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

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

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

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

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

6. 6 CGC: Classical effective theory of QCD describing dynamical gluon fields + static color sources in non- linear regime o Renormalization group equations (JIMWLK/BK) describe how the QCD dynamics changes with energy o A universal saturation scale Q S arises naturally in the theory The Color Glass Condensate In the saturation regime: Strongest fields in nature! McLerran, RV Iancu, Leonidov,McLerran

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

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

9. 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. 10 Hadron wave-fns: universal features T. Ullrich  S (Q S 2 ) << 1 for glue Note: Strong constraints from RHIC A+A: N ch ~ Q S 2 and E T ~ Q S 3 - “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. 11 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 Q S appear universal (see following talk by Sabio Vera)

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

13. 13 Big Bang CGC/ Glasma QGP Little Bang WMAP data (3x10 5 years) Inflation Hot Era Plot by T. Hatsuda

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

15. 15 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 (  S Y) n & (  S  1 ) n terms Small x (JIMWLK) evolution of nucleus B ---sum (  S Y) n & (  S  2 ) n terms O(  S ) but may grow as

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

17. 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. 18 Two particle correlations in the Glasma Can it explain the near side ridge ?

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

20. 20 Same-side peak Little shape change from peripheral to 55% centrality 83-94%55-65% η Δ width STAR Preliminary Large change within ~10% centrality 46-55% STAR Preliminary Smaller change from transition to most central 0-5% STAR Preliminary Evolution of mini-jet with centrality 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. 21 Update: the ridge comes into its own PHOBOS: the ridge extends to very high rapidity PHENIX: sees a ridge Au+Au 200 GeV, 0 - 30% PHOBOS preliminary

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

23. 23 An example of a small fluctuation spectrum…

24. 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 / Q S < 1/  QCD

25. 25 2 particle correlations in the Glasma (I) += 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) Dumitru, Gelis,McLerran, RV, arXiv:0804.3858[hep-ph]]

26. 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. 27 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 p T by opacity effects) - are highly localized transversely, experience same transverse boost R Voloshin, Shuryak Gavin, Pruneau, Voloshin

28. 28 Ridge from flowing Glasma tubes K N ~ 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 (1/3 rd ) in the Ridge relative to the bulk iii) Ridge independent of trigger p T -geometrical effect iv) Signal for like and unlike sign pairs the same at large 

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

30. 30 QCD vacuum and sphaleron transitions Vacua labeled by different Chern-Simons # “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. EBEB (Note: Sphaleron transitions at the Electroweak Transition are a candidate for generating matter-anti-matter asymmetry in the universe)

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

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

33. 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. 34 Measuring charge asymmetry + - m k S.Voloshin, hep-ph/0406311 S. Voloshin et al [STAR Coll.], QM’08 I. Selyuzhenkov et al., STAR Coll., nucl-ex/0510069 Preliminary STAR result

35. 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. 36 Extra Slides

37. 37 2 particle spectrum… Centrality dependence of V r from blast wave fits Centrality dependence of Q S a la Kharzeev-Nardi