1. Dynamics of Nucleus-Nucleus Collisions at CBM energies Frankfurt Institute for Advanced Studies Elena Bratkovskaya 19.09.2006, CBM Workshop „ The Physics of High Baryon Density „, IPHC Strasbourg

2. Introduction FAIR energies are well suited to study dense and hot nuclear matter –  a phase transition to QGP,  chiral symmetry restoration,  in-medium effects Observables for CBM: Observables for CBM:  Excitation function of particle yields and ratios  Transverse mass spectra  Collective flow  Dileptons  Open and hidden charm  Fluctuations and correlations ... Way to study: Experimental energy scan of different observables in order to find an ‚anomalous‘ behaviour in comparison with theory Microscopical transport models provide a unique dynamical description of nonequilibrium effects in heavy-ion collisions

3. HSD – Hadron-String-Dynamics transport approach HSD – Hadron-String-Dynamics transport approach for each particle species i (i = N, R, Y, , , K, …) the phase-space density f i follows the transport equations for each particle species i (i = N, R, Y, , , K, …) the phase-space density f i follows the transport equations with collision terms I coll describing: with collision terms I coll 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 Implementation of detailed balance on the level of 1  2 and 2  2 reactions (+ 2  n multi-meson fusion reactions in HSD) and 2  2 reactions (+ 2  n multi-meson fusion reactions in HSD) Basic concept of HSD

4. hadrons - baryons and mesons including excited states (resonances) hadrons - baryons and mesons including excited states (resonances) strings – excited color singlet states (qq - q) or (q – qbar) strings – excited color singlet states (qq - q) or (q – qbar) Based on the LUND string model & perturbative QCD via PYTHIA leading quarks (q, qbar) & diquarks leading quarks (q, qbar) & diquarks (q-q, qbar-qbar) (q-q, qbar-qbar) NOT included in HSD 2.5 presented here : o explicit parton-parton interactions (i.e. between quarks and gluons) outside strings! o explicit phase transition from hadronic to partonic degrees of freedom o QCD EoS for partonic phase Degrees of freedom in HSD under construction: PHSD – Parton-Hadron-String-Dynamics

5. Dense baryonic matter – average quantities Time evolution of the baryon density in a central cell (A+A, b=0 fm) enormous energy and baryon densities are reached (  >  crit =1 GeV/fm 3 ) at FAIR energies

6. Changes of the particle properties in the hot and dense baryonic medium How to treat in-medium effects in transport approaches? In-medium models:  chiral perturbation theory  chiral SU(3) model  coupled-channel G-matrix approach  chiral coupled-channel effective field theory predict changes of the particle properties in the hot and dense medium, e.g. broadening of the spectral function  meson spectral function

7. From on-shell to off-shell transport dynamics Off-shell transport approach: Generalized transport equations on the basis of the Kadanoff-Baym equations for Greens functions || || Dynamical equations of motion for ‚test-particle‘ propagation in 8-dimensional phase space (r(t), p(t), E(t)): W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445 Application to strangeness: In-medium transition rates with momentum, temperature and density dependent spectral function of antikaons from a coupled channel G-matrix approach W. Cassing, L. Tolos, E.L.B., A. Ramos., NPA 727 (2003) 59 Application to dileptons: In-medium transition rates with momentum and density dependent dynamical spectral functions of vector mesons E.L..B., NPA 686 (2001), HSD predictions for CBM (2006) In-medium transition rates with momentum and density dependent dynamical spectral functions of vector mesons E.L..B., NPA 686 (2001), HSD predictions for CBM (2006)

8. Treatment of multi-particle collisions in transport approaches Treatment of multi-particle collisions in transport approaches W. Cassing, NPA 700 (2002) 618 Multi-meson fusion reactions important for antiproton, antilambda dynamics Generalized collision integral for n m reactions: 

9. Excitation function of particle yields AGSNA49BRAHMS Overview on the experimental meson and strange baryon abundancies from central Au+Au/Pb+Pb collisions versus s 1/2 Overview on the experimental meson and strange baryon abundancies from central Au+Au/Pb+Pb collisions versus s 1/2

10. Excitation function of particle ratios Excitation function of particle ratios Transport models: HSD, UrQMD, GiBUU Exp. data are not well reproduced within the hadron-string picture => evidence for nonhadronic degrees of freedom CBM probes the ‚horn‘ energy range

11. Transverse mass spectra Transverse mass spectra  Transport models: HSD 2.0 (+ Cronin effect) HSD 2.0 (+ Cronin effect) UrQMD 2.0 UrQMD 2.0 UrQMD 2.2 (+ effective resonances with masses 2 < M < 3 GeV and isotropic decay) UrQMD 2.2 (+ effective resonances with masses 2 < M < 3 GeV and isotropic decay) GiBUU GiBUU All transport models fail to reproduce the T- slope without introducing special „tricks“ which are, however, inconsistent with other observables!  3D-fluid hydrodynamical model gives the right slope! Is the matter a parton liquid?

12. Collective flow: v 2 excitation function  Proton v 2 at low energy shows sensitivity to the nucleon potential.  Cascade codes fail to describe the exp. data.  AGS energies: transition from squeeze-out to in-plane elliptic flow

13. Collective flow: elliptic flow at 25 A GeV – predictions for CBM Charged particles Transport models HSD HSD UrQMD UrQMD GiBUU GiBUU QGSM (v. Dubna; QGSM (v. Dubna; v. Oslo-Tuebingen) v. Oslo-Tuebingen) AMPT without string melting AMPT without string melting predict similar v 2 for charged particles (except QGSM)! AMPT with string melting shows much stronger v 2 for charged particles ! Challenge for CBM!

14. Elliptic flow at 25 A GeV – predictions for pions, kaons and protons Elliptic flow at 25 A GeV – predictions for pions, kaons and protons AMPT without string melting shows v 2 similar to other models for all particles ! Including string melting leads to a larger v 2

15. Dileptons Dileptons Dileptons are an ideal probe for vector meson spectroscopy in the nuclear medium and for the nuclear dynamics ! Study of in-medium effects with dilepton experiments: Study of in-medium effects with dilepton experiments:  „History“ – DLS, KEK, SPS (HELIOS)  Novel experiments – HADES, NA60, CERES, PHENIX  Future – CBM High precision NA60 data allow to distinguish among in-medium models! Clear evidence for a broadening of the  spectral function! Direct photons as a possible observable for CBM ?! Direct photons as a possible observable for CBM ?!

16. Dileptons: excitation function Dilepton yield increases with energy due to a higher production of mesons Dilepton yield increases with energy due to a higher production of mesons  melts at practically all energies;  and  show clear peaks on an approx. exponential background in mass!  melts at practically all energies;  and  show clear peaks on an approx. exponential background in mass!

17. Dileptons – HSD predictions for CBM In-medium modifications of e+e- and  +  - spectra are very similar!

18. Open and hidden charm Open and hidden charm  Hidden charm: J/ ,  ‘ Anomalous J/  suppression in A+A (NA38/NA50) Comover dissociation in the transport approaches – HSD & UrQMD: approaches – HSD & UrQMD: NA50 data are consistent with comover absorption models comover absorption models Heavy flavor sector reflects the actual dynamics since heavy hadrons can only be formed in the very early phase of heavy-ion collisions at FAIR/SPS!

19. Open charm: D-mesons Dropping D-meson masses with increasing light quark density might give a large enhancement of the open charm yield at 25 A GeV !Dropping D-meson masses with increasing light quark density might give a large enhancement of the open charm yield at 25 A GeV !

20. Open and hidden charm – HSD predictions for CBM Open charm:  without medium effects: suppression of D-meson spectra by factor ~ 10 relative to the global m T -scaling  with medium effects: restoration of the global m T -scaling for the mesons Hidden charm: J/  suppression due to comover absorption at FAIR is lower than at SPS Open charm Hidden charm CBM

21. FAIR is an excellent facility to study the properties of the sQGP (strongly interacting ‚color liquid‘) as well as hadronic matter FAIR is an excellent facility to study the properties of the sQGP (strongly interacting ‚color liquid‘) as well as hadronic matter Summary Transport theory is the general basis for an understanding of nuclear dynamics on a microscopic level Transport theory is the general basis for an understanding of nuclear dynamics on a microscopic level UrQMD: U+U, 25 A GeV