Elliptic Flow Splitting as a Probe of the QCD Phase Structure at Finite Baryon Chemical Potential

Abstract

Using a partonic transport model based on the 3-flavor Nambu-Jona-Lasinio model and a relativistic hadronic transport model to describe, respectively, the evolution of the initial partonic and the final hadronic phase of heavy-ion collisions at energies carried out in the Beam-Energy Scan program of the Relativistic Heavy Ion Collider, we have studied the effects of both the partonic and hadronic mean-field potentials on the elliptic flow of particles relative to that of their antiparticles. We find that to reproduce the measured relative elliptic flow differences between nucleons and antinucleons as well as between kaons and antikaons requires a vector coupling constant as large as 0.5 to 1.1 times the scalar coupling constant in the Nambu-Jona-Lasinio model. Implications of our results in understanding the QCD phase structure at finite baryon chemical potential are discussed.PACS numbers: 25.75.Ld, 25.75.Nq, 21.30.Fe, 24.10.Lx The main purpose of the experiments involving collisions of heavy nuclei at relativistic energies is to study the properties of produced quark-gluon plasma (QGP) and its phase transition to hadrons. It is known from the lattice Quantum Chromodynamics (QCD) that for QGP of small baryon chemical potential, such as that formed at top energies of the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), the hadron-quark phase transition (HQPT) is a smooth crossover [1,2]. For QGP of finite baryon chemical potential produced at lower collision energies, studies based on various theoretical models have indicated, however, that the HQPT is expected to change to a first-order one [3][4][5][6]. To determine if the critical point, at which the crossover HQPT changes to a first-order one, exists and where it is located in the QCD phase diagram is important for understanding the phase structure of QCD and thus the nature of the strong interaction. To search for the critical point, the Beam-Energy Scan (BES) program has been carried out at RHIC to look for its signals at lower collision energies of √ s N N = 7.7 ∼ 39 GeV.Although there is no definitive conclusion on the existence or the location of the critical point, many interesting phenomena different from those at higher collision energies have been observed [7,8]. Among them is the increasing splitting between the elliptic flow (v 2 ) of particles, i.e, the second Fourier coefficient in the azimuthal distribution of their momenta in the plane perpendicular to the participant or reaction plane, and that of their antiparticles with decreasing collision energy [9]. This result also indicates the breakdown of the number of constituent quark scaling of v 2 [10] at lower collision energies. The latter states that the scaled elliptic flow, which is obtained from dividing the hadron elliptic flow by its * Electronic address: xujun@sinap.ac.cn number of constituent quarks as a function of a similarly scaled transverse kinetic energy, is similar for all hadrons, and this has been considered as an evidence for the existence of QGP...

An explanation of the elliptic flow difference between proton and anti-proton from the UrQMD model with hadron potentials

“…And, from above analyses, this originates from a consideration of the mean-field potential mainly on pre-formed hadrons. This potential effect is similar to the explanation by the AMPT calculations in which a NJL model is inserted for the evolution of partons [8]. But, they are different in details.…”

“…In Ref. [8], it is understood from the repulsive and attractive effects of the partonic vector potential on quarks and antiquarks, respectively. Here a repulsive early pressure on pre-formed hadrons affords enough effect on driving down anti-proton v 2 value because it freezes out earlier and survives from the annihilation process.…”

“…Besides confirmations on previous measurements by collaborations at CERN-SPS, more attention has been drawn on new findings, such as the elliptic flow splitting of particles especially of protons and anti-protons seen at low BES energies [4]. While a constituent quark number scaling of the hadronic elliptic flow indicates the existence of the QGP phase, the splitting might hint the change of its dynamical evolution or even its disappearance which has been explained by several theoretical groups [5][6][7][8][9].…”

“…It is noticed that in the AMPT calculations in Ref. [8] the scattering between quarks and antiquarks is treated to be isotropic for simplicity.…”

“…In Ref. [8], using an updated version of a multiphase transport (AMPT) model in which the evolution of partons in phase space is modeled by a 3-flavor Nambu-Jona-Lasinio (NJL) model, Xu et al found that the splitting effect is attributed to different mean-field potentials for hadrons and anti-hadrons as well as quarks and anti-quarks.…”