Energy and system size dependence in string hadronic models
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Energy and system size dependence in string-hadronic models. Elena Bratkovskaya FIAS, J.W. Goethe Universität Frankfurt am Main 01.04.2005, Bergen. Quark-Gluon-Plasma ?. ‚Little Bangs‘ in the Laboratory. Initial State. Hadronization. time. Au. Au. hadron degrees of freedom.

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Energy and system size dependence in string-hadronic models

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Energy and system size dependence in string-hadronic models

Elena Bratkovskaya

FIAS, J.W. Goethe Universität

Frankfurt am Main

01.04.2005, Bergen

Quark-Gluon-Plasma ?

‚Little Bangs‘ in the Laboratory

Initial State







of freedom



of freedom

quarks and gluons

How can we proove that an equilibrium QGP has been created in central Au+Au collisions ?!

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 fromhadronic to partonic matter (quarks, gluons) at critical energy densityeC~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 mesonicresonances

  • 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 dynamicsfrom low (~100 MeV) to ultrarelativistic (21.3 TeV) energies


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 notreproduced by the transport approaches HSD and UrQMD !

PRC 69 (2004) 015202

Transverse massspectra - 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 withsel(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 gShas 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


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



- elliptic flow


V2 > 0 indicates in-plane emission of particles

V2 < 0 corresponds to a squeeze-out perpendicular to the reaction plane (out-of-plane emission)


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 v2at

  • 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






‚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


  • 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:


|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:


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 HSDat midrapidity recreation by D+Dbar annihilation doesn‘t compensate the absorption by mesons !

  • Charm chemical equilibrationis not fully achieved in transport calculations on the basis of hadronic interactions since theY‘toJ/Yratio still depends on the matrix element forY‘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]

QGPis NOT an ideal gas

as described by pQCD!

Summary I

  • Collective flow signals of QGP

  • SPS: proton flow (NA49)

  • small wiggle in v1 and breakdown of v2at

  • 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:


in K+/p+


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


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

Steffen Bass

Marcus Bleicher

Wolfgang Cassing

Andrej Kostyuk

Marco van Leeuwen

Manuel Reiter

Sven Soff

Horst Stöcker

Henning Weber

Nu Xu



HSD, UrQMD - open codes:

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