The case for adopting the sequential Jacobi's diagonalization algorithm in neutrino oscillation physics

TL;DR

This paper introduces the Sequential Jacobi Diagonalization algorithm, which improves the efficiency and flexibility of analyzing neutrino oscillation parameters by separating linear algebra from numerical integration.

Contribution

It proposes a novel algorithm combining Jacobi's diagonalization with reordering to enhance neutrino oscillation analysis and facilitate model fitting and Monte Carlo simulations.

Findings

Algorithm is trivially parallelizable.

Enables quasi-model-independent solutions.

Speeds up calculations in neutrino physics.

Abstract

Neutrino flavor oscillations and conversion in an interacting background (MSW effects) may reveal the charge-parity violation in the next generation of neutrino experiments. The usual approach for studying these effects is to numerically integrate the Schrodinger equation, recovering the neutrino mixing matrix and its parameters from the solution. This work suggests using the classical Jacobi's diagonalization in combination with a reordering procedure to produce a new algorithm, the Sequential Jacobi Diagonalization. This strategy separates linear algebra operations from numerical integration, allowing physicists to study how the oscillation parameters are affected by adiabatic MSW effects in a more efficient way. The mixing matrices at every point of a given parameter space can be stored for speeding up other calculations, such as model fitting and Monte Carlo productions. This approach has two major computation advantages, namely: being trivially parallelizable, making it a suitable choice for concurrent computation, and allowing for quasi-model-independent solutions that simplify Beyond Standard Model searches.