Rise of azimuthal anisotropies as a signature of the Quark-Gluon-Plasma in relativistic heavy-ion collisions

0.13 MB·English

by  V. P. Konchakovski

Rise of azimuthal anisotropies as a signature of the Quark-Gluon-Plasma
in relativistic heavy-ion collisions
V. P. Konchakovski,1,2 E. L. Bratkovskaya,3,4 W. Cassing,1 V. D Toneev,4,5 and V. Voronyuk2,4,5
1Institute for Theoretical Physics, University of Giessen, Giessen, Germany
2Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
3Institute for Theoretical Physics, University of Frankfurt, Frankfurt, Germany
4Frankfurt Institute for Advanced Studies, Frankfurt, Germany
5Joint Institute for Nuclear Research, Dubna, Russia
Theazimuthalanisotropies of thecollectivetransverseflowofhadronsareinvestigated inalarge
rangeofheavy-ioncollisionenergywithintheParton-Hadron-StringDynamics(PHSD)microscopic
transport approach which incorporates explicit partonic degrees of freedom in terms of strongly
interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD
2
as well as dynamical hadronization and hadronic dynamicsin thefinalreaction phase. The experi-
1
0 mentally observed increase of the elliptic flow v2 with bombarding energy is successfully described
in terms of the PHSD approach in contrast to a variety of other kinetic models based on hadronic
2
interactions. The analysis of higher-order harmonics v3 and v4 shows a similar tendency of grow-
n ing deviations between partonic and purely hadronic models with increasing bombarding energy.
a Thissignalsthattheexcitationfunctionsofazimuthalanisotropiesprovideasensitiveprobeforthe
J
underlingdegrees of freedom excited in heavy-ioncollisions.

1
1 PACSnumbers: 25.75.-q,25.75.Ag

]
h
Introduction. A few decades of experimental studies Anexperimentalmanifestationofthiscollectiveflowis
t
- at the Schwerionen-Synchrotron (SIS), the Alternating the anisotropic emission of particles in the plane trans-
l
c Gradient Synchroton (AGS) and the Super Proton Syn- verse to the beam direction. A quark number scaling
u
chroton (SPS) have shown that the physics of nuclear of the elliptic flow proposed in Ref. [10] was observed
n
collisions at moderate relativistic energies is dominated at RHIC for a broad range of particle species, collision
[
by the nonequilibrium dynamics of hadronic resonance centralities, and transverse kinetic energy, presumably

2 matter, i.e. the confined phase of QCD. The body of interpretedas due to the developmentofsubstantialcol-
v data extends and builds up the knowledge gained about lectivity in the early partonic phase [11].
9
densehadronicmatter,inparticular,attheSPS/CERN. It was shown that higher-order anisotropy harmonics,
3
0 The SPS heavy-ion data have shown several signatures in particular the hexadecupole moment v4, can provide
3 that hinted at the onsetof a quark-gluonplasma (QGP) a more sensitive constraint on the magnitude of η/s and
. formation[1,2]. WiththeRelativisticHeavyIonCollider the freeze-out dynamics, and the ratio v /(v )2 might
9 4 2
0 (RHIC) the center-of-mass energy could be increased by indicate whether a full local equilibrium is achieved in
1 a factor of 10 relative to the SPS, and the experiments the QGP [12]. Recently, the importance of the trian-
1 atRHIC assuredthat a new formof matter – wellabove gular flow v , which originates from fluctuations in the
3
: the deconfinement transition point – was created in the initial collision geometry, has been pointed out [13, 14].
v
i laboratory. The participant triangularity characterizes the triangu-
X
Indeed, the discovery of a large azimuthal anisotropic laranisotropyoftheinitialnuclearoverlapgeometryand
r flow of hadrons at RHIC provides a conclusive evi- arisesfromevent-by-eventfluctuationsintheparticipant-
a
dence for the creation of dense partonic matter in ultra- nucleon collision points and corresponds to a large third
relativisticnucleus-nucleuscollisions. Thestronglyinter- Fouriercomponentintwo-particleazimuthalcorrelations
acting medium in the collision zone can be expected to at large pseudo-rapidity separation ∆η. This fact sug-
achievealocalequilibriumandexhibitanapproximately gests a significant contribution of the triangular flow to
hydrodynamic flow [3–5]. The momentum anisotropy is the ridge phenomenon and broad away-side structures
generatedduetopressuregradientsinacollectiveexpan- observed in the RHIC data [13].
sion of an initial geometry of an “almond-shaped” colli- A large number of anisotropic flow measurements
sion zone produced in noncentral collisions [3, 4]. The have been performed by many experimental groups at
pressure gradients translate early stage coordinate space SIS, AGS, SPS and RHIC energies over the past 20
asymmetrytofinal-statemomentumspaceanisotropy[6]. years. Very recently the azimuthal asymmetry has also
The picture thus emerges that the medium created in been measured at the Large Hadron Collider (LHC) at
ultra-relativistic collisions for a couple of fm/c interacts CERN [15]. The Beam Energy Scan (BES) program
morestronglythanhadronresonancematterandexhibits proposed at RHIC [16] covers the energy interval from
collective properties that resemble those of a liquid of a √sNN = 200 GeV, where partonic degrees of freedom
very low shear viscosity η to the entropy density s ratio, (DOF) play a decisive role, down to the AGS energy
η/s, close to a nearly perfect fluid [7–9]. √sNN 5 GeV, where most experimental data can be
≈
2
described successfully in terms of hadronic DOF Lower- and baryon octets increasing the total entropy.
ing the collision energy and studying the energy depen- On the hadronic side PHSD includes explicitly the
− −
dence of an anisotropic flow allows one to search for the baryon octet and decouplet, the 0 - and 1 -meson
onset of the transition to a phase with partonic DOF at nonets as well as selected higher resonances as in
an early stage of the collision as well as possibly iden- the Hadron-String-Dynamics (HSD) approach [23, 24].
tify the location of the expected critical end-point that Hadrons of higher masses (> 1.5 GeV in case of baryons
terminatesthefirstorderphasetransitionathighquark- and>1.3GeVformesons)aretreatedas“strings”(color
chemical potential [11, 17]. dipoles)thatdecaytotheknown(low-mass)hadrons,ac-
cordingtothe JETSETalgorithm[25]. NotethatPHSD
This work aims to study excitation functions for dif-
andHSDmergeatlowenergydensity,inparticularbelow
ferent harmonics of the charged particle anisotropy in
the critical energy density ǫ 0.5 GeV/fm3.
momentum space in a wide collision energy range, i.e. c
≈
The PHSD approach was applied to nucleus-nucleus
from the AGS to the top RHIC energy regime. We want
to clarify how the interplay of quark and hadron DOF collisions from √sNN 5 to 200 GeV in Refs. [18, 21]
∼
in order to explore the space-time regions of “partonic
is changed with increasing bombarding energy. In this
matter”. It was found that even central collisions at the
study we investigate the excitation function of different
flow coefficients. Our analysis of the STAR/PHENIX top-SPS energy of √sNN = 17.3 GeV show a large frac-
tion of nonpartonic, i.e., hadronic or stringlike matter,
RHIC data – based on recent results of the BES pro-
which can be viewed as a hadronic corona. This finding
gram–willbeperformedwithinthePHSDtransportap-
implies that neither hadronic nor only partonic “mod-
proach[18]thatincludesexplicitpartonicDOFaswellas
els” can be employed to extract physical conclusions in
a dynamic hadronization scheme for the transition from
comparing model results with data. All these previous
partonic to hadronic DOF and vice versa.
findings provide promising perspectives to use PHSD in
The PHSD approach. The dynamics of partons,
the whole range from about √sNN = 5 to 200 GeV for
hadrons and strings in relativistic nucleus-nucleus col-
a systematic study of azimuthal asymmetries of hadrons
lisions is analyzedhere within the Parton-Hadron-String
produced in relativistic nucleus-nucleus collisions.
Dynamics approach [18]. In this transport approach the
Calculational results and comparison to data. The
partonicdynamicsisbasedonKadanoff-Baymequations
anisotropy in the azimuthal angle ψ is usually char-
for Green functions with self-energies from the Dynami-
acterized by the even order Fourier coefficients v =
n
calQuasiParticleModel(DQPM)[19,20]whichdescribes
exp(ın(ψ Ψ )) , n=2,4,...,since for a smoothan-
RP
QCD properties in terms of “resummed” single-particle h − i
gular profile the odd harmonics become equal to zero.
Green functions. In Ref. [21], the actual three DQPM
As noted above, Ψ is the azimuth of the reaction
RP
parameters for the temperature-dependent effective cou-
plane and the brackets denote averaging over particles
pling were fitted to the recent lattice QCD results of
and events. In particular, for the widely used second-
Ref. [22]. The latter lead to a critical temperature T
c ≈ order coefficient, denoted as an elliptic flow, we have
160 MeV which corresponds to a critical energy density
ofǫc ≈0.5GeV/fm3. InPHSDthepartonspectralfunc- v = cos(2ψ 2Ψ ) = p2x−p2y , (1)
tions ρj (j = q,q¯,g) are no longer δ-functions in the in- 2 h − RP i *p2x+p2y+
variantmasssquaredasinconventionalcascadeortrans-
port models but depend on the parton mass and width where p and p are the x and y components of the par-
x y
parameters which were fixed by fitting the lattice QCD ticle momenta. This coefficient can be considered as a
results from Ref. [22]. We recall that the DQPM al- function of centrality, pseudorapidity η, and/or trans-
lows one to extract a potential energy density V from versemomentum p . We note that the reactionplane in
p T
the space-like part of the energy-momentum tensor as PHSD is given by the (x z) plane with the z axis in
−
a function of the scalar parton density ρ . Derivatives the beam direction. Integratedv and v coefficients are
s 3 4
of V with respect to ρ then define a scalar mean-field calculated by the two-particle correlationmethod in line
p s
potential U (ρ ) which enters into the equation of mo- with Ref. [26]:
s s
tion for the dynamic partonic quasiparticles. Further-
cos(nψ nψ )) = v2 +δ , (2)
more, a two-body interaction strength can be extracted h 1− 2 i h ni n
from the DQPM as well from the quasiparticle width whichis basedonthe assumptionthatnonflowcontribu-
in line with Ref. [9]. The transition from partonic to tions δ are smalland accountfor event-by-eventfluctu-
n
hadronic DOF (and vice versa)is described by covariant ations of the event plane. In Fig. 1 the experimental v
2
transition rates for the fusion of quark-antiquark pairs excitation function in the transient energy range is com-
orthree quarks(antiquarks),respectively,obeyingflavor pared to the results from the PHSD calculations; HSD
current-conservation, color neutrality as well as energy- model results are given as well for reference. We note
momentum conservation [18, 21]. Since the dynami- thatthecentralityselectionandacceptancearethesame
cal quarks and antiquarks become very massive close to for the data and models.
the phase transition, the formed resonant “prehadronic” We recall that the HSD model has been very success-
color-dipolestates(qq¯orqqq)areofhighinvariantmass, fulindescribingheavy-ionspectra andrapiditydistribu-
too, and sequentially decay to the ground-state meson tions from SIS to SPS energies. A detailed comparison
3
0.12 30-40%PH, E|ηN| <IX 1 P,A preTul:i m0+.i 7An5au-r1y, GalelV charged 00..0023 PHHSDSD v 3v3 aAllu c +h aArug,e md,i |nηb| i<a s1 v3
0.10 PHSD 0.01
HSD v30.00
0.08 -0.01
minbias, |η| < 1
STAR -0.02
v20.06 PHSD
HSD 0.02 PHHSDSD v v4 v4
4
0.04
v40.01
0.02
0.00
0.00
10 102 10 102
s [GeV] s [GeV]
NN
FIG. 1: Average elliptic flow v2 of charged particles at FIG. 2: Average anisotropic flows v3 and v4 of charged par-
midrapidityfortwocentralityselectionscalculatedwithinthe ticles at mid-pseudorapidity for minimum bias collisions of
PHSD (solid curves) and HSD (dashed curves) approaches. Au+Au calculated within the PHSD (solid lines) and HSD
The v2 STAR data compilation for minimal bias collisions (dashed lines) models.
aretakenfromRef.[27](stars)andthepreliminaryPHENIX
data [28] are plotted bysolid circles.
are treated as massless and their potentials are disre-
garded when they undergo scattering. Note that PHSD
ofHSD results with respectto a largeexperimentaldata and AMPT (with the additional strong hadron melting
setwasreportedinRef.[29]forcentralAu+Au(Pb+Pb) assumption in AMPT) practically give the same ellip-
collisions from AGS to top SPS energies. Indeed, as tic flow at the top RHIC energy of √sNN = 200 GeV.
shown in Fig. 1 (dashed lines), HSD is in good agree- We note that the PHSD model includes more realistic
ment with experiment for both data sets at the lower properties of dynamical quasiparticles especially in the
edge (√sNN 10 GeV) but predicts an approximately vicinity of the critical energy density. Furthermore, the
∼
energy-independentflowv2 atlargerenergiesand,there- quark-gluon transport in PHSD naturally passes on to
fore,doesnotmatchtheexperimentalobservations. This the (hadronic) HSD model at lower √sNN.
behavior is in quite close agreement with another inde- In Fig. 2 we display the PHSD and HSD results for
pendent hadronic model, the UrQMD (Ultra relativistic the anisotropic flows v and v of charged particles at
3 4
Quantum Molecular Dynamics) [30] (cf. with [27]). midpseudorapidity for Au+Au collisions from √sNN =
Fromtheabovecomparisononemayconcludethatthe 5 to 200 GeV. The triangular flow increases with √sNN
riseofv2 withbombardingenergyisnotdue tohadronic having negative values for √sNN ∼< 10 GeV. The pure
interactions and models with partonic DOF have to be hadronic model HSD gives v3 0 for √sNN ∼> (20-
≈
addressed. Indeed, the PHSD approachincorporatesthe 30) GeV. Accordingly, the results from PHSD (solid red
parton medium effects in line with a lQCD equation of lines) are systematically larger than those from HSD
state, as discussed above, and also includes a dynamic (dashed blue lines). Unfortunately, our statistics is not
hadronizationschemebasedoncovarianttransitionrates. high enough to allow for more precise conclusions. The
It is seen from Fig. 1 that PHSD performs better: The hexadecupole flow v stays almost constant in the con-
4
elliptic flow v2 from PHSD (solid curve) is fairly in line sidered energy range; here PHSD gives slightly higher
with the data from the STAR and PHENIX collabora- values than HSD.
tions and clearly shows the growth of v2 with the bom- Thev2 increaseisclarifiedinFig.3wherethepartonic
barding energy. fractionoftheenergydensityatmid-pseudorapiditywith
Since partonic DOF come into play, it is interesting respect to the total energy density in the same pseu-
to compare with another parton-hadron model, i.e. the dorapidity interval is shown. We recall that the repul-
AMPT (A Multi Phase Transport) model [31]. This sive scalarmean field potential U (ρ ) for partons in the
s s
modelisbasedonaperturbativeQCDdescriptionofpar- PHSD model leads to an increase of the flow v as com-
2
tonic interactions, including the production of multiple paredtothatforHSDorPHSDcalculationswithoutpar-
minijetpartonsaccordingtothe numberofbinaryinitial tonic meanfields [21]. As followsfromFig. 3, the energy
collisions. As shown in Ref. [27], the AMPT model pre- fraction of the partons substantially grows with increas-
dicts an approximately constant v2 with √sNN similar ingbombardingenergywhilethedurationofthepartonic
to the hadronic models HSD and UrQMD; however, the phaseisroughlythesame. Accordingly,theincreasingin-
v values match the experimental data at the top RHIC fluence of the repulsive partonic mean-field U (ρ ) leads
2 s s
energy. ThisdiscrepancyisduetoapQCDdescriptionof to an increase of the flow v with bombarding energy.
2
the partonic phase in AMPT where the minijet partons We pointout thatthe increaseof v inPHSD relativeto
2
4
1.0 angular v , and hexadecupole v – are reasonably de-
PHSD: Au + Au 3 4
b = 1 fm, |η| < 1 scribed within the PHSD model in the whole transient
action 0.8 26020 G GeVeV eantemrgoydrearnagteenbaotmurbaalrlydicnognnenecetrignigesthweithhadurlotnraicreplaroticveisssteics
y fr 0.6 19 GeV collisions at RHIC energies where the quark-gluon DOF
g
ner 9 GeV become dominant due to a growing number of partons.
e 0.4
on The smooth growth of the elliptic flow with collision
art energy demonstrates the increasing importance of par-
p 0.2
tonic DOFThis featureis reproducedby neither explicit
0.0 hadronic kinetic models like HSD or UrQMD nor the
0 2 4 6 8 10 12 14
t [fm/c] AMPT model treating the partonic phase on the ba-
sis of pQCD with massless partons and a noninteracting
FIG. 3: The evolution of the parton fraction of the total equation-of-state for the partons. Further signatures of
energydensityatthemid-pseudorapidityfordifferentcollision thetransversecollectiveflow,thehigher-orderharmonics
energies. ofthetransverseanisotropyv andv changeonlyweakly
3 4
from √sNN 7 GeV to the top RHIC energy √sNN =
≈
200 GeV, roughly in agreement with preliminary exper-
HSD is also partly due to the higher interaction rates in imental data. Certainly, new measurements within the
the partonic medium because of a lower ratio of η/s for BES program at RHIC, especially for higher-order har-
partonicdegreesoffreedomatenergydensitiesabovethe monics, will further constrain the partonic dynamics.
criticalenergydensitythanforhadronicmediabelowthe
criticalenergydensity[32,33]. Therelativeincreaseinv Acknowledgements. We are thankful to S. Voloshin for
3
and v in PHSD essentially is due to the higher partonic constructive remarks and O. Linnyk for useful discus-
4
interaction rate and, thus, to a lower ratio η/s in the sions. This work has been supported in part by the
partonic medium, which is mandatory to convert initial DFG Grant WA 431/8-1, the DFG Grant CA 124/7-
spacial anisotropies to final anisotropies in momentum 1, the RFFI Grants 08-02-01003-a, the Ukrainian-RFFI
space [34]. Grant 09-02-90423-ukr-f-a,and the LOEWE center HIC
Conclusions. The anisotropic flows – elliptic v , tri- for FAIR.
2
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