Large N (=3) Neutrinos and Random Matrix Theory

TL;DR

This paper explores the application of large N techniques to the N=3 neutrino generations, using Random Matrix Theory to predict neutrino properties and introduce a new ensemble called the 'Seesaw ensemble.'

Contribution

It introduces the Seesaw ensemble in Random Matrix Theory and applies large N methods to neutrino physics with N=3, providing new predictions and mathematical insights.

Findings

Seesaw mechanism predicts a 1/N^3 hierarchy in neutrino masses.

Predicted theta(13) mixing angle of order 1/N matches experimental data for N=3.

Introduction of the Seesaw ensemble offers a new mathematical framework for hierarchical systems.

Abstract

The large N limit has been successfully applied to QCD, leading to qualitatively correct results even for N=3. In this work, we propose to treat the number N=3 of Standard Model generations as a large number. Specifically, we apply this idea to the neutrino anarchy scenario and study neutrino physics using Random Matrix Theory, finding new results in both areas. For neutrino physics, we obtain predictions for the masses and mixing angles as a function of the generation number N. The Seesaw mechanism produces a hierarchy of order 1/N^3 between the lightest and heaviest neutrino, and a theta(13) mixing angle of order 1/N, in parametric agreement with experimental data when N goes to 3. For Random Matrix Theory, this motivates the introduction of a new type of ensemble of random matrices, the "Seesaw ensemble." Basic properties of such matrices are studied, including the eigenvalue density and the interpretation as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble may be useful in random systems where two hierarchical scales exist.