Chern-Simons number asymmetry from CP violation at electroweak tachyonic preheating

TL;DR

This work analyzes the generation of non-zero Chern-Simons number during a tachyonic electroweak transition in a 1+1D Abelian-Higgs model with a CP-violating coupling, neglecting cosmic expansion. Using real-time lattice simulations and a careful quantum-to-classical initial-condition treatment, it shows that a sizable CS number can emerge from a fast Higgs quench, with both the sign and magnitude depending sensitively on the Higgs-to-W mass ratio $m_H/m_W$ and the CP parameter $\kappa$. The mechanism does not rely on resonant preheating or Kibble-type defect production; the CS asymmetry is initiated by CP-violating dynamics and then partially preserved by sphaleron suppression as the system cools. The results imply potential baryon-number generation in zero-temperature electroweak transitions and motivate extending the analysis to the physically relevant SU(2)-Higgs theory in 3+1 dimensions to assess cosmological impact.

Abstract

We consider the creation of non-zero Chern-Simons number in a model of the early Universe, where the Higgs field experiences a fast quench at the end of inflation and subsequently rolls down its potential barrier. Neglecting the expansion, we perform numerical lattice simulations in the Abelian Higgs model in 1+1 dimensions with an added phenomenological C and P violating term during this stage of so-called tachyonic preheating. The results suggest that even the sign of the Chern-Simons and thus baryon number is dependent on the ratio of the Higgs to W mass. We also discuss the appropriate choice of vacuum initial conditions for classical simulations.