Chiral Transport Theory And Application In Heavy Ion Collision

Recently there is significant interest in understanding the macroscopic quantum transport in many-body system of chiral fermions.A natural many-body framework for describing a system in out of equilibrium is the transport equation in phase space.There are,however,several subtle and confusing issues,particularly related to Lorentz invariance and frame dependence.In this paper,we obtain a complete solution of the covariant chiral transport for massless fermions,by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion in h order.This new result clarifies the origin of the Lorentz invariance and frame dependence issues associated with the first order correction in h.From the so-obtained chiral transport equation,the 3D chiral kinetic theory as well as many peculiar phenomena of chiral fermions naturally as its consequences.A notable example of chiral anomaly is the Chiral Magnetic Effect(CME).Many efforts have been made to search for the CME in the quark-gluon plasma created in heavy ion collisions.A crucial challenge is that the extremely strong magnetic field in such collisions may last only a brief moment and the CME current may occur only in the initial stage when the quark-gluon matter is still far from thermal equilibrium.This thus requires modeling of the CME in an out-of-equilibrium setting.With the recently developed theoretical tool of chiral kinetic theory,we make a first phenomenological study of the CME-induced charge separation during the pre-thermal stage in heavy ion collisions.The effect is found to be very sensitive to the time dependence of the magnetic field and influenced by the initial quark momentum spectrum as well as the relaxation time of the system evolution toward thermal equilibrium.Within the present approach,such pre-thermal charge separation is found to be modest.