On The Origin of Neutrino Mass and Mixing in the Standard Model

TL;DR

This paper explores how adding Majorana masses and flavor symmetries to the Standard Model explains neutrino mixing, mass hierarchy, and the Majorana nature of neutrinos, with implications for cosmology and experiments.

Contribution

It introduces a framework where neutrino masses and mixing arise from relic neutrino entropy considerations and flavor symmetry breaking within the Standard Model.

Findings

Neutrinos have a Majorana mass matrix leading to tri-bimaximal mixing.

The neutrino mass hierarchy is inverted, with no Majorana phases.

Lepton number conservation implies neutrino-less double beta decay will detect relic Majorana neutrinos.

Abstract

One can describe cosmological relic neutrinos by adding Lagrange multipliers to the Standard Model Lagrangian for them. The two possible Lagrange multipliers are a chemical potential, which fixes the mean neutrino/anti-neutrino asymmetry, and a Majorana mass, which fixes the mean spin-entropy. Because these neutrinos originated from a thermal bath, their entropy should be maximal, implying that each state in the background is a symmetric superposition of a neutrino and anti-neutrino. Therefore the Standard Model must be augmented by a flavor-diagonal Majorana neutrino mass matrix. This impacts the propagator via tadpole diagrams due to self-interactions. In the low-energy limit, neutrino self-interactions are entirely off-diagonal because same-flavor four-fermion operators vanish by Pauli exclusion. These interactions must be diagonalized when propagating through a bath of neutrinos, using the U(3) global flavor symmetry. U(3) gets broken broken down to SO(3) by Majorana masses, and down to $A_4$ if the three masses are different. Thus our universe today contains tri-bimaximal mixing and Majorana neutrinos. Neutrino mixing is due to the mismatch between the flavor-diagonal Majorana mass matrix arising at finite density and the self-interaction diagonal finite density propagator. The mass hierarchy is inverted and Majorana phases are absent. Lepton number is conserved and the neutrino-less double beta decay experiment absorbs a pair of neutrinos from the relic background and will prove their Majorana nature.