Magnetic fields in heavy ion collisions: flow and charge transport

Abstract

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity σ and the chiral magnetic conductivity σχ. We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial σχ can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like v1 or sin φ . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Charge-dependent flow induced by magnetic and electric fields in heavy ion collisions

“…by including the time-dependent conductivity; and ii) perform a full magnetohydrodynamical (MHD) simulation. The recent pilot MHD simulation [14] however indicates the same sign of ∆v 1 as our perturbative result. Clearly, more work is needed to improve our understanding of this important issue.…”

Wigner function formalism and the evolution of thermodynamic quantities in an expanding magnetized plasma

“…The proper time dependence of the electromagnetic field created in HICs was indeed the subject of intensive theoretical and experimental studies in the last few years (see e.g. [2][3][4][5]10]). The question about the effect of spacetime dependent magnetic fields on the evolution of thermodynamic quantities is still open.…”

“…Setting, N = 0 in (III.28), we obtain p ⊥ = 0, and ǫ = p = eBT 2 12 , as expected from (III.21). 5 The results presented in (III.28) can be in particular regarded as the high-temperature approximation of the T dependent part of p , p ⊥ , and ǫ arising from the effective action (II.13) [see (II.15), (II. 19) and (II.…”

“…It is widely believed that at τ 0 ∼ 0.2 fm/c after the collision, the created hot plasma enters a state of local thermal equilibrium. There are strong pieces of evidence that at this stage, the dynamics of the created quark matter is well described by relativistic hydrodynamics (for a recent review see [1] and references therein), that, because of extremely large magnetic fields that are also created in noncentral HIC experiments [2][3][4][5], is to be extended to relativistic MHD [6]. Assuming firstly that the plasma expands uniformly in the longitudinal direction with respect to the beam direction, and secondly that the external magnetic field is aligned perpendicular to the plasma velocity, it was recently possible to extend the well-known 1 + 1-dimensional Bjorken solution of relativistic hydrodynamics [7,8] to the so-called "ideal transverse MHD" [9], and to determine the proper time evolution of the magnetic field after the onset of hydrodynamics.…”

Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics

“…The results of such a simplified analytical model, which may be crucial in the search for CME, need to be justified by numerical investigations. Despite significant progress in iMHD [26][27][28], numerical computation of resistive RMHD in the QGP context is still missing.…”