arXiv:nucl-th/0412022v1 7 Dec 2004
Nonequilibrium Models of Relativistic Heavy-Ion
H. St¨ ocker1,2, E. L. Bratkovskaya1, M. Bleicher1, S. Soff1, and
1Institut f¨ ur Theoretische Physik, Johann Wolfgang Goethe – Universit¨ at, Robert
Mayer Str. 8-10, 60054 Frankfurt am Main, Germany
2Frankfurt Institute for Advanced Studies (FIAS), Robert Mayer Str. 8-10, 60054
Frankfurt am Main, Germany
3Physics Department, Tsinghua University, Beijing 100084, China
models on the collective flow observables from AGS to RHIC energies. A critical
discussion of the present status of the CERN experiments on hadron collective flow
is given. We emphasize the importance of the flow excitation function from 1 to 50
A·GeV: here the hydrodynamic model has predicted the collapse of the v1-flow and
of the v2-flow at ∼ 10 A·GeV; at 40 A·GeV it has been recently observed by the
NA49 collaboration. Since hadronic rescattering models predict much larger flow than
observed at this energy we interpret this observation as evidence for a first order phase
transition at high baryon density ρB. Moreover, the connection of the elliptic flow v2to
jet suppression is examined. It is proven experimentally that the collective flow is not
faked by minijet fragmentation. Additionally, detailed transport studies show that the
away-side jet suppression can only partially (< 50%) be due to hadronic rescattering.
Furthermore, the change in sign of v1,v2 closer to beam rapidity is related to the
occurence of a high density first order phase transition in the RHIC data at 62.5, 130
and 200 A·GeV.
We review the results from the various hydrodynamical and transport
PACS numbers: 25.75.-q, 25.75.Ld
1. Introduction: Old and new observables for the QGP phase transition
Lattice QCD results [1, 2] show a crossing, but no first order phase transition to the QGP
for vanishing or small chemical potentials µB, i.e. at the conditions accessible at central
rapidities at RHIC full energies. A first order phase transition does occur according to
the QCD lattice calculations [1, 2] only at high baryochemical potentials or densities, i.e.
at SIS-300 and lower SPS energies and in the fragmentation region of RHIC, y ≈ 4 − 5
[3, 4]. The critical baryochemical potential is predicted [1, 2] to be µc
and the critical temperature Tc≈ 150−160 MeV. We do expect a phase transition also at
finite strangeness. Predictions for the phase diagram of strongly interacting matter for
realistic non-vanishing net strangeness are urgently needed to obtain a comprehensive
picture of the QCD phase structure. Multi-Strangeness degrees of freedom are very
B≈ 400±50 MeV
Nonequilibrium Models of Relativistic Heavy-Ion Collisions2
0 200 400600 80010001200
[Karsch et al.]
0 2 3 = y (RHIC)
[Cleymans et al.]
Au+Au, 11 A GeV
Pb+Pb, 40 A GeV
Pb+Pb, 160 A GeV
Au+Au, 21300 A GeV
µ µB [MeV]
with the critical end point at µB
400 MeV,T ≈ 160 MeV as predicted by
Lattice QCD . In addition, the time
evolution in the T−µ-plane of a central cell
in UrQMD calculations  is depicted for
different bombarding energies. Note, that
the calculations indicate that bombarding
probe a first order phase transition.
RHIC (see insert at the µBscale) this point
is accessible in the fragmentation region
only (taken from ).
The new phase diagram
<∼ 40 A·GeV are needed to
promising probes for the properties of the dense and hot matter . The strangeness
distillation process [6, 7] predicts dynamical de-admixture of s and ¯ s quarks, which yields
unique signatures for QGP creation: high multistrange hyperon-/-matter production,
strangelet formation and unusual antibaryon to baryon ratios ect.
A comparison of the thermodynamic parameters T and µB extracted from the
UrQMD-transport model in the central overlap regime of Au+Au collisions  with
the QCD predictions is shown in Fig 1, where the full dots with errorbars denote the
’experimental’ chemical freeze-out parameters – determined from fits to the experimental
yields – taken from Ref. . The triangular and quadratic symbols (time-ordered in
vertical sequence) stand for temperatures T and chemical potentials µBextracted from
UrQMD transport calculations in central Au+Au (Pb+Pb) collisions at RHIC (21.3
A·TeV), 160, 40 and 11 A·GeV  as a function of the reaction time (separated by 1
fm/c steps from top to bottom). The open symbols denote nonequilibrium configurations
and correspond to T parameters extracted from the transverse momentum distributions,
whereas the full symbols denote configurations in approximate pressure equilibrium in
longitudinal and transverse direction.
During the nonequilibrium phase (open symbols) the transport calculations show
much higher temperatures (or energy densities) than the ’experimental’ chemical freeze-
out configurations at all bombarding energies (≥ 11 A·GeV). These numbers are also
higher than the critical point (circle) of (2+1) flavor - Lattice QCD calculations by the
Bielefeld-Swansea-collaboration  (large open circle) and by the Wuppertal-Budapest-
collaboration . The energy density at µc,Tcis in the order of ≈ 1 GeV/fm3(or slightly
below). At RHIC energies a cross-over is expected at midrapidity, when stepping down
in temperature during the expansion phase of the ’hot fireball’. The baryon chemical
potential µBfor different rapidity intervals at RHIC energies has been obtained from a
statistical model analysis by the BRAHMS Collaboration based on measured antihadron
to hadron yield ratios . For midrapidity one finds µB ≃ 0, whereas for forward
rapidities µB increases up to µB ≃ 130 MeV at y = 3. Thus, only extended forward
rapidity measurement (y ≈ 4 − 5) will allow to probe large µBat RHIC. The detectors
Nonequilibrium Models of Relativistic Heavy-Ion Collisions3
at RHIC at present offer only a limited chemical potential range. This situation changes
at lower SPS (and top AGS) as well as at the future GSI SIS-300 energies: sufficiently
large chemical potentials µBshould allow for a first order phase transition  (to the
right of the critical point in the (T,µB) plane). The transport calculations show high
temperatures (high energy densities) in the very early phase of the collisions, only. Here,
hadronic interactions are weak due to formation time effects and yield little pressure.
Diquark, quark and gluon interactions should cure this problem.
2. Directed and elliptic flow
2.1. General considiration
Hydrodynamic flow and shock formation has been proposed early [13, 14] as the
key mechanism for the creation of hot and dense matter during relativistic heavy-
ion collisions.The full three-dimensional hydrodynamical flow problem is much
more complicated than the one-dimensional Landau model : the 3-dimensional
compression and expansion dynamics yields complex triple differential cross-sections,
which provide quite accurate spectroscopic handles on the equation of state.
bounce-off, the squeeze-out and the antiflow [16, 17, 18, 19, 20] (third flow component
[21, 22]) serve as differential barometers for the properties of compressed, dense matter
from SIS to RHIC. Presently, the most employed flow observables are :
Here, pxdenotes the momentum in x-direction, i.e. the transversal momentum within
the reaction plane and pythe transversal momentum out of the reaction plane. The total
transverse momentum is given as pT =
Thus, v1measures the ”bounce-off”, i.e. the strength of the directed flow in the reaction
plane, and v2gives the strength of the second moment of the azimuthal particle emission
distribution, i.e. ”squeeze-out” for v2< 0 [13, 14, 16, 17, 18, 19, 20]. In particular, it
has been shown [14, 16, 17, 18, 19, 20] that the disappearence or ”collapse” of flow is a
direct result of a first order phase transition.
Several hydrodynamic models have been used in the past, starting with the one-
fluid ideal hydrodynamic approach. It is well known that the latter model predicts
far too large flow effects. To obtain a better description of the dynamics, viscous
fluid models have been developed [24, 25, 26]. In parallel, so-called three-fluid models,
which distinguish between projectile, target and the fireball fluids, have been considered
[29, 30]. Here viscosity effects appear only between the different fluids, but not inside
the individual fluids. The aim is to have at our disposal a reliable, three-dimensional,
relativistic three-fluid model including viscosity [25, 26].
Flow can be described very elegantly in hydrodynamics (cf. Refs. [31, 32, 33, 34])
by a proper choice of initial conditions which have very strong influence on the final
results. In this respect, it is important to consider also microscopic multicomponent
y; the z-axis is in the beam direction.
Nonequilibrium Models of Relativistic Heavy-Ion Collisions4
(pre-) hadron transport theory, e.g. models like qMD , IQMD , RQMD ,
UrQMD  or HSD , as control models for viscous hydro and as background models
to subtract interesting non-hadronic effects from data. If Hydro with and without quark
matter EoS, hadronic transport models without quark matter – but with strings – are
compared to data, can we learn whether quark matter has been formed? What degree
of equilibration has been reached? What does the equation of state look like? How are
the particle properties, self energies, cross sections changed?
To estimate systematic model uncertainties, the results of the different microscopic
transport models also have to be carefully compared. The two robust hadron/string
based models, HSD and UrQMD, are considered in the following.
2.2. Review of AGS and SPS results
Microscopic (pre-)hadronic transport models describe the formation and distributions
of many hadronic particles at AGS and SPS rather well . Furthermore, the nuclear
equation of state has been extracted by comparing to flow data which are described
reasonably well up to AGS energies [41, 42, 43, 21, 44, 45]. Ideal hydro calculations, on
the other hand, predict far too much flow at these energies . Thus, viscosity effects
have to be taken into account in hydrodynamics.
In particular, ideal hydro calculations are factors of two higher than the measured
sideward flow at SIS  and AGS, while the directed flow px/m measurement of the
E895 collaboration shows that the p and Λ data are reproduced reasonably well  in
UrQMD, i.e. in a hadronic transport theory with reasonable cross-sections, i.e. realistic
mean-free-path of the constituents.
Only ideal hydro calculations predict, however, the appearance of a so-called ”third
flow component”  or ”antiflow”  in central collisions. We stress that this only
holds if the matter undergoes a first order phase transition to the QGP. The signal is
that around midrapidity the directed flow, px(y), of protons develops a negative slope!
In contrast, a hadronic EoS without QGP phase transition does not yield such an exotic
”antiflow” (negative slope) wiggle in the proton flow v1(y).
The ideal hydrodynamic directed proton flow px (Fig. 2) shows even negative
values between 8 and 20 A·GeV. An increase back to positive flow is predicted with
increasing energy, when the compressed QGP phase is probed.
predicted minimum of the proton flow in the data? The hydro calculations suggest
that this ”softest point collapse” is at ELab≈ 8 A·GeV. This has not been verified by
the AGS data! However, a linear extrapolation of the AGS data indicates a collapse of
the directed proton flow at ELab≈ 30 A·GeV (Fig. 2).
Recently, substantial support for this prediction has been obtained by the low
energy 40 A·GeV SPS data of the NA49 collaboration  (Fig. 3). These data clearly
show the first proton ”antiflow” around mid-rapidity, in contrast to the AGS data as
well as to the UrQMD and HSD calculations involving no phase transition (Fig. 3,
l.h.s.). Thus, at bombarding energies of 30-40 A·GeV, a first order phase transition to
But, where is the
Nonequilibrium Models of Relativistic Heavy-Ion Collisions5
Figure 2. Left: Measured SIS and AGS proton dpx/dy-slope data compared to a
three-fluid hydro calculation . A linear extrapolation of the AGS data indicates a
collapse of flow at ELab≈ 30 A·GeV, i.e. for the lowest SPS- and the upper FAIR-
energies at GSI. Right: Net-baryon density in momentum space for Pb+Pb at 8 A·GeV
for b=3 fm at time 8.4 fm/c calculated in three-fluid hydro  for condition s/ρ < 10.
the baryon rich QGP most likely is already observed; the first order phase transition
line is crossed (cf. Fig. 1). This is the energy region where the new FAIR- facility at
GSI will operate. There are good prospects that the baryon flow collapses and other
first order QGP phase transition signals can be studied at the lowest SPS energies as
well as at the RHIC fragmentation region y > 4 − 5. These experiments will enable a
detailed study of the first order phase transition at high µBand of the properties of the
baryon rich QGP.
3. Proton elliptic flow collapse at 40 A·GeV - evidence for a first order
phase transition at highest net baryon densities
At SIS energies microscopic transport models reproduce the data on the excitation
function of the proton elliptic flow v2quite well: A soft, momentum-dependent equation
of state [50, 51, 52] seems to account for the data. The observed proton flow v2below
∼ 5 A·GeV is smaller than zero, which corresponds to the squeeze-out predicted by
hydrodynamics long ago [13, 14, 16, 17, 18, 19, 20]. The AGS data exhibit a transition
from squeeze-out to in-plane flow in the midrapidity region. The change in sign of the
proton v2 at 4-5 A·GeV is in accord with transport calculations – UrQMD  and
HSD [44, 45]). At higher energies, 10-160 A·GeV, a smooth increase of the flow v2is
predicted from the string-hadronic transport models. In fact, the 158 A·GeV data of
the NA49 Collaboration suggest that this smooth increase proceeds between AGS and
SPS as predicted.
This is in strong contrast to recent NA49 data at 40 A·GeV (cf. Fig. 3, r.h.s.):
A sudden collapse of the proton flow v2is observed for central, midcentral as well as
for peripheral protons. This collapse of v2for protons around midrapidity at 40 A·GeV
Nonequilibrium Models of Relativistic Heavy-Ion Collisions6
Pb+Pb, 40 A GeV
Pb+Pb, 40 A GeV
pT < 2 GeV/c
pT < 2 GeV/c
Figure 3. Proton directed v1(left) and elliptic v2(right) flow for central, semi-central
and peripheral Pb+Pb collissions at 40 A·GeV. The full squares indicate NA49 data
, the solid lines with open squares show the HSD results whereas the solid lines
with open triangles are the UrQMD results.
is very pronounced while it is not observed at 158 A·GeV. The UrQMD and HSD
calculations, without a phase transition, show a robust, but wrong 3% flow of protons
- in strong contrast to the data.
Thus, the collapse of the v1and v2flow has been observed by NA49  at the same
energy around 40 A·GeV. This is the highest energy – according to [1, 2] and Fig. 1 – at
which a first order phase transition can be reached at the central rapidities of relativistic
heavy-ion collisions. We, therefore, conclude that a first order phase transition at the
highest baryon densities accessible in nature has been seen at these energies in Pb+Pb
3.1. Strong collective flow at RHIC signals a new phase of matter
The rapid thermalization obtained in parton cascade calculations by Xu and Greiner
 by including three-body processes gg ↔ ggg in leading-order pQCD (besides gluon-
Nonequilibrium Models of Relativistic Heavy-Ion Collisions7
HSD, pt > 2 GeV/c
a function of the number of ’participating nucleons’ for |η| ≤ 1 for Au + Au collisions
at√s = 200 GeV in comparison to the ’hit-based analysis’ data of the PHOBOS
Collaboration . Right: The HSD result  for v2for charged hadrons with pT> 2
GeV/c as a function of the number of ’participarting nucleons’ in comparison to the
Left: The HSD result  for the elliptic flow v2for charged hadrons as
and quark- two-body elementary parton-parton scatterings) justifies a posteriori the use
of hydrodynamical calculations for the time evolution of the complex four-dimensional
expansion of the plasma. However, there is no justification for the use of simple ideal
hydrodynamics (i.e. neglecting the important transport coefficients) and simple, smooth
initial conditions in hydrodynamics [25, 26, 54]. PHOBOS data at√s= 130 GeV and
200 GeV suggest energy independent v2(η) distributions. Furthermore, the observed
distribution has a triangular shape in rapidity. This experimental finding is in strong
disagreement with Bjorken boost invariant hydro predictions [55, 12], which fit only the
The predicted average proton v2-values obtained from the SPHERIO hydro code
with NEXUS initial conditons ) are by factors of two higher than simple smooth
initial state hydrodynamic calculations. This indicates that ideal hydro with naive
smooth initial conditions – as used by many authors – do not describe but rather
fit the data.Strong viscosity effects can play a role for particles with pT < 1.2
GeV/c: a decent description of the dynamics requires, however, relativistic viscous hydro
simulations [25, 26, 27]. The NexSpherio simulations  predict very large event-by-
event fluctuations of v2caused by the strongly fluctuating initial conditions (given by
NEXUS). This effect has been also studied in Ref.  where the authors found a strong
influence of spatial eccentricity fluctuations on the determination of elliptic flow.
Microscopic transport simulations (HSD and UrQMD) of particle yields, dN/dy
distributions, etc. give a reasonable description of the RHIC Au+Au data [9, 57]. The
HSD and UrQMD transport approaches are based on string, quark, diquark (q, ¯ q,qq, ¯ q¯ q)
as well as hadronic degrees of freedom but lack explicit gluonic degrees of freedom. At
RHIC, UrQMD and HSD yield reasonable abundances of light hadrons composed of
u,d,s quarks ‡. Do they also predict the collective flow properly?
‡ For a more recent survey on hadron rapidity distributions from 2 to 160 A·GeV in central nucleus-
Nonequilibrium Models of Relativistic Heavy-Ion Collisions8
UrQMD 1.3 (10-70%)
HSD 2.0 (10-70%)
v1 (η η)
v1 (η η)
4 fm < b < 8 fm
UrQMD 1.3 :
4 fm < b < 8 fm
UrQMD 1.3 :
+ Au collisions at√s =62.4 GeV (upper plot) and 200 GeV (lower plot) versus
pseudorapidity η in comparison to the data from STAR  (10-70% centrality, solid
dots) and PHOBOS  (6-55% centrality, open triangles) at√s = 200 GeV. The
solid lines and lines with stars correspond to the UrQMD 1.3 and HSD 2.0 results.
Right: UrQMD 1.3 (lines with symbols)and HSD 2.0 (solid lines) results for the v1for
protons, π+and K+from semi-central Au + Au collisions at√s =62.4 GeV (upper
plot) and 200 GeV (lower plot) versus rapidity y.
Left: The directed flow v1 for charged hadrons from semi-central Au
The left part of Fig. 5 shows the UrQMD 1.3 and HSD 2.0 results for the directed
flow v1 for charged hadrons from semi-central Au + Au collisions at√s =200 GeV
(left lower plot) versus pseudorapidity η in comparison to the data from STAR 
(10-70% centrality, solid dots) and PHOBOS  (6-55% centrality, open triangles) at
√s = 200 GeV. The upper left plot in Fig. 5 presents the UrQMD and HSD predictions
for√s =62.4 GeV. UrQMD 1.3 gives a lower v1as compared to HSD due to the missing
jet production in this version. For the UrQMD 2.0 results (which include PYTHIA
similar to HSD) we refer to Ref. . The right part of Fig. 5 present the UrQMD
1.3 and HSD 2.0 results for v1(y) for protons, π+and K+from semi-central Au + Au
collisions at√s =62.4 GeV (upper plot) and 200 GeV (lower plot). This shows that the
charged particle flow (left part of Fig. 5) can be dominantly attributed to pions. The
nucleus collisions within the HSD and UrQMD transport approaches we refer the reader to Ref. .
Nonequilibrium Models of Relativistic Heavy-Ion Collisions9
proton v1is closer to zero in UrQMD 1.3, while it shows a small ”antiflow” in HSD 2.0.
Further high statistics RHIC data will clarify the situation with the directed flow from
the experimental side.
The UrQMD prediction for the elliptic flow is clearly not compatible with the
measured 6% v2- it is sizeably underestimated . When shortening the formation
time  one can get the model results closer to the data, but more additional initial
pressure – needed to create the missing extra flow – is not justified in the hadronic
The eliptic flow v2at low transverse momenta (Fig. 4 l.h.s.) is underestimated in
the HSD model by ∼ 30% . However, at high transverse momenta (pT> 2 GeV/c)
the v2-flow is underestimated even by a factor of three (Fig. 4, r.h.s.) in the HSD model
. The HSD results are very similar to those of the hadronic rescattering model by
Humanic et al. [61, 62] and agree with the calculations by Sahu et al.  performed
within the hadron-string cascade model JAM . We mention that the microscopic
quark-gluon-string model  inserts in addition short distance vector repulsion in order
to achieve high flow values. Thus, the ”missing” elliptic flow (as well as the inverse slopes
) in hadron-string based models indicate that effective partonic degrees of freedom
in the initial phase are needed to supply the large pressure and early strong interaction
4. High pT suppression
4.1. How much quenching of high pT hadrons is due to (pre-) hadronic final state
A (mini-)jet at RHIC can produce hard particles, with pT above 5 GeV/c, but must
also form soft particles with pT around 2 GeV/c. Jets produced in the center of the
plasma zone have to pass first through the parton phase at very high temperatures, then
through the correlated diquark and constituent quarks and finally through the hadronic
phase that has build up preferentially close to the surface of the fireball. Very high pT
jets with γ > 10 materialize only far outside of the plasma. Most of the jets – observed
at RHIC – are at pT ≈ 4 − 5 GeV/c. More than 50% of the leading jet particles at
pT∼ 5GeV/c are baryons. Pion jets of 5 GeV have a γ ≃ 35, i.e., they form far outside
the plasma. However, HSD-PYTHIA-calculations  show that many pions stem from
decaying rho-jets. But, ρ’s and protons of 5 GeV have γ ≃ 5. Thus, ρ and p-jets
hadronize with roughly 50% probability [59, 70] while passing through the expanding
bulk matter. We point out that all partonic and hadronic models have failed by factors
of 5-10 to predict the observed high baryon abundance.
The PHENIX  and STAR  collaborations reported a suppression of meson
spectra for transverse momenta pT above ∼ 3GeV/c. This suppression is not observed
in d+Au interactions at the same bombarding energy per nucleon [73, 74] and presents
clear evidence for the presence of a new form of matter. However, it is not clear at present
Nonequilibrium Models of Relativistic Heavy-Ion Collisions10
(3) of charged hadrons at 5% (10%)
central Au + Au collisions (√s=200 GeV)
at midrapidity (hatched band).
experimental data are from Refs.
78] and show clearly that an additional
partonic suppression is needed (taken from
The suppression factor RAA
how much of the observed suppression can be attributed to (pre-)hadronic interactions
(FSI) [59, 70]. (In-)elastic collisions of (pre-)hadronic high momentum states with some
of the bulk (pre-)hadrons in the fireball can contribute in particular to the attenuation
of pT ≈ 5GeV/c transverse momentum hadrons at RHIC : Most of the medium
momentum (pre-)hadrons from a ±5 GeV/c double jet will materialize inside the dense
plasma; their transverse momenta being 0-4 GeV/c. The particles are dominantly ρ’s,
K’s and baryons at pT> 2.5GeV/c – hence their formation time is γτF≈ 4 fm/c in the
plasma rest frame. The time for color neutralization can also be very small  for the
leading particle due to early gluon emission.
The (pre-)hadronic interactions with the bulk of the (pre-)hadronic comovers then
must have clearly an effect: they, too, suppress the pT-spectrum .
reactions of the fragmented (pre-)hadrons with (pre-)hadrons of the bulk system cannot
be described by pQCD: The relevant energy scale√s is a few GeV. Such (in-)elastic
collisions are very efficient for energy degradation since many hadrons with lower energies
are produced. On the average, 1 to 2 such interactions can account for up to 50% of
the attenuation of high pT hadrons at RHIC . Hence, the hadronic fraction of the
jet-attenuation had to be addressed.
Such studies have been carried out in Ref.  within the HSD transport approach
. Moderate to high transverse momenta (> 1.5 GeV/c) have been incorporated
by a superposition of p + p collisions described via PYTHIA . We point out that
in Au+Au collisions the formation of secondary hadrons is not only controlled by the
formation time τf, but also by the energy density in the local rest frame, i.e. hadrons are
not allowed to be formed if the energy density is above 1 GeV/fm3§. The interactions
of the leading and energetic (pre-)hadrons with the soft hadronic and bulk matter are
thus explicitly modeled.
Fig. 4.1 shows the nuclear modification factor 
for the most central (5% centrality) Au+Au collisions at RHIC. The Cronin
§ This energy density cut is employed in the default HSD approach.
Nonequilibrium Models of Relativistic Heavy-Ion Collisions 11
enhancement is visible at all momenta.
substantial role in the few GeV region, since heavier hadrons (K∗’s, ρ’s, protons) are
formed 7 times earlier than the rather light pions in the cms frame at fixed transverse
momentum due to the lower Lorentz boost γ < 5.
transverse momenta pT ≥ 6 GeV/c the interactions of formed hadrons are not able to
explain the attenuation observed experimentally. However, the ratio RAAis influenced
by interactions of formed (pre-)hadrons in the pT = 1...5GeV/c range ; a similar
behaviour has also been found in UrQMD simulations .
As pointed out before, the suppression seen in the calculation for larger transverse
momentum hadrons is due to the interactions of the leading (pre-)hadrons with
target/projectile nucleons and the bulk of low momentum hadrons. It is clear that
the experimentally observed suppression can not be quantitatively described by the
(pre-)hadronic attenuation of the leading particles . The ratio RAA(3) decreases
to a value of about 0.5 at 5 GeV for central collisions, whereas the data are around
For particles observable with momenta pT
calculation predicts that still 1/3 of the final observed hadrons have suffered one or more
interactions, whereas the other 2/3 escape freely, i.e., without any interaction (even for
central collisions). This implies that the final high pT hadrons originate basically from
Hadron formation time effects do play a
It was shown in  that for
≥ 4 GeV/c, the HSD transport
4.2. Angular Correlations of Jets – Can jets fake the large v2-values observed?
Fig. 7 (l.h.s.)
4...6GeV/c, pT= 2GeV...pTrig
at√s = 200 GeV (solid line) as well as pp reactions (dashed line) from the HSD model
 in comparison to the data from STAR for pp collisions . Gating on high pT
hadrons (in the vacuum) yields ’near–side’ correlations in Au+Au collisions close to
the ’near–side’ correlations observed for jet fragmentation in the vacuum (pp). This
is in agreement with the experimental observation . However, for the away-side jet
correlations, the authors of Ref.  get only a ∼50% reduction, similar to HIJING,
which has only parton quenching and neglects hadron rescattering. Clearly, the observed
 complete disappearance of the away-side jet (Fig. 7) cannot be explained in the
HSD (pre-)hadronic cascade even with a small formation time of 0.8fm/c. Hence, the
correlation data provide another clear proof for the existence of the bulk plasma.
Although (pre-)hadronic final state interactions yield a sizable (∼ 50%) contribution
to the high pTsuppression effects observed in Au+Au collisions at RHIC, ∼ 50% of the
jet suppression originates from interactions in the plasma phase. The elliptic flow, v2,
for high transverse momentum particles is underestimated by at least a factor of 3 in
the HSD transport calculations  (cf. Fig. 4). The experimentally observed proton
excess over pions at transverse momenta pT > 2.5 GeV/c cannot be explained within
the CGG approach ; in fact, the proton yield at high pT≥ 5 GeV/c is a factor 5-10
 shows the angular correlation of high pT particles (pTrig
, |y| < 0.7) for the 5% most central Au+Au collisions
Nonequilibrium Models of Relativistic Heavy-Ion Collisions 12
to the HSD model for p+p and central Au+Au collisions at midrapidity for pTrig
4...6GeV/c and pT = 2GeV/c...pTrig
plane vs. out-of-plane correlations of the probe (jet+secondary jet fragments) with
the bulk (v2of the plasma at pT> 2GeV/c), prove the existence of the initial plasma
state (STAR-collaboration, preliminary).
Left: STAR data on near-side and away-side jet correlations compared
[59, 69]. Right: High pT correlations: in-
too small. We point out that this also holds for partonic jet-quenching models.
Futhermore, can the attenuation of jets of pT≥ 5GeV/c actually fake the observed
v2-values at pT ≈ 2GeV/c? This question comes about since due to fragmentation
and rescattering a lot of momentum-degraded hadrons will propagate in the hemisphere
defined by the jets.However, their momentum dispersion perpendicular to the jet
direction is so large that it could indeed fake a collective flow that is interpreted as
coming from the high pressure early plasma phase (cf. also Ref. ).
On first sight, Fig. 7 (r.h.s) shows that this could indeed be the case: the in-plane
v2correlations are aligned with the jet axis, the away-side bump, usually attributed to
collective v2 flow (dashed line), could well be rather due to the stopped, fragmented
and rescattered away-side jet! However, this argument is falsified by the out-of-plane
correlations (circles in r.h.s. Fig. 7). The near-side jet is clearly visible in the valley of
the collective flow v2distribution. Note that v2peaks atm ϕ = π/2 relative to the jet
axis! The away-side jet, on the other hand, has completely vanished in the out-of-plane
Where are all the jet fragments gone? Why is there no trace left? Even if the
away-side jet fragments completely and the fragments get stuck in the plasma, leftovers
should be detected at momenta below 2 GeV/c. Hadronic models as well as parton
cascades will have a hard time to get a quantitative agreement with these exciting data!
We propose future correlation measurements which can yield spectroscopic
information on the plasma:
(i) If the plasma is a colorelectric plasma, experiments will - in spite of strong plasma
damping - be able to search for wake-riding potential effects. The wake of the
Nonequilibrium Models of Relativistic Heavy-Ion Collisions13
leading jet particle can trap comoving companions that move through the plasma
in the wake pocket with the same speed (pT/m) as the leading particle. This can
be particular stable for charmed jets due to the deadcone effect as proposed by
Kharzeev et al , which will guarantee little energy loss, i.e. constant velocity
of the leading D-meson. The leading D-meson will practically have very little
momentum degradation in the plasma and therefore the wake potential following
the D will be able to capture the equal speed companion, which can be detected
(ii) One may measure the sound velocity of the expanding plasma by the emission
pattern of the plasma particles travelling sideways with respect to the jet axis: The
dispersive wave generated by the wake of the jet in the plasma yields preferential
emission to an angle (relative to the jet axis) which is given by the ratio of the
leading jet particles’ velocity, devided by the sound velocity in the hot dense
plasma rest frame. The speed of sound for a non-interacting gas of relativistic
massless plasma particles is cs≈
interactions, cs= c. Hence, the emission angle measurement can yield information
of the interactions in the plasma.
√3≈ 57%c, while for a plasma with strong vector
The NA49 collaboration has observed the collapse of both, v1- and v2-collective flow of
protons, in Pb+Pb collisions at 40 A·GeV, which presents first evidence for a first order
phase transition in baryon-rich dense matter. It should be possible to study the nature
of this transition and the properties of the expected chirally restored and deconfined
phase both at the forward fragmentation region at RHIC, with upgraded and/or second
generation detectors, and at the new GSI facility FAIR. According to Lattice QCD
results [1, 2], the first order phase transition occurs for chemical potentials above 400
GeV. Thus, the observed collapse of flow, as predicted in [13, 14], is a clear signal for a
first order phase transition at the highest baryon densities.
A critical discussion of the use of collective flow as a barometer for the equation
of state (EoS) of hot dense matter at RHIC showed that hadronic rescattering models
can explain < 30% of the observed elliptic flow v2for pT> 2 GeV/c. We interpret this
as evidence for the production of superdense matter at RHIC with initial pressure way
above hadronic pressure, p > 1 GeV/fm3.
The fluctuations in the flow, v1and v2, should be measured. Ideal Hydrodynamics
predicts that they are larger than 50 % due to initial state fluctuations. The QGP
coefficient of viscosity may be determined experimentally from the fluctuations observed.
The connection of v2 to jet suppression has been examined.
experimentally that the collective flow is not faked by minijet fragmentation and
theoretically that the away-side jet suppression can only partially (< 50%) be due to
pre-hadronic or hadronic rescattering.
We propose upgrades and second generation experiments at RHIC, which inspect
It is proven
Nonequilibrium Models of Relativistic Heavy-Ion Collisions14
the first order phase transition in the fragmentation region, i.e. at µB ≈ 400 MeV
(y ≈ 4 − 5), where the collapse of the proton flow – analogous to the 40 A·GeV data –
should be seen. Furthermore, the study of Jet-Wake-riding potentials and Bow shocks
caused by jets in the QGP formed at RHIC can give further clues on the equation of
state and transport coefficients of the Quark Gluon Plasma. Moreover, we propose that
the change in sign of v1,v2closer to beam rapidity is related to the occurence of a high
density first order phase transition in the RHIC data at 62.5, 130 and 200 A·GeV.
We like to thank W. Cassing, A. Dumitru, K. Gallmeister, C. Greiner, K. Paech,
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