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