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Classical

Putting the CGC into context. Quantum Field Theory Abelian: QED (high temp) Non-Abelian: QCD-High Temp QFT Lattice Calculations. Single Particle:QM Many Body:Stat-Mech (F-D, B-E, M-B gasses). Quantum. Renomalization Group. R-G allows The addition

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Classical

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  1. Putting the CGC into context Quantum Field Theory Abelian: QED (high temp) Non-Abelian: QCD-High Temp QFT Lattice Calculations Single Particle:QM Many Body:Stat-Mech (F-D, B-E, M-B gasses) Quantum Renomalization Group R-G allows The addition of all tree level QCD graphs in region of “small” s Harder to Calculate Approx Colored Glass Condensate Single particle:Mechanics Many Body: Kinetic Theory of gasses Classical Classical Field Theory Abelian: Maxwell Eqns Non-Abelian: Yang Mills Fields Intrinsically Many body But (non)Abelelian Particles Approx

  2. Relevant regions of calculability for QCD The CGC has split into 2 regions (the CGC and the CQF) Quantum Field Theory Gas Low All Tree graphs via Renormalization group Quantum Kharzeev et al (no “Cronin” – good above pt~4-6 GeV) Colored QuantumFluid Liquid Occupation number calculable in “high Q2” region, I.e. weak coupling but non-perturbative Colored Glass Condensate Solid? Condensate? Classical Dumitru, Gelis, Jililian-Marian (includes “Cronin” No Tree graphs included for now) High Classical Field Theory

  3. Regions • Q2=Sxy • Higher S • Larger A Colored Glass Condensate Saturation More accessible } 10-4 10-5 Colored Quantum Fluid • CGC – region of occ number where lowest order is good enough • CQF – region of occ number where higher order tree graphs are important High Occupation number pQCD Gas 10-4 Moderate Occupation number 1/x Low Occupation number 10-3 RHIC? 10-2 Calculable: s(Q2) ~ small 10-1 QCD Qs (at RHIC) 1 1 10 100 Q (GeV)

  4. Shadow vs Cronin in d+Au : X.N. Wang Cronin only Old HIJING1… shadow New HIJING2… shadow

  5. Prediction of KLMc version of CGC for d+Au GLR

  6. Inclusive Observables - b=0 fm HIJING 1.37 simulation; X.N.Wang and M.Gyulassy, Phys.Rev.Lett. 68, (1992) Z.W.Lin and C.M.Ko, nucl-th/0301025 • Vastly different models give comparable results. • May not be unexpected in view of existing precise p+p and Au+Au data at . • Do models stay within their range of validity??? D.Kharzeev, E.Levin and M.Nardi, hep-ph/0212316

  7. Cronin Effect PHENIX Preliminary Binary scaling

  8. Ivan Vitev 03

  9. Y=0 ~40% ~50% D.Kharzeev et al., hep-ph/0210033 ~200 –250% F.Gelis and J.Jalilian-Marian, hep-ph/0211363 Alternative Suggestions for d+A Y=3-4 A.Dumitru, J.Jalilian-Marian Phys.Rev.Lett. 89 (2002) The way for this saturation picture to hold together is to observe large 50% suppression at y=0 and large 2 enhancement at y=3-4

  10. Experimental Facts RHIC • Includes both enhancement • and suppression • The effect decreases with • The peak and intercept are • pT-stable, i.e. • (Excludes a wavefunction nature) Practical approach: EKS’98 parameterization K.Eskola,V.Kolhinen,and C.Salgado, Eur.Phys.J. C9 (1999) Nuclear Effects on Hadron Production(The Point of View of Relativistic Heavy Ions) Nuclear shadowing Cronin effect Poorly constrained

  11. Summary • Two extreme opposite interpretations of RHIC AA data exists • Evidence for opaque 100 x nuclear density matter • Evidence for deep gluon shadowing (saturation) • Ambiguity due to competition between initial nuclear wavefunction Shadowing, initial state (Cronin) interactions, and final state int. as pointed out in 1992 p+A (or d+A) needed to isolate Initial State effects : shadowing and Cronin • IF RHIC finds R(5 GeV) ~ 1.1-1.3 in d+Au , then interpretation (1) QGP matter was produced in AA And RHIC AA Has chance to map out QCD EOS • IF RHIC finds R(5 GeV)< 0.7 in d+Au , then interpretation (2) and AA= shattered color glass No QGP matter => go to eRHIC to map xGA. • IF 0.7< R(5 GeV) < 1 ??? Back to the drawing board ???

  12. A primer • Going from pp to AA • Geometric effects • Physics effects in AA which are not in parton-parton collisions • Intrinsic kT • Cronin effect • Shadowing

  13. Scaling Soft interactions - production scales with Nparticipants Strings : p< p0 ~ 1-2 GeV Hard interactions - production scales with Nbinary pQCD: p> p0 Initial kT included Models pp,pp – Geometry and intrinsic kT Soft Hard

  14. Prior parton scattering broadens the transverse momentum spectrum (“Cronin effect”). This has the opposite effect of “Jet Quenching.” i.e. it enhances high pt <pt2>A = <pt2>pp + (A-1) Dpt2 Not expected to be a large effect at RHIC energies. Big effect at CERN-SPS energies. pp to pA: the Cronin Effect Hijing MC

  15. Nucleon structure functions are known to be modified in nuclei. Fewer partons than otherwise expected will lead to fewer high Pt particles. Gluon shadowing is not measured, large role at RHIC Measure pA at RHIC! For now depend on peripheral events pp to pA: Nuclear shadowing EKS98 Shadowing No Shadowing (just Cronin) RpAu Hijing Shadowing

  16. Running of S S RHIC 130 central Qs QCD • Renomalization Group Theory gives us a way of summing ALL graphs of a certain kind (in particular “tree graphs”) to all orders At RHIC, QS~1-2 GeV S(QS)~0.3 –0.4

  17. QCD diagrams Tree graphs Loop Graphs

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