A Probability Density Function for Neutrino Masses and Mixings

TL;DR

This paper analytically derives the probability density function for neutrino masses and mixings within the see-saw ensemble, revealing a decoupling that affects predictive power and aligns with existing literature.

Contribution

It provides an analytical expression for the see-saw ensemble's probability density function, highlighting the decoupling between neutrino masses and mixings.

Findings

The probability density function involves a multidimensional integral over light neutrino masses.

Neutrino mixing angles and phases follow the Haar measure.

Decoupling of masses and mixings reduces predictive power.

Abstract

The anarchy principle leading to the see-saw ensemble is studied analytically with the usual tools of random matrix theory. The probability density function for the see-saw ensemble of $N\times N$ matrices is obtained in terms of a multidimensional integral. This integral involves all light neutrino masses, leading to a complicated probability density function. It is shown that the probability density function for the neutrino mixing angles and phases is the appropriate Haar measure. The decoupling of the light neutrino masses and neutrino mixings implies no correlation between the neutrino mass eigenstates and the neutrino mixing matrix and leads to a loss of predictive power when comparing with observations. This decoupling is in agreement with some of the claims found in the literature.