Large Mixing Angles From Many Right-Handed Neutrinos

TL;DR

This paper proposes that many right-handed neutrinos can naturally produce large neutrino mixing angles and small mass hierarchies, aligning with observed neutrino phenomenology.

Contribution

It introduces a scenario where numerous gauge singlet right-handed neutrinos reduce hierarchy and generate large mixing angles through a sum over Yukawa couplings.

Findings

Fits low energy neutrino data well

Predicts normal mass hierarchy for neutrinos

Estimates |m_ee| to be 1-6 meV

Abstract

A beautiful understanding of the smallness of the neutrino masses may be obtained via the seesaw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: right-handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard seesaw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses compared to the quarks and charged leptons, nor the large leptonic mixing angles compared to the small angles of the CKM matrix. In this paper, we will show that the singlet nature of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies - as is suggested, for example, by various string constructions - then the effective low energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings, with the largest ones being the most important. This can reduce hierarchy, and lead to large mixing angles. Assuming a statistical distribution of fundamental parameters, we will show that this scenario leads to a good fit to low energy phenomenology, with only a few qualitative assumptions guided by the known quark and lepton masses. The scenario leads to predictions of a normal hierarchy for the neutrino masses, and a value for the |m_ee| mass matrix element of about 1-6 meV.