The non-central Cu + Au collisions can create strong out-of-plane magnetic fields and in-plane electric fields. By using the HIJING model, we study the general properties of the electromagnetic fields in Cu + Au collisions at 200 GeV and their impact
s on the charge-dependent two-particle correlator $gamma_{q_1q_2}=<cos(phi_1+phi_2-2psi_{RP})>$ (see main text for definition) which was used for the detection of the chiral magnetic effect (CME). Compared with Au + Au collisions, we find that the in-plane electric fields in Cu + Au collisions can strongly suppress the two-particle correlator or even reverse its sign if the lifetime of the electric fields is long. Combining with the expectation that if $gamma_{q_1q_2}$ is induced by elliptic-flow driven effects we would not see such strong suppression or reversion, our results suggest to use Cu + Au collisions to test CME and understand the mechanisms that underlie $gamma_{q_1q_2}$.
The microscopic formulas for the shear viscosity $eta$, the bulk viscosity $zeta$, and the corresponding relaxation times $tau_pi$ and $tau_Pi$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potentia
l by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Pi$ is appropriately chosen, the leading-order result of the ratio, $zeta$ over $tau_Pi$, coincides with the same ratio obtained at vanishing chemical potential. We further discuss the physical meaning of the time-convolutionless (TCL) approximation to the memory function, which is adopted to derive the main formulas. We show that the TCL approximation violates the time reversal symmetry appropriately and leads results consistent with the quantum master equation obtained by van Hove. Furthermore, this approximation can reproduce an exact relation for transport coefficients obtained by using the f-sum rule derived by Kadanoff and Martin. Our approach can reproduce also the result in Baier et al.(2008) Ref. cite{con} by taking into account the next-order correction to the TCL approximation, although this correction causes several problems.
The microscopic formulae of the bulk viscosity $zeta $ and the corresponding relaxation time $tau_{Pi}$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae to the pionic fl
uid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition and $tau_{Pi}$ and $zeta $ are related as $tau_{Pi}=zeta /[beta {(1/3-c_{s}^{2})(epsilon +P)-2(epsilon -3P)/9}]$, where $epsilon $, $P$ and $c_{s}$ are the energy density, pressure and velocity of sound, respectively. The predicted $zeta $ and $% tau_{Pi}$ should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all the three approaches are consistent with the causality condition.
The transport coefficients of causal relativistic dissipative fluid dynamics are calculated both in a field-theoretical and a kinetic approach. We find that the results from the traditional kinetic calculation by Israel and Stewart are modified. The
new expressions for the viscous transport coefficients agree with the results obtained in the field-theoretical approach when the contributions from pair creation and annihilation are neglected.
