CHIC: Caley-Hamilton, Invariants and Constants for Neutrino Oscillation Probabilities and Gradients

TL;DR

This paper introduces CHIC, a software leveraging the Caley-Hamilton theorem to efficiently compute neutrino oscillation probabilities and their derivatives, aiding data analysis and visualization in neutrino physics.

Contribution

It presents a novel analytical approach using matrix invariants for neutrino oscillation calculations, avoiding Hamiltonian diagonalization, and introduces tools for analysis and visualization.

Findings

Efficient computation of oscillation probabilities and derivatives.

Demonstrated utility of probability gradients in data analysis.

Introduced oscillograds for visualizing neutrino mixing features.

Abstract

We use the Caley-Hamilton theorem to derive analytical solutions for the three-flavor neutrino propagation amplitude in a constant-density medium and their derivatives with respect to the mixing parameters. This approach avoids the diagonalization of the Hamiltonian and exploits precomputed matrix invariants to separate the dependence of oscillation probabilities on neutrino energy and propagation baseline. The results are implemented in the CHIC software, which provides simple, fast and efficient computation of oscillation probabilities and their derivatives. Finally, we demonstrate the value of probability gradients for neutrino data analyses and introduce a complementary visualization, the oscillograds, to probe underlying features of neutrino mixing.