QCD under magnetic field: chiral magnetic effect at heavy ion collisions

In this talk, we report our recent studies for the chiral magnetic effect, which signals the P- and CP-violations at the heavy ion collisions. We compute the electric current and its correlations, induced by the external magnetic field, inside the hot and dense QCD matter created in the heavy ion collisions. For this purpose, we employ the instanton-liquid model, modified by the Harrington-Shepard caloron at finite T. We observe that the chiral magnetic effect current and its correlations increase with respect to the magnetic field, whereas they decrease as functions of T, due to the diluting instanton ensemble. It turns out that the numerical results are in good agreement with those from the model-independent analyses and lattice QCD simulations. We also reproduce the charge separations, observed in the STAR experiment, qualitatively well, considering the simplified Lienard-Wiechert potential, screening and size effects.