GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations

Abstract

Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T ≳ 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1 + n ↔ 2 + n scatterings and for all 2 ↔ 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.