Charge asymmetry dependence of the elliptic flow splitting in relativistic heavy-ion collisions

Elliptic flow splitting $\mathrm{\Delta }{v}_2$ between $\overline{u}$ and $u$ quarks as well as between ${\pi }^{-}$ and ${\pi }^{+}$ in midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV is studied, based on the framework of an extended multiphase transport model with the partonic evolution described by the chiral kinetic equations of motion. Within the available statistics, the slope of $\mathrm{\Delta }{v}_2$ between $\overline{u}$ and $u$ quarks with respect to the electric charge asymmetry $A_{\mathrm{ch}}$ from the linear fit is found to be negative, due to the correlation between the velocity and the coordinate in the initial parton phase-space distribution. Simulations with the magnetic field in QGP overestimate the splitting of the spin polarization between $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ observed experimentally, with the latter more consistent with results under the magnetic field in vacuum. Considering the uncertainties from the magnetic field, the quark-antiquark vector interaction, and the hadronization, as well as the hadronic evolution, our study shows that the experimentally observed positive slope of $\mathrm{\Delta }{v}_2$ with respect to $A_{\mathrm{ch}}$ is not likely due to the chiral magnetic wave.

Figure 1

Left: Time evolution of the total light parton number density in central cells and the approximated electrical conductivity of the QGP. Right: Time evolution of the $y$ component of the real magnetic field in vacuum (${\sigma }_{\mathrm{con}}=0$) and in QGP (${\sigma }_{\mathrm{con}}>0$) at the center of the collision system. Results are from simulations for midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 2

Contours of the $y$ component of the real magnetic field ${(\mathbf{\nabla }\times e{\vec{A}}_m)}_y$ in vacuum (first row), the real magnetic field ${(\mathbf{\nabla }\times e{\vec{A}}_m)}_y$ in QGP (second row), and the effective magnetic field ${(\mathbf{\nabla }\times g_V\vec{\rho })}_y$ (third row) at different times in the reaction plane of midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 3

Event distributions of the electric charge asymmetry $A_{\mathrm{ch}}$ for freeze-out partons, initial hadrons right after hadronization, and freeze-out hadrons after hadronic evolution in midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 4

Left: Elliptic flow difference between freeze-out $\overline{u}$ and $u$ quarks as a function of the electric charge asymmetry $A_{\mathrm{ch}}$ in midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV for different scenarios. Right: Correlated relation between the $z$-component velocity $\langle k_z/k\rangle$ and the coordinate $x$ for initial quarks from AMPT and the uncorrelated one for testing purposes.

Figure 5

Elliptic flow difference between ${\pi }^{-}$ and ${\pi }^{+}$ as a function of the electric charge asymmetry $A_{\mathrm{ch}}$ at the initial stage of the hadronic phase right after hadronization in midcentral Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV for different scenarios of partonic dynamics.

Figure 6

Same as Fig. 5, but at the freeze-out stage of the hadronic phase.

Figure 7

Left: Time evolution of the spin polarizations of different quark species for a typical scenario. Right: Spin polarizations of $s$ and $\overline{s}$ quarks at the freeze-out stage of the partonic phase for different scenarios.