In electroweak baryogenesis the baryon asymmetry of the universe is created during the electroweak phase transition. The quantum transport equations governing the dynamics of the plasma particles can be derived in the vev-insertion approximation, which treats the vev-dependent part of the particle masses as a perturbation. We calculate the next-to-leading order (NLO) contribution to the CP-violating source term and CP-conserving relaxation rate, corresponding to Feynman diagrams for the self-energies with four mass insertions. We consider both a pair of Weyl fermions and a pair of complex scalars, that scatter off the bubble wall. We find: (i) The NLO correction becomes large for O $$ \mathcal{O} $$ (1) couplings. If only the Standard Model (SM) Higgs obtains a vev during the phase transition, this implies the vev-insertion approximation breaks down for top quarks. (ii) The resonant enhancement of the source term and relaxation rate, that exists at leading order in the limit of degenerate thermal masses for the fermions/scalars, persists at NLO.

中文翻译：

---

超导序的 vev 插入近似中电弱重子发生的源项

在电弱重子发生中，宇宙的重子不对称是在电弱相变期间产生的。控制等离子体粒子动力学的量子传输方程可以在 vev 插入近似中推导出来，它将粒子质量的 vev 相关部分视为扰动。我们计算了对 CP 违反源项和 CP 守恒松弛率的次前导阶 (NLO) 贡献，对应于具有四个质量插入的自能的费曼图。我们考虑一对外尔费米子和一对从气泡壁散射的复标量。我们发现： (i) 对于 O $$ \mathcal{O} $$ (1) 耦合，NLO 校正变大。如果只有标准模型 (SM) Higgs 在相变期间获得 vev，这意味着 vev 插入近似分解为顶夸克。(ii) 源项和弛豫率的共振增强，在费米子/标量的简并热质量极限中以领先顺序存在，在 NLO 中持续存在。