A Lightning-Fast Three-Flavor Neutrino Oscillation Calculator in Constant-Density Matter with Built-In Uncertainty Propagation

TL;DR

This paper introduces a rapid, accurate three-flavor neutrino oscillation calculator for constant-density matter, capable of uncertainty propagation, suitable for long-baseline experiment analysis.

Contribution

It presents a novel, efficient oscillation calculator combining exact and perturbative methods with built-in uncertainty handling, validated against established models.

Findings

Runs 27x faster with perturbative approximation

Accurately reproduces vacuum and resonance limits

Provides reliable uncertainty confidence bands

Abstract

Neutrino oscillation experiments are entering an era of precision, requiring both fast calculations and reliable uncertainty estimates. We present a compact three-flavor oscillation calculator for constant-density matter, built on analytic perturbative formulas and validated against established series expansions. Using the NuFIT 6.0 global-fit covariance matrix, the tool incorporates up-to-date parameter values and correlations. It accurately computes appearance and disappearance probabilities over 0.3-5 GeV at a 295 km baseline, offering two computation modes: exact Hamiltonian diagonalization for high-fidelity results, and a faster perturbative approximation that runs roughly 27x quicker. A hybrid scheme handles the MSW resonance region, combining speed with accuracy. Uncertainties can be propagated via Monte Carlo sampling or a fast linearized approach, producing reliable confidence bands. The implementation preserves unitarity, reproduces vacuum and resonance limits, and captures high-energy suppression effects. This calculator provides a fast, reliable framework for parameter scans, phenomenological studies, and sensitivity estimates for current and future long-baseline experiments like Hyper-Kamiokande and DUNE.