Cutting rules on a cylinder and simplified diagrammatic approach to $CP$ violation in quantum kinetic theory
April 22, 2022
We briefly explain a novel diagrammatic method for including thermal corrections in $CP$ asymmetric reaction rates entering the quantum Boltzmann equation. In thermal equilibrium, the asymmetries have to cancel precisely due to the $S$-matrix unitarity and $CPT$ invariance. Such cancelations are easy to track in zero-temperature leading-order calculations. However, accounting for medium effects requires modification of the on-shell part of propagators and, consequently, the $CP$ violating rates. In the literature, the correct form of the statistical factors in the asymmetry source term has been obtained employing the real-time-formalism of non-equilibrium field theory in a certain approximation. We demonstrate that the same results can be obtained by summing an infinite sequence of zero-temperature asymmetries. Those are derived from cuttings of forward diagrams drawn on a cylindrical surface, while thermal corrections come from windings of their propagators. The procedure is entirely diagrammatic, and the $CPT$ and unitarity cancelations are formulated for thermally corrected reaction rate asymmetries. The simplification achieved is the primary focus of our work. The aspect of infrared finiteness in higher-order corrections will also be discussed. The contribution is primarily based on our previous work in Refs. [1-3].
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating
very compact bibliographies which can be beneficial to authors and
readers, and in "proceeding" format
which is more detailed and complete.