NeutrinoOsc3Flavor: CP Phase Dependence in Three-Flavor Neutrino Oscillations: A Numerical Study in Vacuum and Matter

TL;DR

NeutrinoOsc3Flavor is a minimal, transparent Python framework for exact three-flavor neutrino oscillation calculations in vacuum and matter, emphasizing correctness, educational use, and benchmarking.

Contribution

It provides a lightweight, fully transparent implementation of three-flavor neutrino oscillations with full CP phase dependence, suitable for verification and educational purposes.

Findings

Accurately solves the Schrodinger equation for neutrino oscillations

Demonstrates excellent agreement between numerical and analytical eigenvalues

Uses CP phase dependence as a diagnostic for numerical stability

Abstract

We present NeutrinoOsc3Flavor, a lightweight and fully transparent computational framework for exact three flavor neutrino oscillation studies in vacuum and constant density matter. The code numerically solves the Schrodinger evolution equation in the flavor basis using explicit construction and diagonalization of the effective Hamiltonian within the PMNS formalism, including full CP Violating phase dependence. In contrast to large scale oscillation toolkits optimized for experimental simulations, NeutrinoOsc3Flavor is designed as a minimal dependency reference implementation, emphasizing analytical traceability, equation level accessibility, and cross platform portability. The framework relies solely on NumPy for numerical linear algebra and runs natively on both Linux and Windows systems without external compilation or specialized libraries. As an internal consistency and validation feature, we implement an independent analytical determination of the matter modified Hamiltonian eigenvalues using the Cardano method and demonstrate excellent agreement with numerical diagonalization. CP Phase dependence is used as a sensitive diagnostic of numerical stability and correctness of the evolution operator in both vacuum and matter. NeutrinoOsc3Flavor is intended as a verification oriented and pedagogical computational tool, suitable for theoretical cross-checks, educational use, and benchmarking of more complex neutrino oscillation software, rather than as a replacement for full experimental simulation frameworks. Here, we consider the DUNE experiments baseline length in the python implementation but in general we can implement any value of baseline length.