Primordial magnetic field generation in the Quark Gluon Plasma phase

In this work we investigate the possibility of generation of primordial magnetic field in the early universe near the QCD phase transition epoch via the collapse of $Z(3)$ domains. The $Z(3)$ domain walls arise in the deconfined phase of the QCD (above $T\sim 200$ MeV) and their collapse leads to a net quark concentration near the wall boundary due to non-trivial reflection of quarks. We look at the response of leptons to this quark excess and find that leptons do not cancel the electric charge concentration due to the quarks. The wall collapse and a net charge concentration can lead to the generation of vorticity and turbulence in the primordial plasma. We estimate the magnitude of the magnetic field generated and find that it can be quite large $\mathcal{O}(10^{15-18}\mathrm{G})$. The mechanism is independent of the order of the QCD phase transition.