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Register a new userDirected flow, a signal for the phase transition in Relativistic Nuclear Collisions?
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The sign change of the slope of the directed flow of baryons has been predicted as a signal for a first order phase transition within fluid dynamical calculations. Recently, the directed flow of identified particles has been measured by the STAR collaboration in the beam energy scan (BES) program. In this article, we examine the collision energy dependence of directed flow $v_1$ in fluid dynamical model descriptions of heavy ion collisions for $sqrt{s_{NN}}=3-20$ GeV. The first step is to reproduce the existing predictions within pure fluid dynamical calculations. As a second step we investigate the influence of the order of the phase transition on the anisotropic flow within a state-of-the-art hybrid approach that describes other global observables reasonably well. We find that, in the hybrid approach, there seems to be no sensitivity of the directed flow on the equation of state and in particular on the existence of a first order phase transition. In addition, we explore more subtle sensitivities like e.g. the Cooper-Frye transition criterion and discuss how momentum conservation and the definition of the event plane affects the results. At this point, none of our calculations matches qualitatively the behavior of the STAR data, the values of the slopes are always larger than in the data.
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The directed flow of identified hadrons is studied within the parton-hadron-string-dynamics (PHSD) approach for the asymmetric system Cu+Au in non-central collisions at $sqrt{s_{NN}}$ = 200 GeV. It is emphasized that due to the difference in the number of protons of the colliding nuclei an electric field emerges which is directed from the heavy to the light nucleus. This strong electric field is only present for about 0.25 fm/c at $sqrt{s_{NN}}$ = 200 GeV and leads to a splitting of the directed flow $v_1$ for particles with the same mass but opposite electric charges in case of an early presence of charged quarks and antiquarks. The microscopic calculations of the directed flow for $pi^pm, K^pm, p$ and $bar{p}$ are carried out in the PHSD by taking into account the electromagnetic field induced by the spectators as well as its influence on the hadronic and partonic quasiparticle trajectories. It is shown that the splitting of the directed flow as a function of pseudorapidity $eta$ and in particular as a function of the transverse momentum $p_t$ provides a direct access to the electromagnetic response of the very early (nonequilibrium) phase of relativistic heavy-ion collisions and allows to shed light on the presence (and number) of electric charges in this phase.
The spinodal amplification of density fluctuations is treated perturbatively within dissipative fluid dynamics for the purpose of elucidating the prospects for this mechanism to cause a phase separation to occur during a relativistic nuclear collision. The present study includes not only viscosity but also heat conduction (whose effect on the growth rates is of comparable magnitude but opposite), as well as a gradient term in the local pressure, and the corresponding dispersion relation for collective modes in bulk matter is derived from relativistic fluid dynamics. A suitable two-phase equation of state is obtained by interpolation between a hadronic gas and a quark-gluon plasma, while the transport coefficients are approximated by simple parametrizations that are suitable at any degree of net baryon density. We calculate the degree of spinodal amplification occurring along specific dynamical phase trajectories characteristic of nuclear collision at various energies. The results bring out the important fact that the prospects for spinodal phase separation to occur can be greatly enhanced by careful tuning of the collision energy to ensure that the thermodynamic conditions associated with the maximum compression lie inside the region of spinodal instability.
The beam energy dependence of the elliptic flow,$v_2$, is studied in mid-central Au+Au collisions in the energy range of $3leq sqrt{s_{NN}} leq 30$ GeV within the microscopic transport model JAM. The results of three different modes of JAM are compared; cascade-,hadronic mean field-, and a new mode with modified equations of state, with a first order phase transition (1.O.P.T.) and with a crossover transition. The standard hadronic mean field suppresses $v_2$, while the inclusion of the effects of a 1.O.P.T. (and also of a crossover transition) does enhance $v_2$ at $sqrt{s_{NN}}<30$ GeV. The enhancement or suppression of the scaled energy flow, dubbed elliptic flowis understood as being due to out of plane- flow, i.e. $v_2<0$, dubbed out of plane - squeeze-out, which occurs predominantly in the early, compression stage. Subsequently, the in-plane flow dominates, in the expansion stage, $v_2 > 0$. The directed flow, dubbed bounce- off, is an independent measure of the pressure, which quickly builds up the transverse momentum transfer in the reaction plane. When the spectator matter leaves the participant fireball region, where the highest compression occurs, a hard expansion leads to larger $v_2$. A combined analysis of the three transverse flow coefficients, radial $v_0$-, directed $v_1$- and elliptic $v_2$- flow, in the beam energy range of $3leqsqrt{s_{NN}}leq10$ GeV, distinguishes the different compression and expansion scenarios: a characteristic dependence on the early stage equation of state is observed. The enhancement of both the elliptic and the transverse radial flow and the simultaneous collapse of the directed flow of nucleons offers a clear signature if 1.O.P.T. is realized at the highest baryon densities created in high energy heavy-ion collisions.
Entropy production in the compression stage of heavy ion collisions is discussed within three distinct macroscopic models (i.e. generalized RHTA, geometrical overlap model and three-fluid hydrodynamics). We find that within these models sim 80% or more of the experimentally observed final-state entropy is created in the early stage. It is thus likely followed by a nearly isentropic expansion. We employ an equation of state with a first-order phase transition. For low net baryon density, the entropy density exhibits a jump at the phase boundary. However, the excitation function of the specific entropy per net baryon, S/A, does not reflect this jump. This is due to the fact that for final states (of the compression) in the mixed phase, the baryon density rho_B increases with sqrt{s}, but not the temperature T. Calculations within the three-fluid model show that a large fraction of the entropy is produced by nuclear shockwaves in the projectile and target. With increasing beam energy, this fraction of S/A decreases. At sqrt{s}=20 AGeV it is on the order of the entropy of the newly produced particles around midrapidity. Hadron ratios are calculated for the entropy values produced initially at beam energies from 2 to 200 AGeV.
Central collisions of gold nuclei are simulated by several existing models and the central net baryon density rho and the energy density eps are extracted at successive times, for beam kinetic energies of 5-40 GeV per nucleon. The resulting trajectories in the (rho,eps) phase plane are discussed from the perspective of experimentally exploring the expected first-order hadronization phase transition with the planned FAIR at GSI or in a low-energy campaign at RHIC.
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