Electromagnetic fields and directed flow in large and small colliding systems at ultrarelativistic energies

The hot and dense QCD matter produced in nuclear collisions at ultrarelativistic energy is characterized by very intense electromagnetic fields which attain their maximal strength in the early pre-equilibrium stage and interplay with the strong vorticity induced in the plasma by the large angular momentum of the colliding system. A promising observable keeping trace of these phenomena is the directed flow of light hadrons and heavy mesons produced in symmetric and asymmetric heavy-ion collisions as well as in proton-induced reactions. In particular, the splitting of the directed flow between particles with the same mass but opposite electric charge as a function of rapidity and transverse momentum gives access to the electromagnetic response of medium in all collision stages and in the different colliding systems. The highest influence of electromagnetic fields is envisaged in the pre-equilibrium stage of the collision and therefore a significant imprint is left on the early-produced heavy quarks. The aim of this review is to discuss the current developments towards the understanding of the generation and relaxation time of the electromagnetic fields embedded in both large and small systems and their impact on the charge-odd directed flow of light and heavy particles, highlighting the experimental results and the different theoretical approaches. Since it is possible to perform realistic simulations of high-energy collisions that incorporate also the generated electromagnetic fields and vorticity, the study of the directed flow can provide unique insight into the early nonequilibrium phase and the ensuing QGP formation and transport properties.