1. Wolfgang Cassing CERN, 04.06.2007 Properties of the sQGP at RHIC and LHC energies

2. Aim:Transport study of relativistic many-body systems Aim: Transport study of relativistic many-body systems Transport theory : off-shell Kadanoff-Baym equations for the Green-functions G < h (x,p) in phase-space representation Actual solutions: Monte Carlo simulations with a large number of test-particles Scetch of an ultrarelativistic nucleus-nucleus collision (S. A. Bass) = Parton-Hadron-String-Dynamics (PHSD)

3. what are the properties of the new medium? Ask lattice QCD  effective approach! At RHIC the strong QGP (sQGP) was found, but

4. From lattice QCD to gluon quasiparticle properties quasiparticle entropy: mass: width: coupling: spectral function: Andre Peshier, PRD 70 (2004) 034016  =  -3p entropy mass width

5. Gluonic quasiparticles of the sQGP T = 1.053 T c T = 1.35 T c T = 3 T c Andre Peshier, PRD 70 (2004) 034016  broad distributions in ( ,k)

6. average glue-glue cross section: percolation parameter: plasma parameter: shear viscosity: PRL 94 (2005) 172301 => The QGP looks like an almost perfect liquid !

7. The Dynamical QuasiParticle Model (DQPM) The quasiparticle entropy density: gluons quarks antiquarks Complex selfenergies, e.g. : + some thermodynamics: energy density:  pressure P interaction measure:

8. The DQPM model assumptions (g, q, q bar ): Spectral functions for partonic degrees of freedom (g, q, q bar ): gluon mass: gluon width: quark width: quark mass:

9. The strong coupling g 2 3 parameters: T s /T c =0.46; c=28.8; =2.42  Quasiparticle properties (N f =3; T c = 0.185 GeV)

10. DQPM thermodynamics (N f =3) some short-hand notations: +: time-like -: space-like

11. Time-like and space-like quantities Example:

12. Time-like and space-like densities ‚densities‘: scalar densities:  time-like densities are small except close to T c !

13. Time-like and space-like energy densities  space-like energy densities dominate except close to T c !  space-like parts are identified with potential energy densities!

14. Thermodynamical consistency ? Total energy density: => matches well the thermodynamical energy density!

15. Potential energy per time-like parton Plasma parameters: Potential energy: huge ! liquid gas  Partonic liquid should persist at LHC !

16. Potential energy versus parton density Potential energy: Parton density: Gluon fraction:  PHSD

17. Self-energies of time-like partons gluons quarks  PHSD

18. Effective 2-body interactions of time-like partons 2 nd derivatives of interaction densities effective interactions turn strongly attractive below 2.2 fm -3 !  PHSD

19. Finite quark chemical potentials energy density pressure parton density pot. energy per particle  slight increase with chemical potential close to T c Fermion potential energy per particle practically independent !

20. Parton densities and gluon fraction fermion densities increase with quark chemical potential fermion densities increase with quark chemical potential gluon densities slightly decrease ! gluon densities slightly decrease !

21. Parton energy densities  increase with chemical potential close to T c ; gluon potential energy density practically independent !

22. Net fermion densities Net fermion densities approximately scale with T 2 and chemical potential  q !

23. Net fermion density – comparison to lQCD Comparison to lQCD Comparison to lQCD : looks quite reasonable ! N f =2; lQCD: C. R. Allton et al., PRD 68 (2003) 014507

24. Dilepton ‚back-to-back‘ radiation from the sQGP Born rate: DQPM rate: N f =2; lQCD: F. Karsch et al., PLB 530 (2002) 147  massive suppression of low mass dileptons of low mass dileptons in line with lQCD ! in line with lQCD !

25. Dilepton radiation from the sQGP – NA60 NA60 data sQGP is here! Preliminary PHSD results: Conjecture: the sQGP shows up already at SPS energies !

26. Summary PHSD Conjecture: the sQGP shows up already at SPS energies !  PHSD Conjecture: the sQGP shows up already at SPS energies ! The dynamical quasiparticle model (DQPM) well matches lQCD (with only 3 parameters) ! The dynamical quasiparticle model (DQPM) well matches lQCD (with only 3 parameters) ! DQPM allows to extrapolate to finite quark chemical potentials presently out of reach for lQCD. DQPM allows to extrapolate to finite quark chemical potentials presently out of reach for lQCD. DQPM separates lime-like quantities from space-like (interaction) regions (needed for off-shell transport). DQPM separates lime-like quantities from space-like (interaction) regions (needed for off-shell transport). DQPM provides mean-fields for gluons and quarks as well as effective 2-body interactions  PHSD DQPM provides mean-fields for gluons and quarks as well as effective 2-body interactions  PHSD and gives transition rates for the formation of hadrons if the average distance is larger than 0.77 fm  PHSD. The plasma parameter G suggests that the sQGP and its related experimental observations (scaling of elliptic flow with parton number etc.) will persist at LHC (i.e. the partonic liquid). The plasma parameter G suggests that the sQGP and its related experimental observations (scaling of elliptic flow with parton number etc.) will persist at LHC (i.e. the partonic liquid).

27. Dilepton radiation from the sQGP – NA60