# Anarchy and Neutrino Physics

## TL;DR

This paper investigates the statistical properties of neutrino masses and mixings within a seesaw-extended Standard Model under the anarchy hypothesis, comparing different seesaw types and their compatibility with experimental data.

## Contribution

It derives probability distributions for neutrino parameters in type I-III seesaw ensembles and compares them to type II, highlighting differences and the better fit of type I-III to data.

## Key findings

- Type I-III seesaw better fits experimental neutrino data.
- Strong preference for normal hierarchy in neutrino masses.
- Hierarchical predictions remain uncertain due to permutation symmetry.

## Abstract

The neutrino sector of a seesaw-extended Standard Model is investigated under the anarchy hypothesis. The previously derived probability density functions for neutrino masses and mixings, which characterize the type I-III seesaw ensemble of $N\times N$ complex random matrices, are used to extract information on the relevant physical parameters. For $N=2$ and $N=3$, the distributions of the light neutrino masses, as well as the mixing angles and phases, are obtained using numerical integration methods. A systematic comparison with the much simpler type II seesaw ensemble is also performed to point out the fundamental differences between the two ensembles. It is found that the type I-III seesaw ensemble is better suited to accommodate experimental data. Moreover, the results indicate a strong preference for the mass splitting associated to normal hierarchy. However, since all permutations of the singular values are found to be equally probable for a particular mass splitting, predictions regarding the hierarchy of the mass spectrum remains out of reach in the framework of anarchy.