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Color Glass Condensate : Theory and Phenomenology

Color Glass Condensate : Theory and Phenomenology. Azfar Adil PHENIX Journal Club. Overview. Evolution DGLAP ( log(Q 2 ) evolution ) BFKL ( log(1/x) evolution) Saturation and CGC Non-Linearities at low x Dipole versus Classical Field Phenomenology Observables at RHIC Implications.

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Color Glass Condensate : Theory and Phenomenology

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  1. Color Glass Condensate :Theory and Phenomenology Azfar Adil PHENIX Journal Club

  2. Overview • Evolution • DGLAP ( log(Q2) evolution ) • BFKL ( log(1/x) evolution) • Saturation and CGC • Non-Linearities at low x • Dipole versus Classical Field • Phenomenology • Observables at RHIC • Implications

  3. A look at DIS • Factored x-sections • x and Q2 set via kinematics • Function f(x,Q2) can be predicted given f(x0,Q02) • This is evolution

  4. BFKL DGLAP BFKL DGLAP The “Phase Diagram” Weigert hep-ph/0501087

  5. Leading Order Evolution • “Wee” radiation is leading order process • Parton starts at distribution f(x0,Q02) and multiply radiates to get to f(x,Q2) • Get “large logarithms” we need to resum

  6. (X4,Q42) (X3,Q32) (X2,Q22) (X1,Q12) DGLAP Evolution • Experimentally access various momentum transfers • Need evolution in Q2 Collinear Factorization

  7. Gluons only Gluons and Quarks at Low-x Distribution functionsxq(x,Q2)and xG(x,Q2) rise steeply at low Bjorken x. Gluons and Quarks Is all this well-described by the standard DGLAP evolution?

  8. Negative gluon distribution! • NLO global fitting based on leading twist DGLAP evolution leads to negative gluon distribution • MRST PDF’s have the same features Does it mean that we have no gluons at x < 10-3 and Q=1 GeV? No!

  9. (X4,Q42) (X3,Q32) (X2,Q22) (X1,Q12) BFKL Evolution • Experimentally access various COM energies • Need evolution in 1/x kT Factorization

  10. BFKL from HERA • HERA DIS data shown to be explainable using BFKL type dynamics • Still have the x- singular behavior (violates unitarity)

  11. Linear Non Linear A Different Point of View • Boost calculation to “dipole” frame • Calculations factorizes into wave function and cross section • Evolution encompassed in dipole cross section

  12. Hints of a Solution • A scaling property seen in DIS e-A dat •  = Q2/Q0(x)2 • Suggests generation of an x dependent scale Q0(x) • Characteristic of ‘saturation’ model of Golec-Biernat-Wusthoff

  13. Non Linearity to Saturation • Resum pomeron loops to get non linear effects • Pomerons are effective at large energies and large densities • Get the BK equations and the Balitsky Heirarchy

  14. Classical Field Picture • In the saturation regime we get N ~ 1/ • Get a background classical field description • Quantum evolution comes from separation between field and source dof JIMWLK Equation Note : Can also be formulated as evolution of Qs or 

  15. McLerran-Venugopalan Model • Assume a Gaussian weight (MV model) • JIMWLK with MV Initial Conditions gives evolution for Qs and  •  can now be used with kT factorized formula to calculate production

  16. RHIC Phenomenology

  17. CGC Forward Suppression • Suppression in RdAu at forward rapidities is said to be indicative of saturation physics • This is unclear because other physics also “works”

  18. RHIC Bulk Production • Models “inspired by” CGC explain well the total particle production, e.g. KLN • Are a viable alternative to phenomenological models as in HIJING

  19. Hirano et al. Nucl-th/0511046 !! Need high viscosity with CGC !!!! Hirano et al. Nucl-th/0511046 Other Implications

  20. The CGC/KLN Bulk Model • Use kT factorized GLR formula • Gluon Distributions depend on Qs • Qs determined locally (Not factorized!!!)

  21. Eccentric CGC • Initial spatial eccentricity causes v2 • For Participant • For CGC

  22. Problems with KLN model • Not factorized • as • Has trouble getting multiplicities for smaller systems (d-Au, p-p) and larger systems (Au-Au) consistently

  23. The Correct Limits • To get a universal CGC theory we need • We also need for • Solution is …

  24. Factorized KLN (fKLN) • Make the replacements • Explicitly factorized • Correct nuclear edge limit • Can now consistently investigate small systems

  25. Start with p-p • Use GLR formula to calculate production • Normalize to p-p data • Set average Qs to 2 GeV2 at RHIC

  26. Move on to A-A

  27. Asymmetric Collisions…

  28. The Bottom Line • fKLN is an improvement • Theoretically Consistent • Phenomenologically Successful • Has different eccentricity • Need to run hydro with it

  29. Conclusions - I • Parton Evolution is Key Prediction of QCD • Get log scaling violations in Q2 and 1/x • DGLAP, BFKL and DLLA not unitary • CGC - a QCD effective field theory • Takes into account fully non perturbative non linear correction • Includes generation of a large scale Qs • Need more work in proving kT factorization as well as complete solutions for JIMWLK

  30. Conclusions - II • KLN one implementation of CGC • Gets centrality dependence • Not factorized • Not good with small systems and nuclear edge • Predicts large spatial eccentricity giving large v2 • fKLN improves KLN • Gets improved and consistent results with smaller systems • Explicitly factorized • Gets smaller eccentricity, needs to be input into hydro

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