Flavour mixing transport theory and resonant leptogenesis

We derive non-equilibrium quantum transport equations for flavour-mixing fermions. We develop the formalism mostly in the context of resonant leptogenesis with two mixing Majorana fermions and one lepton flavour, but our master equations are valid more generally in homogeneous and isotropic systems. We give a hierarchy of quantum kinetic equations, valid at different approximations, that can accommodate helicity and arbitrary mass differences. In the mass-degenerate limit the equations take the familiar form of density matrix equations. We also derive the semiclassical Boltzmann limit of our equations, including the CP-violating source, whose regulator corresponds to the flavour coherence damping rate. Boltzmann equations are accurate and insensitive to the particular form of the regulator in the weakly resonant case $\Delta m \gg \Gamma$, but for $\Delta m \lesssim \Gamma$ they are qualitatively correct at best, and their accuracy crucially depends on the form of the CP-violating source.