Search for the Quark-Gluon Plasma in Heavy Ion Collision

1. Search for the Quark-Gluon Plasma in Heavy Ion Collision V. Greco

2. Outline • Introduction: definitons & concepts - Quark-Gluon Plasma (QGP) - Heavy-Ion-Collisions (HIC) • Theory and Experiments - probes of QGP in HIC - what we have found till now!

3. Introduction I • Goals of the Ultra-RHIC program: • Production of high energy density matter better understanding of the origin of the masses of ordinary nuclei • Produce matter where confinement -> deconf QGP and hadronization • Structure of the nucleon how quantum numbers arise (charge spin, baryon number)

4. Bang Big Bang • e. m. decouple (T~ 1eV , t ~ 3.105 ys) • “thermal freeze-out “ • but matter opaque to e.m. radiation • Atomic nuclei (T~100 KeV, t ~200s) • “chemical freeze-out” • Hadronization (T~ 0.2 GeV, t~ 10-2s) • Quark and gluons We’ll never see what happened t < 3 .105 ys (hidden behind the curtain of the cosmic microwave background) HIC can do it!

5. Little Bang From high rB regime to high T regime AGS SPS RHIC We do not observe hadronic systems with T> 170 MeV (Hagerdon prediction)

6. “Elastic” finite Dt Different stages of the Little Bang Freeze-out Hadron Gas Phase Transition Plasma-phase Pre-Equilibrium

7. Euristic QGP phase transition B1/4 ~ 210 MeV -> Tc~ 145 MeV Free massless gas Bag Model (cosm. cost.) Pressure exceeds the Bag pressure -> quark liberation Extension to finite mB , mI

8. Phase Transition Def. Phase transition of order n-th means the n-th derivative of the free energy F is discontinous Mixed phase I order II order Critical behavior Cross over Not a mixed phase, but a continous modification of the matter between the two phases

9. Quantum ChromoDynamics • Similar to QED, but much richer structure: • SU(3) gauge symmetry in color space • Approximate Chiral Symmetry in the light sector broken in the vacuum. • UA(1) ciral • Scale Invariance broken by quantum effects • Confinement • Chiral Symmetry Restoration

10. f1 (1285) a1 (1260) w (782) r (770) s (400-1200) Mass (MeV) P-S V-A splitting In the physical vacuum p (140) Chiral Symmetry QCD is nearly invariant under rotation among u,d,s associate Axial and Vector currents are conserved Constituent quark masses -> explicit breaking of chiral simmetry • Eight goldstone Bosons (p,K,h) • Absence of parity doublets

11. Lattice QCD Gluon field Continuum limit QCD can be solved in a discretized space ! Lattice QCD is the algorithm to evaluate Z in the Space-time -> static at finite temperature time dim. regulate the temperature Dynamics -> Statistics It is less trivial than it seems, Ex.: fermion action, determinant

12. Lattice QCD Prospectives • Quark –gluon plasma properties (vs density and temperature) • Hadron properties (mass, spin, ) • vacuum QCD structure (istantons ..) • CKM matrix elements (fp,fk,fc,fB) CPU time is very large • quark loops is very time consuming • (mq=∞-> no quark loops = “quenched approximation”) • lattice spacing a -> 0 • baryon chemical potential Limitations • No real time processes • Scattering • Non equilibrium • Physical understanding Effective models are always necessary !!!

13. Polyakov Loop -static quark -only gluon dynamics If quark mass is not infinite and quark loops are present L is not really an order parameter !

14. Lattice QCD Polyakov Loop Chiral Condensate • Coincident transitions: • deconfinement and chiral symmetry restoration • it is seen to hold also vs quark mass

15. Phase Transition to Quark-Gluon Plasma Enhancement of the degrees of freedom towards the QGP Quantum-massless non interacting Gap in the energy density (I0 order or cross over ?)

16. Definitions and concepts in HIC Kinematics Observables Language of experimentalist

17. Au+Au STAR The RHIC Experiments

18. Soft and Hard QGP 99% of particles SOFT(npQCD)string fragmentation in e+e- ,pp… or (pT<2 GeV) string melting in AA (AMPT,HIJING, NEXUS…) HARDminijets from first NN collisions Indipendent Fragmentation : pQCD + phenomenology • Small momentum transfer • Bulk particle production • How ? How many ? How are distributed? • Only phenomenological descriptions available (pQCD doesn’t work)

19. 15 fm b 0 fm Collision Geometry - “Centrality” Spectators Participants S. Modiuswescki For a given b, Glauber model predicts Npart and Nbinary 0 N_part 394

20. Kinematical observables Additive like Galilean velocity Transverse mass Angle respect z beam axis Rapidity -pseudorapidity

21. Energy density a la Bjorken: Time estimate from hydro: Energy Density Estimate e for RHIC: Particle streaming from origin dET/dy ~ 720 GeV  Tinitial ~ 300-350 MeV

22. Collective Flow I: Radial Observable in the spectra, that have a slope due to temperature folded with Radial flow expansion <bT> due to the pressure. Absence Slope for hadrons with different masses allow to separate thermal from collective flow Tf ~ (120 ± 10) MeV <bT> ~ (0.5 ± 0.05)

23. Collective flow II: Elliptic Flow z y x Anisotropic Flow py px Perform a Fourier decomposition of the momentum space particle distributions in the x-y plane • v2 is the 2nd harmonic Fourier coeff. • of the distribution of particles. Measure of the Pressure gradient Good probe of early pressure

24. Statistical Model Temperature Chemical Potential Mass Quantum Numbers Yield Maximum entropy principle There is a dynamical evolution that Leads to such values of Temp. & abundances? Hydro add radial flow, freeze-out hypersurface for describing the differential spectrum Yes, but what is Hydro?

25. Maximum Entropy Principle All processes costrained by the conservation laws Maximizing S with this constraints the solution is the statistical thermal equilibrium The apparent “equilibrium” is not achieved kinetically but statistically !

26. HYDRODYNAMICS 5 partial diff. eq. for 6 fields (p,e,n,u) + Equation of State p(e,nB) Local conservation Laws • No details about collision dynamics (mean free path ->0)

27. Another level of Knoweledge • Follow distribution function time evolution: • Initial non-equilibrium gluon phase • -> final chemical and thermal equlibrated system • How hydrodynamical behavior is reached • Relevance of npQCD cross section • Description of the QCD field dynamics

28. Transport Theory Non-relativistically drifting collision mean field Relativistically at High density gg<->ggg g<->gg Follow distribution function time evolution From the initial non-equilibrium gluon phase To be treated: - Multiparticle collision (elastic and inelastic) - Quantum transport theory (off-shell effect, … ) -Mean field or condensate dynamics

29. Elliptic Flow Hydro Transport Spectra still appear thermal rapidity rapidity

30. Chemical equilibrium with a limiting Tc ~170MeV Thermal equilibrium with collective behavior - Tth ~120 MeV and <bT>~ 0.5 Early thermalization (t < 1fm/c, e ~ 10 GeV) - very large v2 We have not just crashed 400 balls to get fireworks, but we have created a transient state of plasma A deeper and dynamical knowledge of the system is still pending!

31. Outline II • Probes of QGP in HIC • What we have find till now! • strangeness enhancement • jet quenching • coalescence • J/Y suppression • What we have learned • ?

32. Glauber model Binary Collisions N Participants b (fm)