1. Energy and system size dependence in string-hadronic models
Elena Bratkovskaya
FIAS, J.W. Goethe Universität
Frankfurt am Main
, Bergen

2. ‚Little Bangs‘ in the Laboratory
Initial State
Hadronization
time
Quark-Gluon-Plasma ? Au Au
hadron
degrees
of freedom
hadron
degrees
of freedom
quarks and gluons
How can we proove that an equilibrium QGP has been created in central Au+Au collisions ?!

3. energy density versus temperature
The QGP in Lattice QCD
Quantum Cromo Dynamics
(fundamental theory of quark-gluon interactions ):
predicts strong increase of
the energy density e at critical temperature TC ~170 MeV
Possible phase transition from hadronic to partonic matter (quarks, gluons) at critical energy density eC ~1 GeV/fm3
Lattice QCD:
energy density versus temperature
Tc = 170 MeV
Critical conditions - eC ~1 GeV/fm3 , TC ~170 MeV - can be reached in heavy-ion experiments at bombarding energies > 5 GeV/A

4. The phase diagram of QCD
UrQMD initial energy density is higher than the boundary from LQCD
Tri-critical point reached somewhere between 20 and 30 A GeV
-> we are probing a new phase of matter already at AGS!

5. Quark condensate in central Au+Au
Quark condensate drops to zero already at lower AGS energies!
-> we are probing a new phase of matter already at AGS!
HSD calculations:
NPA 674 (2000) 249

6. Signals of QGP Strangeness enhancement Charm suppression
Collective flow (v1, v2)
further signals of QGP:
(not covered in this talk)
Multi-strange particle enhancement in Au+Au
Jet quenching and angular correlations
High pT suppression of hadrons
Nonstatistical event by event correlations ...

7. Concepts: HSD & UrQMD HSD – Hadron-String-Dynamics transport approach
UrQMD – Ultra-relativistic-Quantum-Molecular-Dynamics
Solution of the transport equations with collision terms describing:
elastic and inelastic hadronic reactions:
baryon-baryon, meson-baryon, meson-meson
formation and decay of baryonic and mesonic resonances
string formation and decay
Implementation of detailed balance on the level of 1<->2
and 2<->2 reactions (+ 2<->n multi-meson fusion reactions in HSD)
Degrees of freedom:
baryons + mesons including excited states
strings; q, qbar, (qq), (qbar qbar) (no gluons!)

8. HSD & UrQMD – microscopic models for heavy-ion reactions
very good description of particle production in pp, pA reactions
unique description of nuclear dynamics from low (~100 MeV) to ultrarelativistic (21.3 TeV) energies
HSD
1999 predictions

9. Excitation function of p+, K+, (L+S0) yields
Reasonable description of strangeness by HSD and UrQMD
HSD overestimates pions at low AGS
UrQMD overestimates pions at top AGS and above
(deviations < 20%)
PRC 69 (2004)

10. Excitation function of K+/p+, K-/p-, (L+S0)/p ratios
Experimental K+/p+ ratio shows a peak at ~30 A GeV -,horn‘-
which is not reproduced by the transport approaches HSD and UrQMD !
PRC 69 (2004)

11. Transverse mass spectra - barometer of the reaction
mT=(m2+pT2)1/2 – transverse mass
T - inverse slope parameter
HSD & UrQMD 2.0:
Transverse mass spectra of p+, K+ from p+p and p+A collisions are well reproduced at all energies
Exp. data for light systems C+C and Si+Si at 160 A GeV are reasonably described by HSD and UrQMD
PRL 92 (2004)

12. mT spectra for Au+Au from AGS to RHIC
HSD 2.0 & UrQMD 2.0:
Pion slopes are
only slightly underestimated
by transport
Kaon slopes
are too low
above 5 A GeV!
PRC 69 (2004)

13. ‚Alternative‘ scenarios (HSD)
Hadronic medium effects
should happen: but practically don‘t enhance high mT-spectra (~10%)
String-string interaction –> overlapping strings
small effect on mT-slope with transverse string radius Rs~0.25fm
(depends on Rs)
Isotropic decay of meson-baryon strings
inconsistent with other observables (stopping and larger meson production)
Nonleading parton (quark/diquark) elastic scattering with sel(qq) =selpN/NQuark
low effect at AGS, strong at RHIC, but hadron multiplicities
become too high
Reduced formation time tF ->0 : too large hadron multiplicities
. . .
In all cases the ‚improvement‘ on the mT slope is small or inconsistent with other observables!
PRC 69 (2004)

14. ‚Alternative‘ scenarios: High mass baryon resonances - UrQMD 2.1
UrQMD model in spirit of RQMD:
mB strings of invariant mass 2 < M < 3 GeV are replaced by quasi-particles (= high mass resonances) that decay isotropically according to the Br of the heaviest implemented resonance with the same quantum numbers
 light meson (p,K) emission is suppressed by ~ 25% compared to a string of the same invariant mass
Isotropic mB elastic scattering instead of forward peaked leading hadron scattering
Strangeness suppression factor gS has been enhanced from gS =0.3 (UrQMD 1.3 or 2.0) to 0.5 (UrQMD 2.1)  more strangeness production !
Improves T-slope, however, is inconsistent with other observables!
PRC 69 (2004)

15. Cronin effect at RHIC (HSD)
Cronin effect: initial state semi-hard gluon radiation increases pT spectra already in p+A or d+A
Modelling of the Cronin effect in HSD:
<kT2>AA = <kT2>PP (1+a NPrev)
NPrev= number of previous collisions
parameter a = 0.25 – 0.4
HSD with Cronin eff.
HSD without Cronin eff.
W. Cassing, K. Gallmeister and C. Greiner,
Nucl. Phys. A 735 (2004) 277

16. Cronin effect on p, K+ mT-spectra in A+A (HSD)
Very small effect at AGS
Hardening of the mT spectra at top SPS
Substantial hardening of the mT spectra at RHIC –> large improvement !
Consistent with other observables !
PRC 69 (2004)

17. Inverse slopes T for K+ and K-
In UrQMD and HSD hadronic rescattering has only a small impact on the kaon slope
Cronin effect - initial state semi-hard gluon radiation- leads to the substantial hardening of the mT spectra at RHIC, however, has a very small effect at low energies ||
The hadron-string picture fails?
=> New degrees of freedom (colored partons – qC, ga) are missing ?!
PRL 92 (2004)
PRC 69 (2004)

18. Directed flow v1 & elliptic flow v2Y x z
Non central Au+Au collisions :
interaction between constituents leads to a
pressure gradient => spatial asymmetry is converted to an asymmetry in momentum space =>
collective flow
- directed flow Y
Out-of-plane
- elliptic flow
In-plane
V2 > 0 indicates in-plane emission of particles
V2 < 0 corresponds to a squeeze-out perpendicular to the reaction plane (out-of-plane emission) X
v2 = 7%, v1=0
v2 = 7%, v1=-7%
v2 = -7%, v1=0

19. Directed flow v1 & elliptic flow v2 for Pb+Pb at 40 A GeV
Small wiggle in v1 at midrapidity not described by HSD and UrQMD
Too large elliptic flow v2 at midrapidity from HSD
and UrQMD for all
centralities !
Experimentally:
breakdown of v2 at
midrapidity !
Signature for a first order phase transition !
H. Stöcker, NPA 750 (2005)
E.B. et al., JPG 31 (2005)

20. Directed flow v1 for Au+Au at RHIC
v1 is flat at midrapidity for protons, pions and kaons
HSD shows slightly larger flow than UrQMD
JPG 31 (2005)

21. Elliptic flow v2 in Au+Au at RHIC
HSD, pT>2 GeV/c
huge plasma pressure?!
STAR data on v2 of high pT charged hadrons are NOT reproduced in the hadron-string picture =>
evidence for huge plasma pressure ?!
PHOBOS data on v2 for charged hadrons (all pT) are underestimated in HSD by ~30%
W. Cassing, K. Gallmeister and C. Greiner,
Nucl. Phys. A 735 (2004) 277
PRC 67 (2003)

22. Charmonium in heavy-ion collisionsD
J/Y Y‘ cC
Dbar
‚Charmonium production versus absorption‘
Obviously: there should be ‚normal‘ nuclear absorption, i.e. dissociation of charmonium by inelastic interactions with nucleons of the target/projectile
Charmonium-N dissociation cross section can be fixed from p+A data

23. NA50 Collaboration: J/Y suppression in Pb+Pb
J/Y ‚normal‘ absorption by nucleons
(Glauber model) ||
Experimental finding:
extra suppression in A+A collisions; increasing with centrality

24. Scenarios for charmonium suppression in A+A
QGP color screening
[Matsui and Satz ’86]
but (!)
Lattice QCD predicts (2004):
J/Y can exist up to ~2 TC ! +
Regeneration of J/Y in QGP at TC: [Braun-Munzinger, Thews, Ko et al. `01]
J/Y+g <-> c+cbar+g
Comover absorption
[Gavin & Vogt, Capella et al.`97]:
charmonium absorption by low energy inelastic scattering with ‚comoving‘ mesons (m=p,h,r,...):
J/Y+m <-> D+Dbar
Y‘+m <-> D+Dbar
cC+m <-> D+Dbar
Meson absorption cross section –
strongly model dependent
sabsmesons ~1-10 mb
Existing exp. data at SPS (by NA50 Collaboration) are also consistent with comover absorption models !

25. J/Y suppression in S+U and Pb+Pb at SPS
Models:
Comover model in the transport approach – HSD/UrQMD
Comover model in the Glauber approach:
(1) without transition to QGP:
Charmonia suppression increases gradually with energy density [Capella et al.]
(2) with transition to QGP:
Charmonia suppression sets in
abruptly at threshold energy
densities, where cC is melting, J/Y is melting [Blaizot et al.]
Statistical coalescence model (SCM) [Kostyuk et al.]
PRC 69 (2004)

26. Y‘ suppression in S+U and Pb+Pb at SPS
Matrix element for
Y‘ + mesons <-> D+Dbar
Set 1: |MJ/Y|2=|McC|2=|MY‘|2=|M0|2
Set 2:
|MJ/Y|2=|McC|2=|M0|2
|MY‘|2= 1.5 |M0|2
PRC 69 (2004)

27. J/Y suppression in Au+Au at RHIC
Time dependence of the rate of J/Y absorption by mesons and recreation by D+Dbar annihilation:
NDD~16
At RHIC the recreation of J/Y by D+Dbar annihilation is important !
New data with higher statistics are needed to clarify the nature of J/Y suppression!

28. Y‘ suppression in Au+Au at RHIC
Y‘ is strongly suppressed in HSD at midrapidity  recreation by D+Dbar annihilation doesn‘t compensate the absorption by mesons !
Charm chemical equilibration is not fully achieved in transport calculations on the basis of hadronic interactions since the Y‘ to J/Y ratio still depends on the matrix element for Y‘ coupling to mesons
This allows to distinguish the different scenarios of charmonia suppression !
PRC 69 (2004)

29. HSD: v1 of D+Dbar and J/Y from Au+Au versus pT and y at RHIC
D-mesons and J/Y follow roughly the charged particle flow around midrapidity !
nucl-th/ ; PRC (2005)

30. HSD: v2 of D+Dbar and J/Y from Au+Au versus pT and y at RHIC
Collective flow from hadronic interactions is too low at midrapidity !
HSD: D-mesons and J/Y follow the charged particle flow => small v2 < 3%
STAR data show very large collective flow of D-mesons v2~15%!
=> strong initial flow of
non-hadronic nature!
nucl-th/ ; PRC (2005)

31. AMPT model: v2 of D+Dbar from Au+Au versus pT at RHIC
AMPT multi-phase transport model:
(B. Zhang, L.-W. Chen and C.-M. Ko)
Minijet partons from hard proceses (ZPC- Zang‘s parton cascade)
+ strings from soft processes (HIJING)
Parton (q, qbar) scattering cross sections (3-10 mb)
„To describe the large electron elliptic flow observed in available experimental data requires a charm quark scattering cross section that is much larger than given by perturbative QCD“
[nucl-th/ ]
QGP is NOT an ideal gas
as described by pQCD!

32. Summary I SPS: proton flow (NA49)
Collective flow signals of QGP
SPS: proton flow (NA49)
small wiggle in v1 and breakdown of v2 at
midrapidity are not described by HSD and
UrQMD
signature for a first order phase transition ?!
RHIC: v2 of charged hadrons at high pT (STAR)
STAR data on v2 of high pT charged hadrons are NOT reproduced in the hadron-string picture
=> evidence for a huge plasma pressure ?!
HSD, pT>2 GeV/c
huge plasma pressure!

33. Summary II Strangeness signals of QGP: Charm signals of QGP: ‚horn‘
in K+/p+
‚step‘
in slope T
Exp. data are not reproduced in terms of hadron-string
picture => evidence for nonhadronic degrees of freedom
Charm signals of QGP:
STAR experiment at RHIC observed very strong collective flow v2 of charm D-mesons
=> evidence for strong nonhadronic interactions in the very early phase of the reaction

34. Outlook The Quark-Gluon-Plasma is there!
But what are the properties of this phase ?!
Initial idea (1970 – 2003):
QGP is a weakly interacting
gas of colored but almost massless quarks and gluons
State of the art 2005:
QGP is a strongly interacting
and almost ideal „color liquid“ !
New phase diagram of QCD
A. Peshier, W. Cassing, PRL (2005)

35. Thanks to my coauthors HSD & UrQMD Collaboration Steffen Bass
Marcus Bleicher
Wolfgang Cassing
Andrej Kostyuk
Marco van Leeuwen
Manuel Reiter
Sven Soff
Horst Stöcker
Henning Weber
Nu Xu
HSD & UrQMD
Collaboration
HSD, UrQMD - open codes: