Strong gluon fields in nucleons & nuclei

1. Strong gluon fields in nucleons & nuclei Raju Venugopalan Brookhaven National Laboratory EIC meeting, Hampton Univ., May 19th-23rd, 2008

2. Talk Outline • The CGC and the nuclear “oomph” • From CGC to Glasma: high energy factorization • Some remarkable features of the Glasma

3. The Bjorken limit • Operator product expansion (OPE), Factorization theorems, machinery of precision physics in QCD

4. The Regge-Gribov limit • Physics of strong fields in QCD, Multi-particle production, Novel universal properties of QCD ?

5. Small x -gluon recombination non-linear evolution (BK/JIMWLK) Mechanism of gluon saturation Gribov,Levin,Ryskin Mueller,Qiu Large x - bremsstrahlung linear evolution (DGLAP/BFKL) p, A Saturation scale QS(x) - dynamical scale below which non-linear (“higher twist”) QCD dynamics is dominant

6. 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 • Renormalization group equations (JIMWLK/BK) • describe how the QCD dynamics changes with energy • A universal saturation scale QS arises naturally in the theory

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

8. Nuclear “Oomph”:Saturation scale grows with A High energy compact (1/Q < Rp) probes interact coherently across nuclear size 2 RA - experience large field strengths Extension of dipole models to nuclei Kowalski, Teaney, PRD68 (2003) Kowalski, Lappi, RV, PRL100 (2008) Resulting A dependence of QS2 ~ A1/3

9. Nuclear “oomph” (II): Diffractive DIS Kowalski,Lappi,Marquet,RV (2008) Very large fraction of e+A events (~ 25%) are diffractive* - nucleus either intact (“non breakup”) or breaks up into nucleons separated from the hadronic final state by a large rapidity gap * Results broadly agree on large magnitude of effect with other models albeit details may vary

10. Hadron wave-fns: universal features for glue S(QS2) << 1 T. Ullrich • Note: Strong constraints from RHIC A+A: Nch ~ QS2 and • ET ~ QS3 - “day 1” A+A at LHC will provide important confirmation • Careful analysis gives values consistent with above plot to ~15% T. Lappi, arXiv:07113039 [hep-ph]

11. Road map of the strong interactions • Can we learn something from the AdS-CFT (QCD) about possible universality between weak coupling strong fields & • QCD at strong coupling ? • Remarkably, many results expressed in terms of QS appear universal (see following talk by Sabio Vera)

12. Glasma Ludlam, McLerran, Physics Today (2003) Glasma (\Glahs-maa\): Noun:non-equilibrium matter between Color Glass Condensate (CGC) & Quark Gluon Plasma (QGP)

13. Little Bang Big Bang Hot Era WMAP data (3x105 years) QGP Inflation CGC/ Glasma Plot by T. Hatsuda

14. How is Glasma formed in a Little Bang ? • Problem: Compute particle production in field theories with strong time dependent sources

15. O(S) but may grow as NLO and QCD Factorization Gelis,Lappi,RV arXiv:0804.2630 [hep-ph] What small fluctuations go into wave fn. and what go into particle production ? Small x (JIMWLK) evolution of nucleus A -- sum (SY)n & (S 1)n terms Small x (JIMWLK) evolution of nucleus B ---sum (SY)n & (S 2)n terms

16. “Holy Grail” spectrum of small fluctuations. First computations and numerical simulations underway Gelis,Fukushima,McLerran Gelis,Lappi,RV From Glasma to Plasma • NLO factorization formula: • With spectrum, can compute T - and match to hydro/kinetic theory

17. Relating the Glasma to the wavefunction • The Ridge in two particle correlations • P and CP violation in heavy ion collisions • Elliptic flow & flow fluctuations

18. Two particle correlations in the Glasma Can it explain the near side ridge ?

19. Ridgeology* * Rudy Hwa Near side peak+ ridge (from talk by J. Putschke,STAR collaboration) Jet spectra Ridge spectra STAR preliminary STAR preliminary inclusive inclusive pt,assoc,cut pt,assoc,cut

20. 83-94% 55-65% 46-55% 0-5% STAR Preliminary STAR Preliminary STAR Preliminary STAR Preliminary ηΔ width Large change within ~10% centrality Smaller change from transition to most central Little shape change from peripheral to 55% centrality Evolution of mini-jet with centrality Same-side peak Binary scaling reference followed until sharp transition at ρ ~ 2.5 ~30% of the hadrons in central Au+Au participate in the same-side correlation M. Daugherty Session IX, QM2008

21. Au+Au 200 GeV, 0 - 30% PHOBOS preliminary Update: the ridge comes into its own PHOBOS: the ridge extends to very high rapidity PHENIX: sees a ridge

22. For particles to have been emitted from the same Event Horizon, causality dictates that If Yis as large as (especially) suggested by PHOBOS, correlations were formed very early - in the Glasma…

23. An example of a small fluctuation spectrum…

24. Z Z T T After a HI collision, classical fields form a Glasma flux tube with longitudinal chromo E & B fields Typical size of flux tube in transverse direction is 1 / QS < 1/QCD

25. 2 particle correlations in the Glasma (I) Dumitru, Gelis ,McLerran, RV, arXiv:0804.3858[hep-ph]] = + Leading (classical) contribution Note:Interestingly, computing leading logs to all orders, both diagrams can be expressed as the first diagram with sources evolved a la JIMWLK Hamiltonian Gelis, Lappi, RV (2008)

26. 2 particle spectrum (II) Simple “Geometrical” result: •  4 (more accurate result requires numerical soln. of YM eqns. - in progress. with K_N  0.3

27. R 2 particle spectrum (III) Not the whole story… particle emission from the Glasma tubes is isotropic in the azimuth Particles correlated by transverse flow (or at high pT by opacity effects) - are highly localized transversely, experience same transverse boost Voloshin, Shuryak Gavin, Pruneau, Voloshin

28. Ridge from flowing Glasma tubes KN ~ 0.1 (energy & centrality dep. of flow courtesy of Paul Sorensen) Gets many features right: i) Same flavor composition as bulk matter ii) Large multiplicity (1/3rd) in the Ridge relative to the bulk iii) Ridge independent of trigger pT-geometrical effect iv) Signal for like and unlike sign pairs the same at large 

29. Gluons Quarks P and CP violation in the Glasma Kharzeev; Kharzeev, McLerran, Warringa Lagrangean invariant under scale (dilatations) and chiral transformations for massless quarks ( Left Right ) Both symmetries broken by quantum effects - anomalies

30. QCD vacuum and sphaleron transitions Vacua labeled by different Chern-Simons #  EB “Over the barrier” sphaleron transitions can change the topological charge in an event => the index theorem tells us that this induces a induce a net chirality. (Note: Sphaleron transitions at the Electroweak Transition are a candidate for generating matter-anti-matter asymmetry in the universe)

31. Real time Chern-Simons diffusion At finite T In the Glasma Arnold, Moore, PRD73 (2006) Kharzeev, Krasnitz, RV, Phys. Lett. B545 (2002)

32. The Chiral Magnetic effect in the Glasma Kharzeev,McLerran,Warringa, 0711.0950 Heavy Ion Collisions at RHIC: Largest Terrestrial magnetic fields!

33. Magnetic fields + Sphaleron transitions = Chiral Magnetism Red arrow - momentum; blue arrow - spin; In the absence of topological charge no asymmetry between left and right (fig.1) ;the fluctuation of topological charge (fig.2) in the presence of magnetic field induces electric current (fig.3)

34. m + - k Measuring charge asymmetry S.Voloshin, hep-ph/0406311 Preliminary STAR result S. Voloshin et al [STAR Coll.], QM’08 I. Selyuzhenkov et al., STAR Coll., nucl-ex/0510069

35. Summary • Non-linear dynamics of QCD strongly enhanced in nuclei • Factorization theorems linking these strong fields in the wavefunction to early time dynamics (Glasma) are becoming available • These strong fields have important consequences and may explain recent remarkable data from RHIC

36. Extra Slides

37. 2 particle spectrum… Centrality dependence of Vr from blast wave fits Centrality dependence of QS a la Kharzeev-Nardi