RHIC’s little bang: from Glasma to Plasma Raju Venugopalan BNL

1. RHIC’s little bang: from Glasma to Plasma Raju Venugopalan BNL CERN, Nov. 2nd, 2007

2. Outline of Talk • From nuclear wavefunction to Glasma • Bulk features ( LO in A+A ) • Detailed properties (NLO in A+A) • Intriguing possibilities / further work

3. Y Soft Hard P_t Traditional view of nuclear wavefunctions Loge (Energy) Bulk of hadronic cross-section A

4. Hadron wavefunctions: universal features Weak coupling CGC EFT = classical fields + strong stochastic sources RG eqns. (JIMWLK/BK) describe energy evolution Figure by T. Ullrich-based on Kowalski, Lappi, RV ; arXiv:0705.3047 Successful CGC phenomenology of HERA e+p; NMC e+A; RHIC d+A & A+A RV, arXiv:0707.1867

5. Glasma (\Glahs-maa\): Noun: non-equilibrium matter between CGC & QGP T.Lappi & L. McLerran; Kharzeev, Krasnitz, RV • What are the properties of the Glasma ? • How does it thermalize to the QGP ? • What are the initial conditions • for hydrodynamic flow ?

6. Big Bang Little Bang Present (13.7 x 109 years) RHIC data WMAP data (3x105 years) Hot Era QGP Inflation CGC/ Glasma Plot by Tetsuo Hatsuda

7. Big Bang vs Little Bang Decaying Inflaton with occupation # 1/g2 Decaying Glasma with occupation # 1/g2 Explosive amplification of low mom. small fluctuations (preheating) Explosive amplification of low mom. small fluct. (Weibel instabilities) Int. of fluctutations/inflaton -> thermalization Int. of fluctutations/inflaton -> thermalization ? Other common features: topological defects, turbulence ?

8. THE LITTLE BANG How can we compute multiparticle production ab initio in HI collisions ? Non-perturbative for questions of interest in this talk • perturbative VS non-perturbative, strong coupling VS weak coupling AdS/CFT ? Interesting set of issues … not discussed here

9. Shattering the CGC: Probability to produce n >> 1 particles in HI collisions: P_n obtained from cut vacuum graphs in field theories with strong time dependent sources.

10. In standard field theory, For theory with time dependent sources, Generating functional of Green’s functions with sources

11. Probability to produce n-particles:

12. General formula: Gelis, RV ; NPA776 (2006) • probability of vacuum-vacuum diagrams • with r cuts “combinants” (Gyulassy-Kauffman) Observations: • P_n is non-perturbative for any n and for coupling g << 1 - no simple power counting in g II) Even at tree level, P_n is not a Poisson dist.

13. Systematic power counting for the average multiplicity I) Leading order: Cutkosky’s rules => sum of all Feynman tree diagrams = solution of classical equations of motion with retarded b.c.

14. Before Collision: Nucleus is a sheet of plane polarized Chromo- E & B fields After Collision: E & B fields-longitudinal! -generate topological Chern-Simons charge Z Z T T Kharzeev, Krasnitz, RV Lappi, McLerran

15. Krasnitz,Nara,RV Lappi 2+1-D (boost inv.) num. simulations of Yang-Mills Eqns. 2D Bose-Einstein pert. tail Energy density ~ 16 - 40 GeV/fm^3 at 0.3 fm at RHIC

16. Evidence of non-linear saturation regime at RHIC ? Global multiplicity observables in AA described in CGC models: Au-Au mult. at eta=0 Kharzeev,Levin,Nardi Krasnitz, RV

17. M. Nardi W. Busza dN/deta extrapolations to LHC Central Pb+Pb collisions at LHC energy Gelis,Stasto,RV ALICE Tech. Proposal, M. Nardi, various models and fits Our estimated charged particle multiplicity ~ 1000-1500

18. But… Initial N ~ Final N => little entropy production Initial ET >> Final ET => lots of P dV work (Close to) ideal hydrodynamics…

19. Hydro+ CGC Initial Conditions Good description of multiplicity and pT distributions Hirano, Nara

20. Azimuthal Anisotropy-Elliptic flow Ollitrault

21. /s FROM VISCOUS HYDRODYNAMICS Romatschke2, arXiv:0706.1522 Song & Heinz, arXiv.0709.0742 Dusling & Teaney, arXiv:0710.5932 /s Preliminary calculations give very low -important to have independent theory (lattice) insight into eta/s H.B. Meyer, arXiv:0704.1801 Nakamura et al., hep-lat/0406009

22. Large eccentricity from the Glasma ? Hirano et al., nucl-th/0511046; Nara et al. nucl-th/0605012 Lappi, RV, nucl-th/0609021 Glasma Glauber Glauber • Large initial eccentricity • compensated by larger • viscosity

23. Temporal evolution of the Glasma Classical field Classical field / Particle Particle f < 1

24. The “bottom up” scenario Baier, Mueller, Schiff, Son Scale for scattering of produced gluons (for t > 1/Q_s) set by Multiple collisions: Thermalization for: Problem with bottom up: mD can become imaginary-Weibel instability! Arnold, Lenaghan, Moore

25. In the glasma, boost invariant E & B fields initially longitudinal Anisotropic mom. dists. very unstable-Weibel instability of E.M. plasmas “Rapidity dependent” fluctuations (quantum/NLO) explode - generating longitudinal pressure - may hold key to thermalization

26. Gelis+RV II) Multiplicity at next-to-leading order:O ( g^0 ) Gluon pair production contribution One loop corrections to classical field Remarkably, both terms can be computed with retarded b.c. - initial value problem 3+1-D real time simulations

27. Romatschke, RV : PRL, PRD (2006) 3+1-D simulations: Exponential growth of transverse E & B fields Rapid cascade of modes to ultraviolet - Kolmogorov turbulence leads to fast thermalization ? Arnold, Moore, Mueller, Shoshi, Wong, Bodeker, Rummukainen

28. Fluctuations become of order of the background field when Expect Large deflections of particle trajectories on this time scale Caveat: numerical simulations are for much smaller values: Need more careful systematics on large lattices.

29. New era of jet studies Further ramifications: Near side peak + ridge Away side Mach cone Interactions of particles + turbulent color fields-explain ridge and cone? Romatschke; Bass, Majumder, Muller Bass, Muller, Wang Turbulent thermalization may lead to anomalously low viscosity Asakawa, Bass, Muller

30. Jet spectra Ridge spectra Yield (pt,assoc > pt,assoc,cut) Yield (pt,assoc > pt,assoc,cut) STAR preliminary STAR preliminary inclusive inclusive pt,assoc,cut pt,assoc,cut Two particle correlations: variance at LO in Glasma Gelis, RV: NPA 779 (2006), 177 Sensitive to long range rapidity correlations ~ Unstable to rapid growth in Glasma - Isotropizes associated particle ?

31. Open Issues First estimate of spectrum of initial quantum fluctuations in little Bang Fukushima, Gelis, McLerran a) High energy factorization (analogous to collinear factorization) for full NLO estimate Gelis, Lappi, RV b) Kinetic theory of Glasma field+ decay particles “Turbulent thermalization” Gelis, Jeon, RV: arXiv: 0706.3775

32. Conclusions I.Ab initio calculations (to NLO) of the initial Glasma in HI collisions are becoming available II. Deep connections between QCD factorization and turbulent thermalization III. Quantifying how the Glasma thermalizes strongly constrains parameters of the (near) perfect fluid IV. Possible explanation of interesting structures from jet+medium interactions

33. EXTRA SLIDES

34. P. Kolb, U. Heinz nucl-th/0305084 P. Huovinen nucl-th/0305064 Flow of different particle species is large, sets in early (~ 1 fm) and is consistent with ideal relativistic hydrodynamics

35. Charm suppression and flow H. Zhang, sect 5c F. Laue, sect 5a