Large N (=3) neutrinos and random matrix theory

Abstract

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 θ 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.