Cutting rules on a cylinder: a simplified diagrammatic approach to quantum kinetic theory

Abstract

Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work presents an alternative framework using the zero-temperature quantum field theory, S-matrix unitarity, and classical Boltzmann equation as starting points leading to a set of rules for calculations of thermal corrections to reaction rates. Statistical factors due to on-shell intermediate states are obtained from the cuts of forward diagrams with multiple spectator lines. It turns out that it is equivalent to cutting closed diagrams on a cylindrical surface.

Mass-derivative relations for leptogenesis

“…(6). As discussed in our previous work [20], drawing these diagrams on a cylindrical surface corresponds to the winding of the Higgs internal line in Fig. 2a.…”

“…( 12) in a consistent way, we have explained in full detail the procedure in Ref. [20]. In short, we start with the diagram with the lowest winding numbers for all particles (the diagram in Fig.…”

“…4 In a general nonequilibrium case, it may seem unclear what the classical density fH is, while f H corresponds to the mean occupation number of a particular single-particle state in the Fock space. Nevertheless, for bosonic particles, one may formally define fH = f H /(1 + f H ) and proceed along the same lines [20]. The N i → l H decay rate, on the other hand, with quantum statistical factors for the final states, equals…”

“…In our work, the diagrammatic representation developed in Refs. [19,20] is used to study the connection of the two approaches to thermal masses and infrared finiteness at a given perturbative order. It is shown that some of the 2 ↔ 3 contributions are directly related to the Higgs thermal mass effects in the N i → l H decay kinematics.…”

“…Section 3 deals with the inclusion of quantum thermal corrections using the cylindrical diagrammatic representation of Ref. [20]. Finally, in Sect.…”