From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes

TL;DR

This paper introduces a method to efficiently interpolate neutrino evolution matrices across energies and trajectories, improving computational speed and accuracy in modeling fast oscillations in neutrino physics.

Contribution

The authors present a novel technique to extrapolate neutrino evolution matrices reliably, preserving unitarity and applicable to arbitrary matter profiles, enhancing theoretical predictions and Monte Carlo simulations.

Findings

Enables accurate interpolation of neutrino oscillation amplitudes.

Guarantees unitarity of the evolution matrix during extrapolation.

Applicable to arbitrary matter density profiles and Hamiltonian models.

Abstract

In this note we describe how to complement the neutrino evolution matrix calculated at a given energy and trajectory with additional information which allows to reliably extrapolate it to nearby energies or trajectories without repeating the full computation. Our method works for arbitrary matter density profiles, can be applied to any propagation model described by an Hamiltonian, and exactly guarantees the unitarity of the evolution matrix. As a straightforward application, we show how to enhance the calculation of the theoretical predictions for experimentally measured quantities, so that they remain accurate even in the presence of fast neutrino oscillations. Furthermore, the ability to "move around" a given energy and trajectory opens the door to precise interpolation of the oscillation amplitudes within a grid of tabulated values, with potential benefits for the computation speed of Monte-Carlo codes. We also provide a set of examples to illustrate the most prominent features of our approach.