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

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,... ( 1994 -> ) Non-linear evolution equations: JIMWLK and BK “Laws of motion” in the x-Q plane

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/0506148 eRHIC: electron-ion collider at RHIC

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

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)

Testing dipole cross sections

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

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

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

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

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

Structure functions at HERA KKT KKT Structure functions at HERA KKT

Longitudinal structure functions at HERA KKT

Structure functions at HERA DHJ

Structure functions at HERA DHJ

Forward hadron production at RHIC BRAHMS

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. C44 577 (2005) M.S. Kugeratski, V.P. Gonçalves, M.V. Machado, F.S. N., Phys. Lett. B44 577 (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)

Electron-Ion Collisions

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

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

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

A Q2

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

Nuclear diffractive structure functions

A=2 A=197

A=2 A=197

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. C46 413 (2006) M.S. Kugeratski, V.P. Gonçalves, F.S. N., Eur. Phys. J. C46 465 (2006)

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 0805.1255 [hep-ph]

A and b dependence N. Armesto (2002)

bCGC Armesto – GBW H. Kowalski, L. Motika, G. Watt, hep-ph/0606.272 G. Watt, arXiv 0712.2670 Armesto – GBW N. Armesto (2002)

Results Data: E665, ZPC (1995)

Not very sensitive to saturation effects

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

Now Now Before Before

Conclusion Future not very promising signals of saturation The ratio still grows with A up to 0.25 - 0.30 (not 0.30 – 0.40) Future Improve the dipole cross sections Diffractive structure function Kowalski, Lappi, Marquet, Venugopalan (2008)

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

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

Eskola,Kohlinen,Salgado, EPJC (1999)

Golec-Biernat and Wüsthoff, PRD(1999)

Color dipole approach

Numerical solution of the BK: Boer, Utermann, Wessels hep-ph/0701219 Numerical solution of the BK: DHJ + BK1 BK2 DHJ + BRAHMS