Return of the grand unified theory baryogenesis: Source of helical
  hypermagnetic fields for the baryon asymmetry of the universe
  It has been considered that baryogenesis models without a generation of
$B$-$L$ asymmetry such as the GUT baryogenesis do not work since the asymmetry
is washed out by the electroweak sphalerons. Here, we point out that helical
hypermagnetic fields can be generated through the chiral magnetic effect with a
chiral asymmetry generated in such baryogenesis models. The helical
hypermagnetic fields then produce baryon asymmetry mainly at the electroweak
symmetry breaking, which remains until today. Therefore, the baryogenesis
models without $B$-$L$ asymmetry can still be the origin of the present baryon
asymmetry. In particular, if it can produce chiral asymmetry mainly carried by
right-handed electrons of order of $10^{-3}$ in terms of the chemical potential
to temperature ratio, the resultant present-day baryon asymmetry can be
consistent with our Universe, although simple realizations of the GUT
baryogenesis are hard to satisfy the condition. We also argue the way to
overcome the difficulty in the GUT baryogenesis. The intergalactic magnetic
fields with $B_0\sim 10^{-16 \sim 17}$ G and $\lambda_0 \sim 10^{-2\sim3}$ pc
are the smoking gun of the baryogenesis scenario as discussed before.
