Abstract
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 ∆m » Γ, but for ∆m ≲ Γ they are qualitatively correct at best, and their accuracy crucially depends on the form of the CP-violating source.
Highlights
Quantum coherence, and the related mixing and oscillation of quantum states, plays an important role in many interesting phenomena in particle physics and in the early universe
Several different types of coherence may be relevant depending on the problem: particle production is driven by the particle-antiparticle coherence, and coherent mixing of left- and right-moving particles can be the engine for creating the particle-antiparticle asymmetry during the electroweak phase transition
Coherence between different flavour states powers the familiar phenomenon of neutrino oscillations as well as the particle-antiparticle asymmetry generation in leptogenesis, which is the main topic of this paper
Summary
The related mixing and oscillation of quantum states, plays an important role in many interesting phenomena in particle physics and in the early universe. The cQPA is a two-step approximation where the structure of the Wightman function is solved first in a collisionless approximation in the Wigner representation This results in a spectral shell structure, including particle and coherence shells, which is used to solve the full dynamical equation.
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