# Multi-flavor effects in Stimulated Transitions of Neutrinos

## TL;DR

This paper develops an approximate analytic framework for understanding multi-flavor neutrino transitions under arbitrary time-dependent perturbations, revealing phenomena like induced transparency and controllable opacity in three-flavor systems.

## Contribution

It introduces a general analytic solution for multi-flavor neutrino evolution with arbitrary Fourier mode perturbations, extending previous two-flavor models and uncovering new control effects.

## Key findings

- Analytic solutions match numerical results within a few percent.
- Discovery of induced transparency in two Fourier mode perturbations.
- Identification of a third mode that can manipulate transition probabilities.

## Abstract

A neutrino subject to an external, time-dependent perturbing potential can be forced to make transitions between its flavor states. A neutrino with three (or more) flavors can exhibit phenomena that cannot occur if the neutrino had just two. We present an approximate analytic solution for the temporal evolution of a multi-flavor neutrino in response to an arbitrary perturbing Hamiltonian that has been decomposed into its Fourier modes. We impose no restriction upon the number of flavors nor upon the structure of the perturbing Hamiltonian, the number of Fourier modes, their amplitude or their frequencies. We apply the theory to study three-flavor neutrino transformation due to perturbations built from two and three Fourier modes. For the case of two Fourier modes we observe the equivalent of "induced transparency" from quantum optics whereby transitions between a given pair of states are suppressed due to the presence of a resonant mode between another pair. When we add a third Fourier mode we find a new effect whereby the third mode can manipulate the transition probabilities of the two mode case so as to force complete transparency or, alternatively, restore "opacity" meaning the perturbative potential regains its ability to induce neutrino transitions. In both applications we demonstrate how the analytic solutions are able to match the amplitude and wavenumber of the numerical results to within a few percent.