Structure of electroweak dumbbells

TL;DR

This paper investigates the magnetic field structures of electroweak dumbbells, revealing a novel twisted magnetic field component with a different decay rate, which has implications for understanding magnetic fields from the electroweak phase transition.

Contribution

It introduces the concept of twisted electroweak dumbbells and characterizes their unique magnetic field behavior compared to untwisted cases.

Findings

Untwisted dumbbells produce dipole magnetic fields falling off as 1/r^3.

Twisted dumbbells generate a magnetic field that falls off as cosθ/r^2.

Twisted configurations may influence magnetic field coherence after the electroweak phase transition.

Abstract

We analyze the magnetic field of electroweak dumbbells. While the magnetic field of the untwisted dumbbell is given by the usual dipole formula and falls of as $1/r^3$, dumbbells with twist have a novel twisted magnetic field that only falls off as $\cos\theta/r^2$ (in spherical coordinates). We comment on the relevance of twisted electroweak dumbbells for understanding the coherence of the magnetic field generated at the electroweak phase transition.