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The CGC and the Cronin effect

The CGC and the Cronin effect. This is my attempt to understand the reconciliation between the Jamal-Marian CGC “Cronin” calculation and the Kharzeev et al prediction for dA. It is not meant to be a tutorial on the CGC but simply to clarify a few points. Hope its helpful. Richard Seto

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The CGC and the Cronin effect

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  1. The CGC and the Cronin effect This is my attempt to understand the reconciliation between the Jamal-Marian CGC “Cronin” calculation and the Kharzeev et al prediction for dA. It is not meant to be a tutorial on the CGC but simply to clarify a few points. Hope its helpful Richard Seto Apr 3, 2003 Updated Apr 5 – not much changed

  2. 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

  3. 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

  4. Regions • Q2=Sxy • Higher S • Larger A Colored Glass Condensate Saturation More accessible } 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)

  5. Notes on the CGC • Dima is only willing to predict total charged spectrum at high pt and not pions • I don’t completely understand why but you can ask • (it has something to do with the unkown fragmentation functions of very virtual quarks, different than the almost on-shell nature of fragmenting quarks in e+e- ) • They ignore final state interactions (jet suppression, flow, coalecence…) If these are present then they “hide” the CGC • Hence we cannot make a direct comparison with the 0 which I believe is the cleanest handle we have on jets • Our charged suppression is ~ 0.5 so Rd+Au=RAu+Au=0.5=0.7 • My guess as to the relationship between “shadowing” and the CGC • The CGC is really a word describing a region (high occ number) which can be calculated from “first principles” using QCD. It is less a model than an approximation. Hence it can describe shadowing from “first principles” • Its not clear that the CGC theorists agree with each other on all this

  6. Predictions HIJING 1.37 simulation; X.N.Wang and M.Gyulassy, Phys.Rev.Lett. 68, (1992) D.Kharzeev, E.Levin and M.Nardi, hep-ph/0212316 dNch/d Not much Difference Between “standard” Models and CGC b=0 fm More standard “jet suppression” models “CGC” Vitev Rd+Au=RAu+Au 0.5=0.7<1 RAA RAA>1 See next page 2 pT 4 6

  7. Typical prediction for dA for final state Interaction “jet quenching” scenarios New CGC “Cronin”Calculation From Jililian-Marian et al A guess of what would happen If CGC Cronin were added to CQF-CGC Band of dA prediction from Dima et al (CQF-CGC) tot charged Dima believes His calculation Is OK at high pt 6 GeV Where cronin-like Effects are small Y=0 Phenix AA data

  8. Exp result: Multiplicity: is as CGC ( or other models) predicts High pt dA: NOT suppressed RHIC in regime in which CGC affects only low pt (mult) but not high pt Exp result: Multiplicity: is as CGC ( or other models) predicts High pt dA: suppressed RHIC in regime in which CGC affects high pt A couple possibilities for the CGC Colored Glass Condensate Colored Glass Condensate 10-4 10-4 Colored Quantum Fluid Colored Quantum Fluid pQCD Gas pQCD Gas 10-4 10-4 1/x 1/x RHIC? 10-3 10-3 RHIC? 10-2 10-2 10-1 10-1 Qs (at RHIC) Qs (at RHIC) 1 1 Q (GeV) Q (GeV) 1 1 10 100 10 100

  9. Summary (mostly from MG) • Two extreme opposite interpretations of RHIC AA data existsEvidence for opaque 100 x nuclear density matterEvidence 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 CroninIF RHIC finds R(5 GeV) ~ 1.1-1.3 in d+Au , theninterpretation (1) QGP matter was produced in AA And RHIC AA Has chance to map out QCD EOS(rks) CGC may still give us theinitial stateIF RHIC finds R(5 GeV)< 0.7 in d+Au , theninterpretation (2) and AA= shattered color glassNo QGP matter => go to eRHIC to map xGA.IF RHIC finds 0.7< R(5 GeV) < 1 Back to the drawing board ???(rks) probably combination of both

  10. Running of S S RHIC 130 central Qs QCD- RG and the CGC • Renomalization Group Theory gives us a way of summing ALL graphs of a certain kind (in particular “tree graphs”) • For the CGC these are to first order in Sln(1/x)lnQ2 • For PQCD this is all graphs usually to first order in lnQ2 At RHIC, QS~1-2 GeV S(QS)~0.3 –0.4

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