Energy and system size dependence in string-hadronic models Elena Bratkovskaya FIAS, J.W. Goethe Universität Frankfurt am Main 01.04.2005, Bergen

‚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 ?!

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

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!

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

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 ...

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!)

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

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) 015202

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) 015202

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) 032302

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) 015202

‚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) 015202

‚Alternative‘ scenarios: High mass baryon resonances - UrQMD 2.1 UrQMD 2.1 - 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) 015202

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

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) 015202

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) 032302 PRC 69 (2004) 015202

Directed flow v1 & elliptic flow v2 Y 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

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)

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)

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) 054905

Charmonium in heavy-ion collisions D 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

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

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 !

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) 054903

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) 054903

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!

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) 054903

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/0409047; PRC (2005)

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/0409047; PRC (2005)

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/0502056] QGP is NOT an ideal gas as described by pQCD!

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!

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

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)

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: http://www.th.physik.uni-frankfurt.de/~brat/hsd.html http://www.th.physik.uni-frankfurt.de/~urqmd.html