Abstract
We investigate the charge-dependent flow induced by magnetic and electric fields in heavy ion collisions. We simulate the evolution of the expanding cooling droplet of strongly coupled plasma hydrodynamically, using the iEBE-VISHNU framework, and add the magnetic and electric fields as well as the electric currents they generate in a perturbative fashion. We confirm the previously reported effect of the electromagnetically induced currents, that is a charge-odd directed flow $\Delta v_1$ that is odd in rapidity, noting that it is induced by magnetic fields (\`a la Faraday and Lorentz) and by electric fields (the Coulomb field from the charged spectators). In addition, we find a charge-odd $\Delta v_3$ that is also odd in rapidity and that has a similar physical origin. We furthermore show that the electric field produced by the net charge density of the plasma drives rapidity-even charge-dependent contributions to the radial flow $\langle p_T \rangle$ and the elliptic flow $\Delta v_2$. Although their magnitudes are comparable to the charge-odd $\Delta v_1$ and $\Delta v_3$, they have a different physical origin, namely the Coulomb forces within the plasma.
Highlights
Large magnetic fields B are produced in all noncentral heavy-ion collisions by the moving and positively charged spectator nucleons that “miss,” flying past each other rather than colliding, as well as by the nucleons that participate in the collision
We have described the effects of electric and magnetic fields on the flow of charged hadrons in noncentral heavy-ion collisions by using a realistic hydrodynamic evolution within the iEBE-VISHNU framework
Three different effects contribute: the Coulomb field of the spectator ions, the Lorentz force due to the magnetic field sourced by the spectator ions, and the electromotive force induced by Faraday’s law as that magnetic field decreases
Summary
Large magnetic fields B are produced in all noncentral heavy-ion collisions (those with nonzero impact parameter) by the moving and positively charged spectator nucleons that “miss,” flying past each other rather than colliding, as well as by the nucleons that participate in the collision. In previous work [1] three of the authors noted that the magnetic field produced in a heavy-ion collision could result in a measurable effect in the form of a charge-odd contribution to the directed flow coefficient v1 This contribution has the opposite sign for positively vs negatively charged hadrons in the final state and is odd in rapidity. The azimuthal asymmetry of the almond-shaped collision zone in a collision with nonzero impact parameter, its remaining symmetries under x ↔ −x and y ↔ −y, and the orientation of the magnetic field B perpendicular to the beam and impact parameter directions together mean that the currents induced by the Faraday and Lorentz effects (illustrated in Fig. 1) make a charge-odd and rapidity-odd contribution to all the odd flow harmonics, to v1. V we discuss the validity of the various approximations used in our calculations, discuss other related work, and present an outlook
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