1. Parton-Hadron-String-Dynamics at NICA energies Elena Bratkovskaya Institut für Theoretische Physik, Uni. Frankfurt Round Table Discussion IV: Round Table Discussion IV: ‚Searching for the mixed phase of strongly interacting matter at the Nuclotron-based Ion Collider fAcility (NICA)‘ 9-12 September 2009, JINR, Dubna

2. Our ultimate goals: Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma Search for the critical point Search for the critical point Study of the in-medium properties of hadrons at high baryon density and temperature Study of the in-medium properties of hadrons at high baryon density and temperature The phase diagram of QCD NICA

3. The QGP in Lattice QCD T c = 170 MeV Lattice QCD: energy density versus temperature energy density versus temperature Quantum Cromo Dynamics : predicts strong increase of the energy density  at critical temperature T C ~170 MeV  Possible phase transition from hadronic to partonic matter (quarks, gluons) at critical energy density  C  ~1 GeV/fm 3 Critical conditions -  C  ~1 GeV/fm 3, T C ~170 MeV - can be reached in heavy-ion experiments at bombarding energies > 5 GeV/A

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

5. Strangeness enhancement Strangeness enhancement Multi-strange particle enhancement in A+A Multi-strange particle enhancement in A+A Charm suppression Charm suppression Collective flow (v 1, v 2 ) Collective flow (v 1, v 2 ) Thermal dileptons Thermal dileptons Jet quenching and angular correlations Jet quenching and angular correlations High p T suppression of hadrons High p T suppression of hadrons Nonstatistical event by event fluctuations and correlations Nonstatistical event by event fluctuations and correlations...... Experiment: measures final hadrons and leptons Signals of the phase transition: How to learn about physics from data? Compare with theory!

6. Statistical models: Statistical models: basic assumption: system is described by a (grand) canonical ensemble of non-interacting fermions and bosons in thermal and chemical equilibrium [ -: no dynamics] [ -: no dynamics] Ideal hydrodynamical models: Ideal hydrodynamical models: basic assumption: conservation laws + equation of state; assumption of local thermal and chemical equilibrium [ -: - simplified dynamics] [ -: - simplified dynamics] Transport models: Transport models: based on transport theory of relativistic quantum many-body systems - off-shell Kadanoff-Baym equations for the Green-functions S < h (x,p) in phase-space representation. Actual solutions: Monte Carlo simulations with a large number of test-particles [ +: full dynamics | -: very complicated] [ +: full dynamics | -: very complicated] Basic models for heavy-ion collisions  Microscopic transport models provide a unique dynamical description of nonequilibrium effects in heavy-ion collisions

7. HSD microscopic transport model - basic concept HSD – Hadron-String-Dynamics transport approach Basic concept: Generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for Greens functions G < h (x,p) in phase-space representation (accounting for the first order gradient expansion of the Wigner transformed Kadanoff-Baym equations beyond the quasiparticle approximation). Actual solutions: Monte Carlo simulations with a large number of test-particles Monte Carlo simulations with a large number of test-particles Degrees of freedom in HSD:  hadrons - baryons and mesons including excited states (resonances)  strings – excited color singlet states (qq-q) or (q-qbar)  leading quarks (q, qbar) & diquarks (q-q, qbar-qbar) HSD – a microscopic model for heavy-ion reactions: very good description of particle production in pp, pA reactions very good description of particle production in pp, pA reactions unique description of nuclear dynamics from low (~100 MeV) to ultrarelativistic (~20 TeV) energies unique description of nuclear dynamics from low (~100 MeV) to ultrarelativistic (~20 TeV) energies

8. Hadron-string transport models versus observables Reasonable description of strangeness by HSD and UrQMD (deviations < 20%) works very well, but where do we fail ? NICA NICA NICA NICA NICA

9. Hadron-string transport models versus observables ‚horn‘ in K + /  + ‚step‘ in slope T Exp. data are not reproduced in terms of the hadron-string picture => evidence for nonhadronic degrees of freedom Strangeness signals of QGP Strangeness signals of QGP

10. Transport description of the partonic and hadronic phase Parton-Hadron- String-Dynamics (PHSD)

11. From hadrons to partons In order to study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma – we need a consistent transport model with  explicit parton-parton interactions (i.e. between quarks and gluons) outside strings!  explicit phase transition from hadronic to partonic degrees of freedom  lQCD EoS for partonic phase => phase transition is always a cross-over Parton-Hadron-String-Dynamics (PHSD) QGP phase described by input from the Dynamical QuasiParticle Model DQPM Dynamical QuasiParticle Model (DQPM) Transport theory: off-shell Kadanoff-Baym equations for the Green-functions S < h (x,p) in phase-space representation with the partonic and hadronic phase A. Peshier, W. Cassing, PRL 94 (2005) 172301; A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; arXiv:0907.5331 [nucl-th], NPA‘09; W. Cassing, EPJ ST 168 (2009) 3

12. The Dynamical QuasiParticle Model (DQPM)  Interacting quasiparticles : massive quarks and gluons massive quarks and gluons with spectral functions T = 1.053 T c T = 1.35 T c T = 3 T c DQPM well matches lQCD DQPM well matches lQCD DQPM provides mean-fields for gluons and quarks as well as effective 2-body interactions DQPM provides mean-fields for gluons and quarks as well as effective 2-body interactions and gives transition rates for the formation of hadrons  PHSD Gluon‘s  Peshier, Cassing, PRL 94 (2005) 172301; Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

13. PHSD - basic concepts Initial A+A collisions – HSD: string formation and decay to pre-hadrons Fragmentation of pre-hadrons into quarks: Dynamical QuasiParticle Model ( Fragmentation of pre-hadrons into quarks: using the quark spectral functions from the Dynamical QuasiParticle Model (DQPM) approximation to QCD Partonic phase: quarks and gluons (= ‚dynamical quasiparticles‘) with off-shell spectral functions (width, mass) defined by DQPM elastic and inelastic parton-parton interactions: elastic and inelastic parton-parton interactions: using the effective cross sections from the DQPM q + qbar (flavor neutral) gluon (colored) gluon + gluon gluon (possible due to large spectral width) q + qbar (color neutral) hadron resonances Hadronization: based on DQPM - massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell mesons and baryons: gluons  q + qbar; q + qbar  meson (or string); q + q +q  baryon (or string) (strings act as ‚doorway states‘ for hadrons) Hadronic phase: hadron-string interactions – off-shell HSD DQPM: Peshier, Cassing, PRL 94 (2005) 172301; DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

14. PHSD: hadronization Consequences: Consequences:  Hadronization: q+qbar or 3q or 3qbar fuse to a color neutral hadrons (or strings) which furtheron decay to hadrons in a microcanonical fashion, i.e. obeying all conservation laws (i.e. 4- momentum conservation, flavor current conservation) in each event  Hadronization yields an increase in total entropy S (i.e. more hadrons in the final state than initial partons ) and not a decrease as in the simple recombination model !  Off-shell parton transport roughly leads a hydrodynamic evolution of the partonic system E.g. time evolution of the partonic fireball at temperature 1.7 T c with initialized at  q =0 W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; arXiv:0907.5331 [nucl-th], NPA‘09; W. Cassing, EPJ ST 168 (2009) 3

15. PHSD: Expanding fireball Time-evolution of parton density Time-evolution of hadron density Expanding grid: Δz(t) = Δz 0 (1+a t) ! PHSD: spacial phase ‚co-existence‘ of partons and hadrons, but NO interactions between hadrons and partons (since it is a cross-over)

16. Application to nucleus-nucleus collisions energy balance particle balance central Pb + Pb at 158 A GeV only about 40% of the converted energy goes to partons; the rest is contained in the ‚large‘ hadronic corona! Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

17. Partonic phase at NICA energies partonic energy fraction vs centrality and energy Dramatic decrease of partonic phase with decreasing energy and centrality Dramatic decrease of partonic phase with decreasing energy and centrality Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

18. Proton stopping at SPS / NICA  looks not bad in comparison to NA49 data, but not sensitive to parton dynamics (PHSD = HSD)! but not sensitive to parton dynamics (PHSD = HSD)! Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

19. Rapidity distributions of , K +, K -  pion and kaon rapidity distributions become slightly narrower Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

20. PHSD: Transverse mass spectra at SPS / NICA Central Pb + Pb at SPS energies PHSD gives harder spectra and works better than HSD at top SPS (and top NICA) energies PHSD gives harder spectra and works better than HSD at top SPS (and top NICA) energies  However, at low SPS (and low NICA) energies the effect of the partonic phase is NOT seen in rapidity distributions and m T spectra Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

21. Rapidity distributions of strange baryons  PHSD similar to HSD, reasonable agreement with data Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

22. Rapidity distributions of (multi-)strange antibaryons  enhanced production of (multi-) strange anti-baryons in PHSD strange antibaryons _ _  +  0 multi-strange antibaryon _  + Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

23. Centrality dependence of (multi-)strange (anti-)baryons  enhanced production of (multi-) strange antibaryons in PHSD strange antibaryons _ _  +  0 multi-strange antibaryon _  + multi-strange baryon   - strange baryons  +  0 Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

24. Number of s-bar quarks in hadronic and partonic matter  significant effect on the production of (multi-) strange antibaryons due to a slightly enhanced s-sbar pair production in the partonic phase from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process! Number of s-bar quarks in antibaryons for central Pb+Pb collisions at 158 A GeV from PHSD and HSD Cassing & Bratkovskaya, arXiv:0907.5331 [nucl-th], NPA (2009)

25. What is the matter at NICA ?! The phase trajectories (  (t),  (t)) for a central cell in central Au+Au collisions:   huge energy and baryon densities are reached (  >  crit =1 GeV/fm 3 ) at FAIR energies (> 5 A GeV), however, the phase transition might be NOT a cross-over at FAIR or NICA! J. Randrup et al., CBM Physics Book; PRC75 (2007) 034902   1st order phase transition with a critical point?   co-existance of partonic and hadronic degrees of freedom (in a mixed phase)?

26. Summary Some exp. data are not well reproduced in terms of the hadron-string picture => evidence for nonhadronic degrees of freedom Some exp. data are not well reproduced in terms of the hadron-string picture => evidence for nonhadronic degrees of freedom PHSD provides a consistent description of off-shell parton dynamics in line with lattice QCD; the repulsive mean fields generate transverse flow PHSD provides a consistent description of off-shell parton dynamics in line with lattice QCD; the repulsive mean fields generate transverse flow The Pb + Pb data at top SPS energies are rather well described within PHSD including baryon stopping, strange antibaryon enhancement and meson m T slopes (will be also seen at top NICA energies) The Pb + Pb data at top SPS energies are rather well described within PHSD including baryon stopping, strange antibaryon enhancement and meson m T slopes (will be also seen at top NICA energies) At low SPS / NICA energies PHSD gives practically the same results as HSD (except for strange antibaryons) when the lQCD EoS (where the phase transition is always a cross-over) is used At low SPS / NICA energies PHSD gives practically the same results as HSD (except for strange antibaryons) when the lQCD EoS (where the phase transition is always a cross-over) is used  Is the matter at NICA a ‚mixed phase‘ of hadrons and partons?

27. Open problems Is the critical energy/temperature provided by the lQCD calculations sufficiently accurate? Is the critical energy/temperature provided by the lQCD calculations sufficiently accurate? How to describe a first-order phase transition in transport ? How to describe a first-order phase transition in transport ? How to describe parton-hadron interactions in a ‚mixed‘ phase? How to describe parton-hadron interactions in a ‚mixed‘ phase?

28. HSD & PHSD Team Wolfgang Cassing Olena Linnyk Volodya Konchakovski Viatcheslav D. Toneev and the numerous experimental friends and colleagues ! Thanks