1. School on Heavy Ion Phenomenology, Bielefeld, September 2005 RHIC Phenomenology:Quantum Chromo-Dynamicswith relativistic heavy ions D. Kharzeev BNL

2. Quarks and the Standard Model 1/2 of all “elementary” particles of the Standard Model are not observable; they are confined within hadrons by “color” interactions

3. Theoretical notion of color: “The red-haired man”by Daniil Kharms (1905-1942)from “Blue Notebook No.10” Once there was a red-haired man who had no eyes or ears. Neither did he have any hair, so he was called “red-haired” only theoretically … Therefore there’s no knowing whom we are even talking about. In fact we better not say anything about him...

4. Outline • Quantum Chromo-Dynamics - the theory of strong interactions • Classical dynamics and quantum anomalies • QCD phase diagram • A glimpse of RHIC data • New facets of QCD at RHIC and LHC: • Color Glass Condensate • (strongly coupled) Quark-Gluon Plasma • links between General Relativity and QCD

5. What is QCD? QCD = Quark Model + Gauge Invariance local gauge transformation: .i

6. QCD and the origin of mass quarks gluons Invariant under scale ( ) and chiral Left Right transformations in the limit of massless quarks .i Experiment: u,d quarks are almost massless… … but then… all hadrons must be massless as well! Where does the “dark mass” of the proton come from?

7. QCD and quantum anomalies Classical scale invariance is broken by quantum effects: scale anomaly trace of the energy- momentum tensor “beta-function”; describes the dependence of coupling on momentum Hadrons get masses coupling runs with the distance

8. Asymptotic Freedom At short distances, the strong force becomes weak (anti-screening) - one can access the “asymptotically free” regime in hard processes and in super-dense matter (inter-particle distances ~ 1/T) number of flavors number of colors

9. B Asymptotic freedom and Landau levels of 2D parton gas The effective potential: sum over 2D Landau levels V Paramagnetic response of the vacuum: H 1. The lowest level n=0 of radius is unstable! 2. Strong fields Short distances

10. QCD and the classical limit Classical dynamics applies when the action is large in units of the Planck constant (Bohr-Sommerfeld quantization) (equivalent to setting ) weak field => Need weak coupling and strong fields .i strong field

11. Building up strong color fields:small x (high energy) and large A (heavy nuclei) Bjorken x : the fraction of hadron’s momentum carried by a parton; high energies s open access to small x = Q2/s the boundary of non-linear regime: partons of size 1/Q > 1/Qs overlap Large x small x Because the probability to emit an extra gluon is ~ as ln(1/x) ~ 1, the number of gluons at small x grows; the transverse area is limited transverse density becomes large

12. Strong color fields in heavy nuclei At small Bjorken x, hard processes develop over .large longitudinal distances Density of partons in the transverse plane as a new dimensionful parameter Qs (“saturation scale”) All partons contribute coherently => at sufficiently small x and/or .large A strong fields, weak coupling!

13. Non-linear QCD evolutionand population growth time rapidity Color glass condensate Linear evolution: T. Malthus (1798) r - rate of maximum population growth Unlimited growth!

14. Resolving the gluon cloud at small x and short distances ~ 1/Q2 number of gluons “jets”: high momentum partons

15. Population growth in a limited environment “logistic equation” K - maximum sustainable population; define x Pierre Verhulst (1845) t Stable population: The limit is universal (no dependence on the initial condition)

16. Population growth in a limited environment:a (short) path to chaos Discrete version: bifurcations leading to chaos John von Neumann Fixed points “logistic map” ( limit of the popu- lation) Rate of growth (the value of ) High energy evolution starts here.

17. Semi-classical QCD: experimental tests

18. Hadron multiplicities:the effect of parton coherence

19. Semi-classical QCD and total multiplicities in heavy ion collisions Expect very simple dependence of multiplicity .on atomic number A / Npart: Npart:

20. Classical QCD in action

21. Classical QCD dynamics in action The data on hadron multiplicities in Au-Au and d-Au collisions support the quasi-classical picture Kharzeev & Levin, Phys. Lett. B523 (2001) 79

22. Gluon multiplication in a limited (nuclear) environment The ratio of pA and pp cross sections DK, Levin, McLerran; DK, Kovchegov,Tuchin; Albacete,Armesto, Kovner,Wiedemann; … transverse momentum At large rapidity y (small angle) expect suppression of hard particles!

23. Quantum regime at short distances: the effect of the classical background 1) Small x evolution leads to anomalous dimension 2) Qs is the only relevant dimensionful parameter in the CGC; .thus everything scales in the ratio 3) Since Tthe A-dependence is changed Expect high pT suppression at sufficiently small x

24. Phase diagram of high energy QCD

25. Model predictions D. Kharzeev, Yu. Kovchegov and K. Tuchin, hep-ph/0307037 I. Vitev nucl-th/0302002 v2 CGC at y=0 Y=0 As y grows Y=3 Y=-3 Very high energy R. Debbe, BRAHMS Coll., Talk at DNP Meeting, Tucson, November 2003

26. Nuclear Modification of Hard Parton Scattering R.Debbe, BRAHMS, QM’04

27. Color Glass Condensate: confronting the data • BRAHMS • data, • = 0, 1, 2.2, 3.2 DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045

28. Color Glass Condensate: confronting the data • BRAHMS • data, RCP • = 0, 1, 2.2, 3.2 DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045

29. Confronting the RHIC data DK & K.Tuchin STAR Collaboration charm hadrons

30. Centrality dependence R.Debbe, BRAHMS, QM’04

31. PhenixPreliminary Au d

32. PhenixPreliminary Au d

33. PhenixPreliminary Cronin effect & anti-shadowing? d Color Glass? Shadowing? Au

34. Newly Found State of Matter Could Yield Insights Into Basic Laws of Nature By JAMES GLANZ Published: January 13, 2004 OAKLAND, Calif., Jan. 12 — A fleeting, ultradense state of matter, comparable in some respects to a bizarre kind of subatomic pudding, has been discovered deep within the core of ordinary gold atoms, scientists from Brookhaven National Laboratory said at a conference here Monday… Shattered Glass Seeking the densest matter: the color glass condensate By David Appell April 19, 2004

35. How dense is the produced matter? The initial energy density achieved: mean transverse momentum of produced gluons about 100 times nuclear density ! the density of the gluons in the transverse plane and in rapidity gluon formation time

36. What happens at such energy densities? Phase transitions: deconfinement Chiral symmetry restoration UA(1) restoration Data from lattice QCD simulations F. Karsch et al critical temperature ~ 1012 K; cf temperature inside the Sun ~ 107 K

37. Strongly coupled QCD plasma Interactions are important! (strongly coupled Quark-Gluon Plasma) C. Bernard, T.Blum, ‘97 Bielefeld

38. Coulomb potential in QCD Spectral representation in the t-channel: If physical particles can be produced (positive spectral density), then unitarity implies screening Gluons Quarks (transverse)

39. Coulomb potential in QCD - II Missing non-Abelian effect: instantaneous Coulomb exchange dressed by (zero modes of) transverse gluons Negative sign (the shift of the ground level due to perturbations - unstable vacuum! ): Anti-screening

40. Screening in Quark-Gluon Plasma These diagrams are enhanced at finite temperature: (scattering off thermal gluons and quarks) This diagram is not: => At high enough T, screening wins

41. Screening in the QGP Strong force is screened by the presence of thermal gluons and quarks T-dependence of the running coupling develops in the non-perturbative region at T < 3 Tc F.Karsch’s lecture; F.Zantow’s talk

42. sQGP Lecture by F.Karsch

43. Percolation deconfinement, CGC? Lecture by H. Satz

44. sQGP: more fluid than water? Perfect fluid A.Nakamura and S.Sakai, hep-lat/0406009 KSS bound: strongly coupled SUSY QCD = classical supergravity

45. Charge fluctuations in sQGP Lecture by F.Karsch Hadron resonance gas QQ bound states Dynamical quarks S.Ejiri, F.Karsch and K.Redlich, 05

46. Hydro limit STAR PHOBOS Do we see the QCD matter at RHIC ? I. Collective flow => Lectures by J.-Y. Ollitrault Au-Au collisions at RHIC produce strongly interacting matter shear viscosity - to - entropy ratio hydrodynamics: QCD liquid is more fluid than water, SUSY Yang-Mills (AdS-CFT corr.) :

47. Azimuthal anisotropy as a measure of the interaction strength v2

48. Azimuthal anisotropy defined

49. R Do we see the QCD matter at RHIC? II. Suppression of high pT particles => Lectures by U.Wiedemann consistent with the predicted parton energy loss from induced gluon radiation in dense QCD matter J/Y suppression -> F.Fleuret, H.Satz

50. Jets (high momentum partons) - I Jet d’Eau Geneva 3-jet event, LEP Geneva