0909.3090 (Bob McElrath)

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

Bob McElrath

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.

View original: http://arxiv.org/abs/0909.3090