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Color Glass Condensate : Theory and Phenomenology

This comprehensive overview delves into the theory and phenomenology of Color Glass Condensate (CGC) in high-energy physics. Discussing key topics such as DGLAP and BFKL evolution, distribution functions of gluons and quarks, implications for observables at RHIC, and more, this analysis sheds light on the intricate dynamics of QCD and perturbative/non-linear corrections. Various models like MRST PDFs, BFKL, and KLN are examined, highlighting challenges such as unitarity violations and the need for better solutions like the dipole frame approach and JIMWLK Equation. The study also evaluates the implications of CGC on forward suppression and bulk production at RHIC, proposing the fKLN model as a viable improvement over existing models for a more consistent description across different collision systems. The text advocates for further research to refine the CGC framework, address its limitations, and enhance its applicability across diverse particle collision scenarios.

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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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