Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order

TL;DR

This paper calculates the next-to-leading order corrections to the CP-violating source term in electroweak baryogenesis, revealing the limitations of the vev-insertion approximation and confirming the persistence of resonant enhancements at NLO.

Contribution

It provides the first NLO computation of source terms in the vev-insertion approximation for electroweak baryogenesis, extending previous leading-order analyses.

Findings

NLO corrections become significant for order-one couplings.

Vev-insertion approximation breaks down for top quarks if only the SM Higgs gets a vev.

Resonant enhancement persists at NLO in the degenerate mass limit.

Abstract

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 $\mathcal O(1)$ 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.