Electromagnetic fields from the extended Kharzeev-McLerran-Warringa model in relativistic heavy-ion collisions.

Based on the Kharzeev-McLerran-Warringa (KMW) model that estimates the strong electromagnetic (EM) fields generated in relativistic heavy-ion collisions, we generalize the formulas of EM fields in the vacuum by incorporating the longitudinal position dependence, the generalized charge density distribution and retardation correction. We further generalize the formulas of EM fields in the QGP medium by incorporating a constant Ohm electric conductivity. Using the extended KMW model, we observe a slower time evolution and a more reasonable impact parameter $b$ dependence of the magnetic field strength than those from the original KMW model in the vacuum. The constant electric conductivity from lattice QCD data helps further prolong the time evolution of magnetic field, so that the magnetic field strength at the thermal freeze-out time matches the required magnetic field strength for the explanation of the observed difference in global polarizations of $\Lambda$ and $\bar{\Lambda}$ hyperons in Au+Au collisions at RHIC. These generalized formulations in the extended KMW model could be potentially useful for many EM fields relevant studies in relativistic heavy-ion collisions at lower colliding energies and for various species of colliding nuclei.