Charge-dependent anisotropic flow in high-energy heavy-ion collisions from a relativistic resistive magneto-hydrodynamic expansion
Kouki Nakamura, Takahiro Miyoshi, Chiho Nonaka, Hiroyuki R. Takahashi
Abstract
We have investigated the charge-dependent anisotropic flow in high-energy heavy-ion collisions, using relativistic resistive magneto-hydrodynamics (RRMHD). We consider the optical Glauber model as an initial model of the quark-gluon plasma (QGP) and the solution of the Maxwell equations with source term of the charged particles in two colliding nuclei as initial electromagnetic fields. The RRMHD simulation is performed with these initial conditions in Au-Au and Cu-Au collisions at $\sqrt{{s}_{NN}}=200$ GeV. We have calculated the charge-odd contribution to the directed flow $\mathrm{\ensuremath{\Delta}}{v}_{1}$ and elliptic flow $\mathrm{\ensuremath{\Delta}}{v}_{2}$ in both collisions based on electric charge distributions as a consequence of RRMHD. Our results show that the $\mathrm{\ensuremath{\Delta}}{v}_{1}$ and $\mathrm{\ensuremath{\Delta}}{v}_{2}$ are approximately proportional to the electrical conductivity ($\ensuremath{\sigma}$) of the medium. In the $\ensuremath{\sigma}=0.023\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ case, our result of $\mathrm{\ensuremath{\Delta}}{v}_{1}$ is close to STAR data in Au-Au collisions, while it is slightly overestimated in forward and backward rapidity regions. Furthermore, in Cu-Au collisions, $\mathrm{\ensuremath{\Delta}}{v}_{1}$ has a nonzero value at $\ensuremath{\eta}=0$. We conclude that the charge-dependent anisotropic flow is a good probe to extract the electrical conductivity of the QGP medium in high-energy heavy-ion experiments.