Electroweak Sphaleron in a Magnetic field

TL;DR

This study uses lattice simulations to analyze how an external hypermagnetic field influences the electroweak sphaleron rate and the electroweak cross-over temperature, revealing magnetic field-dependent shifts and behaviors in baryon number violation.

Contribution

It provides the first detailed lattice simulation analysis of the sphaleron rate under external hypermagnetic fields across the electroweak cross-over, including the effects on the phase transition temperature.

Findings

The electroweak cross-over temperature decreases with increasing magnetic field.

The sphaleron rate varies quadratically with small magnetic flux and linearly with stronger fields.

Strong magnetic fields can restore electroweak symmetry, reaching the symmetric phase rate.

Abstract

Using lattice simulations we calculate the rate of baryon number violating processes, the sphaleron rate, in the Standard Model with an external (hyper)magnetic field for temperatures across the electroweak cross-over, focusing on the broken phase. Additionally, we compute the Higgs expectation value and the pseudocritical temperature. The electroweak cross-over shifts to lower temperatures with increasing external magnetic field, bringing the onset of the suppression of the baryon number violation with it. When the hypermagnetic field reaches the magitude $B_Y \approx 2 T^2$ the cross-over temperature is reduced from $160$ GeV to $145$ GeV. In the broken phase for small magnetic fields the rate behaves quadratically as a function of the magnetic flux. For stronger magnetic fields the rate reaches a linear regime which lasts until the field gets strong enough to restore the electroweak symmetry where the symmetric phase rate is reached.