1. Electron ion collisions and the Color Glass Condensate
F.S. Navarra
University of São Paulo

2. Introduction Higher energy/resolution: proton has more gluons
Well understood with BFKL and DGLAP
Linear evolution: gluon splitting g -> g g
High densities: non-linear evolution
gluon recombination g g -> g
Gribov, Levin, Ryskin (1983)
Saturation: Color Glass Condensate
McLerran, Venugopalan, Iancu,
Al Müller, Levin, Kharzeev, Balitsky,
Kovchegov,... ( > )
Non-linear evolution equations:
JIMWLK and BK
“Laws of motion” in the x-Q plane

3. Evidence at RHIC: suppression of the Cronin peak in the forward region
BRAHMS
High energy hadronic collisions: LHC
Confirmation of CGC
High energy e-nucleus collisions: eRHIC
Deshpande, Milner,Venugopalan,Vogelsang,
hep-ph/
eRHIC: electron-ion collider at RHIC

4. Saturation scale
Saturation condition: target area completely filled by gluons
QS : saturation scale
dilute (linear)
dense (saturation)
is large !
CGC visible when
LHC : x may be small
eRHIC : A may be large

5. Color dipole approach b from the numerical solution of the BK equation
Nikolaev, Zakharov (1991),
A. Müller (1994) b
proton
quark
antiquark
from the numerical solution
of the BK equation
Analytical form for
to fit data and understand the physics !
(Study of parton distributions in DIS --> study of dipole cross sections)

6. Testing dipole cross sections

7. Dipole cross sections GBW Golec-Biernat Wüstoff (1999)
Satisfies unitarity and color transparency:
when or
when

8. More generally:
Most of the physics is in the “anomalous dimension”:
when
when
(from approximate solutions of BFKL, BK)

9. BK BFKL IIM Iancu, Itakura, Munier (2004) large dipoles small dipoles
linear
saturation

10. KKT KKTm DHJ GKMN Kharzeev, Kovchegov, Tuchin (2004) Machado (2006)
Dumitru, Hayashigaki, Jalilian-Marian (2006)
DHJ
GKMN
Gonçalves, Kugeratski, Machado, F.S. N. (2006)

11. Comparison with data Structure functions at HERA
Forward hadron production at RHIC

12. Structure functions at HERA
KKT
KKT
Structure functions at HERA
KKT

13. Longitudinal structure functions at HERA
KKT

14. Structure functions at HERA
DHJ

15. Structure functions at HERA
DHJ

16. Forward hadron production at RHIC
BRAHMS

17. Conclusions I
KKT and DHJ were fitted to RHIC data but do not fit HERA data
The slightly modified versions KKTm and GKMN fit HERA data
M.S. Kugeratski, V.P. Gonçalves, F.S. N., Eur. Phys. J. C (2005)
M.S. Kugeratski, V.P. Gonçalves, M.V. Machado, F.S. N., Phys. Lett. B (2006)
Future:
Better numerical solutions of the evolution equations
BK at NLO
Albacete, PRL (2007)
Impact parameter
Global data analysis
Better parametrizations (with more physical content)

18. Electron-Ion Collisions

19. Nuclear diffractive DIS
Nuclear inclusive DIS
We assume IIM and rescale
Nuclear diffractive DIS
Golec-Biernat,
Wüsthoff
(1999)
We assume that

20. with IIM
R = full / linear
Saturation reduces
by a factor 2 (low x and large A)

21. Ratio of Cross Sections
It works for e-p !
grows with W
falls with x
falls with
grows with A

22. A Q2

23. Nuclear diffractive structure functions
Wüsthoff (1997); Golec-Biernat, Wüsthoff (1999)
Forshaw,Sandapen,Shaw (2004)

24. Nuclear diffractive structure functions

25. A=2
A=197

26. A=2
A=197

29. Conclusions II
In the saturation region F2 is reduced with respect to the linear
case by 20 % in ep and 50 % in eA (in the IIM model !)
The ratio
grows weakly with W and falls weakly with x
falls with Q2 and grows with A up to 0.37
becomes flat in
with increasing A
changed by saturation effects
is less important for large A
is very flat in
this is due to saturation !
M.S. Kugeratski, V.P. Gonçalves, F.S. N., Eur. Phys. J. C (2006)
M.S. Kugeratski, V.P. Gonçalves, F.S. N., Eur. Phys. J. C (2006)

30. Recent Improvements Dipole cross section impact parameter dependent
More realistic atomic number dependence
No “nuclear diffractive slope”
Comparison with existing data on nuclear DIS
Comparison with collinear factorization models: DS, EPS-08
Cazaroto, Carvalho, Gonçalves, Navarra, arXiv [hep-ph]

31. A and b dependence
N. Armesto (2002)

32. bCGC Armesto – GBW H. Kowalski, L. Motika, G. Watt, hep-ph/0606.272
G. Watt, arXiv
Armesto – GBW
N. Armesto (2002)

33. Results
Data: E665, ZPC (1995)

35. Not very sensitive to saturation effects

36. Diffraction Before: Now: GBW (1999)
Kowalski, Lappi, Venugopalan (2008)
Kowalski, Lappi, Marquet, Venugopalan (2008)

37. Now
Now
Before
Before

38. Conclusion Future not very promising signals of saturation The ratio
still grows with A up to (not 0.30 – 0.40)
Future
Improve the dipole cross sections
Diffractive structure function
Kowalski, Lappi, Marquet, Venugopalan (2008)

39. is large !
CGC visible when
LHC : x may be small
eRHIC : A may be large

40. Diffractive overlap function:
Saturation suppresses larger dipoles (more for larger nuclei)

45. Eskola,Kohlinen,Salgado, EPJC (1999)

46. Golec-Biernat and Wüsthoff, PRD(1999)

49. Color dipole approach

51. Numerical solution of the BK:
Boer, Utermann, Wessels hep-ph/
Numerical solution of the BK:
DHJ +
BK1
BK2
DHJ +
BRAHMS