Probing the $B+L$ violation process with the observation of cosmic magnetic field

TL;DR

This paper explores the connection between electroweak $B+L$ violation, sphaleron decay, and the generation of helical magnetic fields, proposing an observational method to probe baryon asymmetry via cosmic magnetic fields.

Contribution

It presents the first three-dimensional lattice simulation linking sphaleron decay to helical magnetic field production during electroweak phase transition.

Findings

Sphaleron decay correlates with changes in Chern-Simons number and helical magnetic fields.

Helical magnetic fields with fractional helicity up to 0.2 can be detected by Cherenkov Telescope Array.

Proposes a novel observational approach to study baryon asymmetry through cosmic magnetic fields.

Abstract

We investigate the $B+L$ violation process by performing three-dimensional lattice simulations in an electroweak theory with first-order phase transition and the electroweak sphaleron decay. The simulation results indicate that the Chern-Simons number changes along with the helical magnetic field production when the sphaleron decay occurs. Our study suggests that, for the electroweak phase transition with nucleation rate being smaller than $\sim \mathcal{O}(10)$, the helical magnetic field with the fractional magnetic helicity $\epsilon_M\leq 0.2$ can be probed by Cherenkov Telescope Array through the intergalactic magnetic field measurements. Based on our numerical results, we suggest a method to probe the baryon asymmetry generation of the Universe, which is a general consequence of the electroweak sphaleron process, through the astronomical observation of the corresponding helical magnetic field.