Vector-current correlation and charge separation via the chiral-magnetic effect

Abstract

We investigate the vector-current correlation Pi_{mu nu} (VCC) in the presence of a strong external magnetic field (B_0 in the z direction) at low temperature (T<T^chi_c) with C- and CP-violations, indicated by the nonzero chiral-chemical potential (mu_chi>0), i.e. the chiral-magnetic effect (CME). For this purpose, we employ the instanton-vacuum configuration at finite T with nonzero topological charge (Q_t>0). From the numerical calculations, it turns out that the longitudinal component of the connected VCC is liner in B_0 and shows a bump, representing a corresponding vector meson at |Q|=(300~400) MeV for T=0. The bump becomes enhanced as T increases and the bump position shifts to a lager |Q| value. In the limit of |Q|->0, the transverse component of the connected VCC disappears, whereas the longitudinal one remains finite and gets insensitive to B_0 with respect to T, due to diluting instanton contributions. Considering a simple collision geometry of HIC and some assumptions on the induced magnetic field and screening effect, we can estimate the charge separation (ChS) as a function of centrality using the present results for VCC. The numerical results show a qualitative agreement with experiments for the Au+Au and Cu+Cu collisions. These results are almost independent on the source of CME, instanton or sphaleron, as long as the CME current is linear in B_0.