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

2. Overview Evolution Saturation and CGC Phenomenology
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
11/21/2018

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
11/21/2018

4. The “Phase Diagram”
BFKL
DGLAP
Weigert hep-ph/
11/21/2018

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
11/21/2018

6. DGLAP Evolution Experimentally access various momentum transfers
(X1,Q12)
(X2,Q22)
(X4,Q42)
(X3,Q32)
Experimentally access various momentum transfers
Need evolution in Q2
Collinear Factorization
11/21/2018

7. Gluons and Quarks at Low-x
Distribution functions xq(x,Q2) and xG(x,Q2) rise steeply at low Bjorken x.
Gluons and Quarks
Gluons only
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!
11/21/2018

9. BFKL Evolution Experimentally access various COM energies
(X1,Q12)
(X2,Q22)
(X4,Q42)
(X3,Q32)
Experimentally access various COM energies
Need evolution in 1/x
kT Factorization
11/21/2018

10. BFKL from HERA
HERA DIS data shown to be explainable using BFKL type dynamics
Still have the x- singular behavior (violates unitarity)
11/21/2018

11. A Different Point of View
Boost calculation to “dipole” frame
Calculations factorizes into wave function and cross section
Evolution encompassed in dipole cross section
Linear
Non Linear
11/21/2018

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
11/21/2018

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
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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 
11/21/2018

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
11/21/2018

16. RHIC Phenomenology
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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”
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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
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19. Other Implications !! Need high viscosity with CGC !!!!
Hirano et al. Nucl-th/
Need high viscosity
with CGC !!!!
Hirano et al. Nucl-th/ !!
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20. The CGC/KLN Bulk Model Use kT factorized GLR formula
Gluon Distributions depend on Qs
Qs determined locally (Not factorized!!!)
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21. Eccentric CGC Initial spatial eccentricity causes v2 For Participant
For CGC
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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
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23. The Correct Limits To get a universal CGC theory we need
We also need for
Solution is …
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24. Factorized KLN (fKLN) Make the replacements Explicitly factorized
Correct nuclear edge limit
Can now consistently investigate small systems
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25. Start with p-p Use GLR formula to calculate production
Normalize to p-p data
Set average Qs to 2 GeV2 at RHIC
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26. Move on to A-A
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27. Asymmetric Collisions…
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28. The Bottom Line fKLN is an improvement Has different eccentricity
Theoretically Consistent
Phenomenologically Successful
Has different eccentricity
Need to run hydro with it
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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
11/21/2018

30. Conclusions - II KLN one implementation of CGC fKLN improves KLN
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
11/21/2018