framework, arguing for spatially resolved density profiles rather than a single effective density. It introduces a hierarchy of density models—from two-layer crust/mantle to PREM-based profiles and perturbations around PREM—and provides a formalism to propagate density uncertainties through the oscillation evolution via multi-layer and perturbative approaches. The work underscores that CP–matter degeneracies induced by Earth-density uncertainties can bias CP inferences and advocates for incorporating geophysically informed density profiles into the analysis pipelines of next-generation experiments like DUNE, with a focus on energy-resolved CP robustness and joint inference of CP violation and matter effects.

Abstract

Earth matter density uncertainties play a non trivial role in three flavor neutrino oscillations in matter, particularly for the muon to electron appearance channel that underpins CP violation measurements in long baseline experiments. We demonstrate that when realistic spatial variations of the Earths density are taken into account, the oscillation probabilities acquire additional, energy dependent structures that cannot be captured by path-averaged density approximations. We show that mismodeling of the matter density profile can introduce degeneracies that obscure genuine leptonic CP violating effects, thereby degrading parameter sensitivity and biasing the inference of the CP phase. Identifying energy regions in which CP sensitivity remains robust against matter density uncertainties is therefore essential. These considerations indicate that marginalization over a single effective density parameter is insufficient for next generation precision measurements and motivate the incorporation of spatially resolved Earth density profiles in the analysis frameworks of future long-baseline neutrino oscillation experiments.

Figures (2)

• Figure 1: Comparison of the $\nu_\mu \rightarrow \nu_e$ appearance probability at the DUNE baseline ($L = 1300~\mathrm{km}$) in vacuum and in matter. The solid blue (dashed orange) curve shows the neutrino (antineutrino) probability in constant-density matter, while the thin gray curve corresponds to the vacuum approximation. The shaded region indicates the energy range around the first oscillation maximum, where DUNE has maximal sensitivity. The oscillation parameters are fixed to representative best-fit values ($\theta_{12}=33.44^\circ$, $\theta_{13}=8.57^\circ$, $\theta_{23}=49.2^\circ$, $\delta_{\rm CP}=197^\circ$), assuming normal mass ordering.
• Figure 2: Dependence of the $\nu_\mu \rightarrow \nu_e$ appearance probability at DUNE on the assumed average Earth matter density. The probability is shown as a function of neutrino energy for density variations of $\pm5\%$ and $\pm10\%$ around a reference value of $\rho = 2.848~\mathrm{g\,cm^{-3}}$, appropriate for the $1300~\mathrm{km}$ baseline.