Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density

TL;DR

This paper introduces a refined, exact algorithm for calculating neutrino oscillation probabilities in constant matter density, offering improved speed and detailed parameter behavior analysis compared to previous methods.

Contribution

The paper presents a new, faster exact algorithm for neutrino oscillation calculations in constant matter density, with implementation details and comparison to existing tools.

Findings

The new method is roughly twice as fast as GLoBES.

Oscillation probabilities are expressed in terms of mixing angles, mass differences, and matter density.

Certain probabilities show no dependence on specific mixing parameters.

Abstract

A recently published method for solving the neutrino evolution equation with constant matter density is further refined and used to lay out an exact algorithm for computing oscillation probabilities, which is moderately faster than previous methods when looping through neutrinos of different energies. In particular, the three examples of $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival, $\overset{\scriptscriptstyle{(-)}}{\nu}_\mu$ survival and $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ appearance probabilities are written in terms of mixing angles, mass differences and matter electron density. A program based on this new method is found to be roughly twice as fast as, and in agreement with, the leading GLoBES package. Furthermore, the behaviour of all relevant effective parameters is sketched out in terms of a range of neutrino energies, or matter electron densities. For instance, the $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival probability in constant matter density is found to have no dependence on the mixing angle $\theta_{23}$ or the CP-violating phase $\delta_{13}$.