# Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis

## TL;DR

This paper reviews the theoretical frameworks and calculational methods for understanding matter-antimatter asymmetry in the early Universe, focusing on leptogenesis and electroweak baryogenesis, and introduces a quantum field theory-based approach for systematic analysis.

## Contribution

It develops a first-principles quantum field theory approach using the closed time-path method to derive and improve fluid equations for baryogenesis calculations.

## Key findings

- Derived equations governing matter-antimatter asymmetry production.
- Highlighted the importance of coherence effects and mixing in baryogenesis.
- Provided a systematic scheme for phenomenological modeling based on quantum field theory.

## Abstract

We review the production of the matter-antimatter asymmetry in the early Universe, that is baryogenesis, in out-of-equlibrium conditions induced by decays of heavy particles or by the presence of phase boundaries. The most prominent examples are given by leptogenesis and electroweak baryogenesis, respectively. For both cases, we derive the equations that govern the production of the asymmetries. We first use intuitive arguments based on classical fluid equations in combination with quantum-field-theoretical effects of CP-violation. As for a more thorough approach that is well-suited for systematic improvements, we obtain the real-time evolution of the system of interest using the closed time-path method. We thus provide a simple and practicable scheme to set up phenomenological fluid equations based on first principles of quantum field theory. Necessary for baryogenesis are both, CP even as well as odd phases in the amplitudes. A possibility of generating the even phases is the coherent superposition of quantum states, i.e. mixing. These coherence effects are essential in resonant leptogenesis as well as in some scenarios of electroweak baryogenesis. Recent theoretical progress on asymmetries from out-of-equlibrium decays may therefore also be applicable to baryogenesis at phase boundaries.