  Chiral anomaly is a fundamental aspect of quantum theories with chiral
fermions. How such microscopic anomaly manifests itself in a macroscopic
many-body system with chiral fermions, is a highly nontrivial question that has
recently attracted significant interest. As it turns out, unusual transport
currents can be induced by chiral anomaly under suitable conditions in such
systems, with the notable example of the Chiral Magnetic Effect (CME) where a
vector current (e.g. electric current) is generated along an external magnetic
field. A lot of efforts have been made to search for CME in heavy ion
collisions, by measuring the charge separation effect induced by the CME
transport. A crucial challenge in such effort, is the quantitative prediction
for the CME signal. In this paper, we develop the Anomalous-Viscous Fluid
Dynamics (AVFD) framework, which implements the anomalous fluid dynamics to
describe the evolution of fermion currents in QGP, on top of the neutral bulk
background described by the VISH2+1 hydrodynamic simulations for heavy ion
collisions. With this new tool, we quantitatively and systematically
investigate the dependence of the CME signal to a series of theoretical inputs
and associated uncertainties. With realistic estimates of initial conditions
and magnetic field lifetime, the predicted CME signal is quantitatively
consistent with measured change separation data in 200GeV Au-Au collisions.
Based on analysis of Au-Au collisions, we further make predictions for the CME
observable to be measured in the planned isobaric (Ru-Ru v.s. Zr-Zr ) collision
experiment, which could provide a most decisive test of the CME in heavy ion
collisions.
