The Sphaleron in a Magnetic Field and Electroweak Baryogenesis

TL;DR

This paper investigates how primordial magnetic fields influence the sphaleron energy and electroweak baryogenesis, concluding that magnetic fields do not facilitate baryogenesis despite affecting the phase transition.

Contribution

It computes the sphaleron energy in a magnetic field and demonstrates that magnetic fields lower the energy barrier, counteracting potential benefits for baryogenesis.

Findings

Magnetic fields lower the sphaleron energy barrier.

Stronger phase transitions are required to preserve baryon asymmetry.

Magnetic fields do not aid electroweak baryogenesis.

Abstract

The presence of a primordial magnetic field in the early universe affects the dynamic of the electroweak phase transition enhancing its strength. This effect may enlarge the window for electroweak baryogenesis in the minimal supersymmetric extension of the standard model or even resurrect the electroweak baryogenesis scenario in the standard model. We compute the sphaleron energy in the background of the magnetic field and show that, due to the sphaleron dipole moment, the barrier between topologically inequivalent vacua is lowered. Therefore, the preservation of the baryon asymmetry calls for a much stronger phase transition than required in the absence of a magnetic field. We show that this effect overwhelms the gain in the phase transition strength, and conclude that magnetic fields do not help electroweak baryogenesis.