Longitudinal distribution of initial energy density and directed flow of charged particles in relativistic heavy-ion collisions

Abstract

We study the origin of the directed flow of charged particles produced in relativistic heavy-ion collisions. Three different initial conditions, Bozėk-Wyskiel, CCNU and Shen-Alzhrani, of energy density distributions are coupled to the (3+1)-dimensional viscous hydrodynamic model CLVisc, and their effects on the development of the anisotropic medium geometry, pressure gradient and radial flow are systematically compared. By comparing to experimental data at both RHIC and LHC, we find that the directed flow provides a unique constraint on the tilt of the initial medium profile in the plane spanned by the impact parameter and space-time rapidity. Within midrapidity, the counter-clockwise tilt is shown to be a crucial source of the positive/negative force by the pressure gradient along the impact parameter (x) direction at backward/forward rapidity, which drives a negative slope of the x component of the medium flow velocity with respect to rapidity, and in the end the same feature of the charged particle directed flow.

Probing the initial longitudinal density profile and electromagnetic field in ultrarelativistic heavy-ion collisions with heavy quarks

“…A. Hydrodynamic evolution of the QGP Before studying the heavy quark interaction with the QGP medium, we first discuss the evolution of the QGP fireballs within the (3+1)-D viscous hydrodynamic model CLVisc [57] coupled with the tilted initial energy density distribution in the reaction plane of non-central heavy-ion collisions [54,55].…”

“…where W N represents the weight contributed by wounded nucleons, n BC represents contributions from binary collisions [55], and the collision hardness parameter α measures the relative contributions between the two. Following our recent studies [54,55], the asymmetric distribution with respect to the beam axis is introduced into W N as in which T 1 and T 2 , containing the nucleon-nucleon inelastic scattering cross section σ NN , are the density distribution of participant nucleons from the two colliding nuclei traveling in the positive and negative z directions respectively [55]; and H t tan(η s /η t ) reflects the strength of imbalance between particle emission in the forward and backward spacetime rapidities (η s ) along the direction of impact parameter (b). In the present work, we adopt H t = 3.9 for 10-80% Au+Au collisions at √ s NN = 200 GeV and H t = 0.70 for 10-40%…”

“…These values have been adjusted in Ref. [55] for a satisfactory description of the soft hadron v 1 in their corresponding collision systems. Additionally, in Eq.…”

“…1, where a counter-clockwise tilted geometry in the x-η s plane with respect to the longitudinal direction can be seen. This tilted initial condition was shown essential for understanding the directed flow of soft hadrons emitted from the QGP [55]. Since heavy quarks are produced from the initial hard scatterings within the overlapping region between the two colliding nuclei, their initial spatial distribution is expected to be symmetric about the y-η s plane.…”

“…The heavy quark evolution through the QGP is described using a modified Langevin approach [13,53] that incorporates the thermal diffusion of heavy quarks inside the QGP, medium-induced gluon emission, as well as the Lorentz force due to the electromagnetic field. With the tilted geometry of the initial energy density distribution with respect to the longitudinal direction [54,55], the spacetime evolution profile of the QGP is simulated with the (3+1)-D viscous hydrodynamic model CLVisc [56][57][58][59]. Within this sophisticated framework, we find that the heavy meson v 1 is dominated by the heavy quark interaction with the tilted QGP medium at the RHIC energy, while by the heavy quark interaction with the electromagnetic field at the LHC energy.…”