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. Big Bang Hadronization ( T~ 0.2 GeV, t~ 10 -2 s ) Quark and gluons Atomic nuclei ( T~100 KeV, t ~200s ) “chemical freeze-out” opaque but matter opaque to e.m. radiation e. m. decouple ( T~ 1eV, t ~ 3. 10 5 ys ) “thermal freeze-out “ We’ll never see what happened t < 3. 10 5 ys (hidden behind the curtain of the cosmic microwave background) HIC can do it! Bang

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

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

7. Bag Model ( cosm. cost.) Euristic QGP phase transition Pressure exceeds the Bag pressure -> quark liberation Extension to finite     B 1/4 ~ 210 MeV  T c ~ 145 MeV Free massless gas

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

9. Quantum ChromoDynamics Similar to QED, but much richer structure 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.  U A (1)  iral  Scale Invariance broken by quantum effects Confinement Chiral Symmetry Restoration

10. Chiral Symmetry  Eight goldstone Bosons (  )  Absence of parity doublets 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      a    f   P-S V-A splitting In the physical vacuum Mass (MeV)

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

12. Lattice QCD CPU time is very large  quark loops is very time consuming (m q = ∞  no quark loops = “quenched approximation”)  lattice spacing a  0  baryon chemical potential Prospectives Quark –gluon plasma properties (vs density and temperature) Hadron properties (mass, spin, ) vacuum QCD structure (istantons..) CKM matrix elements (f ,f k,f c,f B ) Limitations  No real time processes  Scattering  Non equilibrium  Physical understanding Effective models are always necessary !!!

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

14. Lattice QCD Chiral CondensatePolyakov Loop 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 (I 0 order or cross over ?)

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

17. The RHIC Experiments STAR Au+Au

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

19. Collision Geometry - “Centrality” 0 N_ part 394 15 fm b 0 fm Spectators Participants For a given b, Glauber model predicts N part and N binary S. Modiuswescki

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

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

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

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

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

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 Local conservation Laws 5 partial diff. eq. for 6 fields (p,e,n,u) + Equation of State p(e,n B )  No details about collision dynamics (mean free path  0)

27. Follow distribution function time evolution 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 Another level of Knoweledge

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

29. Spectra still appear thermal Elliptic Flow Hydro Transport rapidity

30. Chemical equilibrium with a limiting T c ~170MeV Thermal equilibrium with collective behavior - T th ~120 MeV and ~ 0.5 Early thermalization (  < 1fm/c,  ~ 10 GeV) - very large v 2 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/  suppression What we have learned ?

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