Universal features of QCD dynamics in hadrons & nuclei at high energies

1. Universal features of QCD dynamics in hadrons & nuclei at high energies Raju Venugopalan Brookhaven National Laboratory TIFR, Mumbai, Feb. 12th-14th, 2008

2. Outline of Talk • CGC-brief overview • The CGC and DIS • Dipole models and RHIC data • Open questions/future work

3. The Color Glass Condensate McLerran, RV Iancu, Leonidov,McLerran In the saturation regime: Strongest fields in nature! • CGC: Classical effective theory of QCD describing • dynamical gluon fields + static color sources in non-linear regime • Novel renormalization group equations (JIMWLK/BK) • describe how the QCD dynamics changes with energy • A universal saturation scale QS arises naturally in the theory

4. Saturation scale grows with energy Typical gluon momenta are large Typical gluon kT in hadron/nuclear wave function Bulk of high energy cross-sections: obey dynamics of novel non-linear QCD regime Can be computed systematically in weak coupling

5. Saturation scale grows with A High energy compact (1/Q < Rp) probes interact coherently across nuclear size 2 RA - experience large field strengths Pocket formula: Enhancement of QS with A => non-linear QCD regime reached at significantly lower energy in A than in proton • Pocket formula holds up under detailed analysis Kowalski, Lappi, RV

6. New window on universal properties of the matter in nuclear wavefunctions Iancu, RV, hep-ph/0303204 A Can we quantify the various regimes ?

7. DIS Measure of resolution power Measure of inelasticity Measure of momentum fraction of struck quark quark+anti-quark mom. dists. gluon mom. dists

8. Hadronic tensor: In full generality, Quark Green function in background gauge field A of hadron In the CGC, Can compute W systematically in expansion about classical field (no OPE!) McLerran, RV (1999) RV, Acta Phys Polon (1999) Gelis, Peshier

9. q z * r 1-z q P Golec-Biernat-Wusthoff model: Parameters: Q0 = 1 GeV;  = 0.3; x0 = 3* 10-4 ; 0 = 23 mb Bj, Kogut, Soper Nikolaev,Zakharov A. H. Mueller

10. Evidence from HERA for geometrical scaling Golec-Biernat, Stasto,Kwiecinski x< 0.01 0 < Q2 < 450 GeV2   = Q2 / QS2 F2 D VM, DVCS V F2D Marquet, Schoeffel hep-ph/0606079 • Scaling seen for F2D and VM,DVCS for same QS as F2 Gelis et al., hep-ph/0610435 • Scaling confirmed by “Quality factor” analysis • Recent NLO BK analysis: Albacete, Kovchegov,hep-ph-0704.0612

11. At small x, need to solve JIMWLK/BK equation for energy evolution of Proper treatment of NLO contributions essential Triantafyllopolous;Balitsky; Albacete,Gardi,Kovchegov,Weigert,Rummukainen

12. Simple dipole models of small x dynamics Bartels,Golec-Biernat,Kowalski Kowalski,Teaney I) IPsat model: QS defined by Leading log generalization of Gaussian MV model (logs in x don’t dominate logs in Q2) II)b-CGC model: Iancu,Itakura,Munier Kowalski,Motyka,Watt Captures small x BK dynamics (S=0.63 is BK anomalous dimension)

13. Dipole Models-excellent fits to HERA data Kowalski et al., hep-ph/0606272 Also see Forshaw et al. hep-ph/0608161

14. Caveat: Saturation scale extracted from HERA data inconsistent with model assumptions ? Model assumes Typical sat. scale is rather low... QS2 << 1 GeV2

15. é e MX * P P P’ Diffractive DIS-smoking gun for saturation • 15% of all events at HERA are hard diffractive events & diff /tot independent of energy • Naturally explained in dipole saturation models -IPsat and bCGC give good fits (Marquet (2007))

16. Strong color fields more accessible in nuclei Nuclear profile more uniform- study centrality dependence

17. Evidence of geometrical scaling in nuclear DIS Freund et al., hep-ph/0210139 Geometrical scaling Nuclear shadowing: • Data scale as a function of  = Q2 / QS2

18. Extension of dipole models to nuclei Resulting A dependence of QS2 ~ A1/3 Kowalski,Teaney Kowalski,Lappi,RV

19. Diffractive DIS off nuclei Kowalski,Lappi,Marquet,RV • Very large fraction of e+A events (25-30%) are • diffractive • - nucleus either intact (“non breakup”) • or breaks up into nucleons separated from • the hadronic final state by a large rapidity gap

20. Estimates of the saturation scale from RHIC A

21. Proton-Nucleus collisions in the CGC

22. Obtain kT factorization formula: Kovchegov, Mueller M. Braun Kharzeev,Kovchegov,Tuchin Dumitru, McLerran; Blaizot, Gelis, RV Gelis, Mehtar-Tani Solve classical Yang-Mills equations: with two light cone sources Proton source Nuclear source

23. = Encodes both multiple scattering and shadowing effects Compute in CGC EFT Unintegrated distribution: with the path ordered exponentials in the adjoint representation

24. Dipole models in D+A: Kharzeev,Kovchegov,Tuchin Albacete,Armesto,Salgado,Kovner,Wiedemann Blaizot, Gelis, RV D-Au pt spectra compared to CGC prediction Hayashigaki, Dumitru, Jalilian-Marian Forward pp @ RHIC as well Boer, Dumitru, PRD 74, 074018 (2006) Review: Jalilian-Marian, Kovchegov, hep-ph/0505052

25. Natural explanation for limiting fragmentation + deviations in CGC Jalilian-Marian Extrapolation of BK-fit to RHIC LF data to LHC dn/dy|_{y=0} = 1500-2250 in A+A at LHC Gelis,Stasto, RV, hep-ph/0605087

26. … = Pair cross-section: Amputated time ordered quark propagator in classical background field

27. Blaizot, Gelis, RV Result not kt factorizable in general -can however be “factorized” into novel multi-parton distributions These multi-parton distributions can be computed: in closed form in Gaussian (MV) approximation - study multiple scattering effects b) Quantum evolution of distributions determined by JIMWLK or BK RG eqns. - study shadowing effects as well

28. Blaizot, Gelis, RV; Tuchin Interpretation: Wilson line correlators - the last appears in pair production only Simplify greatly in large N_c limit x-evolution can be computed with Balitsky-Kovchegov eqn.

29. Numerical solns. of Yang-Mills eqns. for A+A with dipole initial conditions(Lappi)

30. Quantifying the various regimes T.Ullrich-based on Kowalski, Lappi, RV ; PRL 100, 022303 (2008)

31. Open questions • Most estimates are leading order - is the picture robust at NLO/NLL ? Balitsky;Albacete,Gardi,Kovchegov,Rummukainen,Weigert • Lack of consistency between dipole models of DIS and hadronic collisions - need “global fits” of well motivated dipole models Lappi,Marquet,Soyez,RV

32. Backup slides

33. Universal gluodynamics & energy dependence of QS A.H. Mueller, hep-ph/0301109 QS2(b) A p A1/3 Small x QCD RG eqns. predict (fixed b) QS approaches universal behavior with increasing energy (Y) for all hadrons and nuclei -can the approach to this behavior be tested ?

34. In eA DIS, cleanly access cross-over region from weak field to novel strong field QCD dynamics ? (Talks by Surrow/Newman) Weak field regime Q2 >> QS2 Strong field regime Q2 << QS2 Qualitative change in final states: eg., 1/Q6 1/Q2 change in elastic vector meson production McDermott,Guzey,Frankfurt,Strikman; Review: Frankfurt, Strikman, Weiss