Quantum mechanics of leptogenesis

Thermal leptogenesis is an attractive mechanism that explains in a simple way the matter–antimatter asymmetry of the universe. It is usually studied via the Boltzmann equations, which describes the time evolution of particle densities or distribution functions in a thermal bath. The Boltzmann equations are classical equations and suffer from basic conceptual problems and they lack to include many quantum phenomena. We show how to address leptogenesis systematically in a purely quantum way, by describing non-equilibrium excitations of a Majorana particle in the Kadanoff–Baym equations with significant emphasis on the initial and boundary conditions of the solutions. We apply our results to thermal leptogenesis, computing analytically the asymmetry generated, comparing it with the semiclassical Boltzmann approach. The non-locality of the Kadanoff–Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry. The insertion of standard model decay widths to the particles excitations of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes.