Investigating effects of the electrical conductivity of QCD matter on charge-dependent directed flow

Charge-dependent directed flow is an important observable of electromagnetic fields in relativistic heavy-ion collisions. We demonstrate how the difference in charge-dependent directed flows between protons and antiprotons is sensitive to the resistivity, inverse of quark-gluon plasma's electric conductivity, over different collision centralities. Our model numerically solves the (3 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mo>+</a:mo></a:math> 1)-dimensional relativistic resistive magnetohydrodynamic equations, assuming the electric conductivity to be a scalar. For this work, we focus on symmetric Au <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mo>+</b:mo></b:math> Au collisions at the top Relativistic Heavy-Ion Collider energy of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msqrt><c:mi>s</c:mi></c:msqrt><c:mo>=</c:mo><c:mn>200</c:mn></c:mrow></c:math> GeV. We illustrate the time evolution of the electromagnetic fields in our model and connect that to the charge-dependent directed flow results. Our results highlight the importance of modeling quark-gluon plasma's electric conductivity for charge-dependent observables in relativistic heavy-ion collisions.