  We apply a generic framework of linear sigma models for revealing a mechanism
of the mysterious phenomenon, the chiral magnetic effect, in quark-gluon
plasma. An electric current arises along a background magnetic field, which is
given rise to by Q-balls (non-topological solitons) of the linear sigma model
with axial anomaly. We find additional alternating current due to quark mass
terms. The hadronic Q-balls, baby boson stars, may be created in heavy-ion
collisions.
