Modified Magnetohydrodynamics Around the Electroweak Transition

TL;DR

This paper investigates how the electroweak transition affects chiral asymmetries and magnetic fields, concluding that significant magnetic field amplification is unlikely during the transition, despite the influence of the chiral anomaly.

Contribution

It provides a detailed analysis of MHD solutions around the electroweak transition considering the chiral anomaly, highlighting the evolution of chiral asymmetry and magnetic fields.

Findings

Chiral asymmetry grows before the transition and decreases afterward.

No significant magnetic field amplification occurs during the transition.

Chiral asymmetry can generate helical magnetic fields from non-helical ones.

Abstract

We analyse solutions of the MHD equations around the electroweak transition taking into account the effects of the chiral anomaly. It is shown that a transition that is not of the first order has direct consequences on the evolution of the asymmetry between left- and right-handed leptons. Assuming an initial chiral asymmetry in the symmetric phase at temperatures higher than the transition temperature, as well as the existence of magnetic fields, it is demonstrated that the asymmetry typically grows with time, until it undergoes a fast decrease at the transition, and then eventually gets damped at lower temperatures in the broken phase. We argue that it is unlikely to have any significant magnetic field amplification as a consequence of the electroweak transition in the Standard model, even when the chiral anomaly is introduced. The presence of a chiral asymmetry between left- and right-handed charge carriers naturally leads to the creation of helical magnetic fields from non-helical fields and this can have consequences on their subsequent evolution.