Some aspects of collisional sources for electroweak baryogenesis

TL;DR

The paper develops a controlled, gradient-expanded framework based on the 2PI Schwinger-Keldysh formalism to compute CP-violating sources arising from fermion-scalar collisions in a space-dependent mass background relevant to electroweak baryogenesis. It demonstrates that CP-violating sources appear in the fermionic collision term at first order in gradients (while scalar sources vanish at this order) and that the CP-violating effects combine with the semiclassical force to drive baryogenesis; it also shows that the relaxation time approximation can produce unphysical CP-violating sources. The findings underscore the need for a two-loop self-energy analysis for reliable quantitative predictions. The work clarifies the distinct roles of fermionic versus scalar sectors and provides a framework applicable to chiral fermions interacting with Higgs-like condensates during a first-order electroweak phase transition.

Abstract

We consider the dynamics of fermions with a spatially varying mass which couple to bosons through a Yukawa interaction term and perform a consistent weak coupling truncation of the relevant kinetic equations. We then use a gradient expansion and derive the CP-violating source in the collision term for fermions which appears at first order in gradients. The collisional sources together with the semiclassical force constitute the CP-violating sources relevant for baryogenesis at the electroweak scale. We discuss also the absence of sources at first order in gradients in the scalar equation, and the limitations of the relaxation time approximation.

Figures (4)

• Figure 1: The Schwinger closed-time-path (CTP) used in the derivation of the 2PI effective action (\ref{['EffectiveAction']}).
• Figure 2: The diagrams contributing to the 2PI effective action (\ref{['EffectiveAction0']}-\ref{['EffectiveAction2']}) up to two loops for the Lagrangian (\ref{['lagrangian0']}) with the fermion-scalar Yukawa coupling term (\ref{['lagrangian1']}). The full (dressed) fermionic and bosonic propagators are denoted by $S$ ( solid blue lines) and $\Delta$ ( dashed red lines), respectively.
• Figure 3: The Dyson-Schwinger equations at one loop obtained by varying the 2PI effective action (\ref{['EffectiveAction0']}-\ref{['EffectiveAction2']}) with respect to the fermionic and bosonic propagators. The corresponding tree-level Lagrangian is given by (\ref{['lagrangian0']}-\ref{['lagrangian1']}). The full (dressed) fermionic and bosonic propagators are denoted by $S$ ( solid blue lines) and $\Delta$ ( dashed red lines), respectively.
• Figure 4: Shown as a function of $|m|/T$ is the expression $|m|^2{\cal I}_f(|m|,m_\phi)$, which appears in the collisional source (46) arising in the fermionic kinetic equation at one loop. For simplicity we have set $T=1$.