Quantum Field Theory Classical FD BE MB gasses
Quantum Field Theory Classical (F-D, B-E, M-B gasses) t ula r rde to lc a C Ha Colored Glass Condensate Single particle: Mechanics Many Body: Kinetic Theory of gasses Particles e Renomalization Group Abelian: QED (high temp) Non-Abelian: QCD-High Temp QFT Lattice Calculations Single Particle: QM Many Body: Stat-Mech Approx Quantum Putting the CGC into context Approx R-G allows The addition of all tree level QCD graphs in region of “small” s Classical Field Theory Abelian: Maxwell Eqns Non-Abelian: Yang Mills Fields Intrinsically Many body But (non)Abelelian
Relevant regions of calculability for QCD Solid? Condensate? Liquid Low Gas Quantum Field Theory High Occupation number Classical Quantum The CGC has split into 2 regions (the CGC and the CQF) All Tree graphs via Renormalization group Colored Quantum Fluid calculable in “high Q 2” region, I. e. weak coupling but non-perturbative Colored Glass Condensate Classical Field Theory Kharzeev et al (no “Cronin” – good above pt~4 -6 Ge. V) Dumitru, Gelis, Jililian-Marian (includes “Cronin” No Tree graphs included for now)
Regions -4 10 -5 10 -4 Colored Glass Condensate High Occupation number Q 2=Sxy Colored Quantum Fluid Moderate Occupation number 1/x 10 -3 p. QCD Gas Low Occupation number RHIC? • 10 -2 Calculable: s(Q 2) ~ small 10 -1 1 QCD 1 Saturation –Higher S More } –Larger A accessible Qs (at RHIC) 10 • CGC – region of occ number where lowest order is good enough CQF – region of occ number where higher order tree graphs are important 100 Q (Ge. V)
Shadow vs Cronin in d+Au : X. N. Wang Cronin only Old HIJING 1… shadow New HIJING 2… shadow
Prediction of KLMc version of CGC for d+Au GLR
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
Cronin Effect m i l e Pr y r a in PHENIX Binary scaling
Ivan Vitev 03
Alternative Suggestions for d+A Y=0 ~40% ~50% D. Kharzeev et al. , hep-ph/0210033 ~200 – 250% Y=3 -4 A. Dumitru, J. Jalilian-Marian Phys. Rev. Lett. 89 (2002) F. Gelis and J. Jalilian-Marian, hep-ph/0211363 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
Nuclear Effects on Hadron Production (The Point of View of Relativistic Heavy Ions) Nuclear shadowing Cronin effect RHIC Poorly constrained Practical approach: EKS’ 98 parameterization Experimental Facts • Includes both enhancement and suppression • The effect decreases with K. Eskola, V. Kolhinen, and C. Salgado, Eur. Phys. J. C 9 (1999) • The peak and intercept are p. T-stable, i. e. (Excludes a wavefunction nature)
Summary • Two extreme opposite interpretations of RHIC AA data exists 1. 2. • 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 Ge. V) ~ 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 Ge. V)< 0. 7 in d+Au , then interpretation (2) and AA= shattered color glass No QGP matter => go to e. RHIC to map x. GA. • IF 0. 7< R(5 Ge. V) < 1 ? ? ? Back to the drawing board ? ? ?
A primer • Going from pp to AA – Geometric effects • Physics effects in AA which are not in parton-parton collisions – Intrinsic k. T – Cronin effect – Shadowing
Models pp, pp – Geometry and intrinsic k. T § Scaling § Soft interactions - production scales with Nparticipants § Strings : p< p 0 ~ 1 -2 Ge. V § Hard interactions - production scales with Nbinary § p. QCD : p> p 0 § Initial k. T included Soft Hard
pp to p. A: the Cronin Effect • Prior parton scattering broadens the transverse momentum spectrum (“Cronin effect”). This has the opposite effect of “Jet Quenching. ” – i. e. it enhances high pt <pt 2>A = <pt 2>pp + (A-1) Dpt 2 – Not expected to be a large effect at RHIC energies. Big effect at CERN-SPS energies. Hijing MC
pp to p. A: Nuclear shadowing EKS 98 Shadowing § is not measured, § large role at RHIC § Measure p. A at RHIC! § For now depend on peripheral events No Shadowing (just Cronin) Rp. Au § Nucleon structure functions are known to be modified in nuclei. Fewer partons than otherwise expected will lead to fewer high Pt particles. § Gluon shadowing Hijing Shadowing
QCD • Renomalization Group Theory gives us a way of summing ALL graphs of a certain kind (in particular “tree graphs”) to all orders Running of S S RHIC 130 central Qs At RHIC, QS~1 -2 Ge. V S(QS)~0. 3 – 0. 4
QCD diagrams Tree graphs Loop Graphs
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