Tracing Electromagnetic Response through Charge Splitting of Directed Flow in the Quark-Gluon Plasma

Abstract

Experimentally observed charge splitting of directed flow, $\Delta v_1\equiv v_1(h^+)-v_1(h^-)$, exhibits both a sign reversal at midrapidity and the amplitude change from Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV to Pb+Pb at $\sqrt{s_{\rm NN}}=5.02$ TeV. We study this behavior within a unified $(3+1)$-dimensional viscous hydrodynamic model that incorporates an electromagnetic source term in the bulk evolution of the quark-gluon plasma (QGP) and an electromagnetic correction to the Cooper--Frye particlization. The beam-energy dependence of $\Delta v_1$ can be described by varying the effective electrical conductivity between RHIC and LHC energies, with values consistent with the conductivity scale indicated by lattice-QCD calculations. We find that the sign reversal emerges from the competition between momentum distortions induced by the electric and magnetic field which is controlled by the conductivity during the QGP evolution. The model further predicts the mass-dependent charge splittings for identified pions, kaons, and protons, providing further constraints on their respective relaxation times and the corresponding electromagnetic interaction. These results establish the charge splitting of directed flow as a quantitative probe of the electromagnetic response and the space-time evolution of the QGP.