1. From Glasma to Plasma in Heavy Ion Collisions Raju Venugopalan Brookhaven National Laboratory Topical Overview Talk, QM2008, Jaipur, Feb. 4th, 2008

2. 2 What is the Glasma ? Glasma (\Glahs-maa\): Noun: non-equilibrium matter between Color Glass Condensate (CGC) & Quark Gluon Plasma (QGP) Ludlam, McLerran, Physics Today (2003)

3. 3 Why is the Glasma relevant ? o Intrinsic interest: The Glasma is key to quantitative understanding of matter produced in HI collisions  How does bulk matter flow in the Glasma influence transport in the perfect fluid ?  How do jets interact with the Glasma ? o Initial conditions for the QGP: Glasma fields are among strongest Electric & Magnetic fields in nature. What are their properties ?

4. 4 Big Bang CGC/ Glasma QGP Little Bang WMAP data (3x10 5 years) Inflation Hot Era Plot by T. Hatsuda

5. 5 Big Bang vs. Little Bang Decaying Inflaton field with occupation # 1/g 2 Decaying Glasma field with occupation # 1/g 2 Explosive amplification of low mom. small fluctuations ( preheating ) Explosive amplification of low mom. small fluctuations ( Weibel instability ?) Interaction of fluct./inflaton - thermalization Interaction of fluct./Glasma - thermalization ? Other common features: topological defects, turbulence ?

6. 6 Before the Little Bang  Nuclear wavefunction at high energies  Renormalization Group (JIMWLK/BK) equations sum leading logs and high parton densities  Successful CGC phenomenology of HERA e+p; NMC e+A; RHIC d+A & A+A Review: RV, arXiv:0707.1867, DIS 2007 Bremsstrahlung Recombination + = Saturation:  SY SY

7. 7 Hadron wave-fns: universal features T. Ullrich (see talk) -based on Kowalski, Lappi, RV ; PRL 100, 022303 (2008) CGC Effective Theory = classic fields + strong stochastic sources >> 1  Upcoming test: current RHIC d+Au run - eg., forward di- jets (talk by C. Marquet)  Theory developments: running coupling in BK Balitsky;Albacete,Gardi,Kovchegov,Rummukainen,Weigert  S (Q S 2 ) << 1

8. 8 How is Glasma formed in a Little Bang ?  Problem: Compute particle production in field theories with strong time dependent sources

9. 9 Glasma dynamics perturbative vs non-perturbative Non-perturbative for questions of interest in this talk Interesting set of issues…not discussed here ( talks by Rajagopal and Iancu ) strong coupling vs weak coupling

10. 10 Systematic expansion for multiplicity moments ( =O(1/g 2 ) and all orders in (g  ) n ) In QCD, solve Yang-Mills Eqns. for two nuclei Glasma initial conditions from matching classical CGC wave-fns on light cone Kovner, McLerran, Weigert

11. 11 Numerical Simulations of classical Glasma fields LO Glasma fields are boost invariant Krasnitz, Nara, RV Lappi (see talk) for from extrapolating DIS data to RHIC energies

12. 12 LO Glasma Multiplicity Au-Au mult. at eta=0 Krasnitz, RVKharzeev, Levin, Nardi I) RHIC II) LHC Pb+Pb at  = 0 ≈ 950 - 1350 for N part = 350 ( See Armesto talk for other LHC predictions ) Gelis,Stasto,RV

13. 13 Flow in the Glasma (I) Large initial E T  Q S & N CGC  N had consistent with strong isentropic flow. Initial conditions for hydro Hirano, Nara CGC- type initial conditions leave room for larger dissipation (viscosity) in hydro stage ? Hirano et al., ; Drescher,Nara Lappi, RV v 2   (initial eccentricity)

14. 14 Flow in the Glasma (II) Partial thermalization and v 2 fluctuations: Bhalerao,Borghini, Blaizot,Ollitrault Knudsen # K = /R with 1/K =  c S dN/dy /area Drescher,Dumitru, Gombeaud,Ollitrault Partial thermalization fit suggests CGC gives lower v2 than Glauber K0K0

15. 15 Flow in the Glasma (III) o What’s the “pre-thermal” flow generated in the Glasma ? Glasma v2 Krasnitz, Nara, RV: PLB 554, 21 (2003) Glasma flow important for quantifying viscosity of sQGP Classical fieldClassical field / ParticleParticle f < 1

16. 16 The unstable Glasma (I) LO boost invariant E & B fields: - purely longitudinal for  = 0 + - generate small amounts of topological charge Kharzeev,Krasnitz,RV Lappi,McLerran p X,p Y pZpZ Such configurations may lead to very anisotropic mom. dists.  Weibel instability (see C. Greiner’s talk)

17. 17 The unstable Glasma (II) Small rapidity dependent quantum fluctuations of the LO Yang-Mills fields grow rapidly as E  and B  fields as large as E L and B L at time increasing seed size 2500 Romatschke, RV:PRL,PRD(2006)

18. 18 The unstable Glasma (III) Frequency of maximally unstable k  mode grows rapidly (Numerical studies by Frankfurt group - C. Greiner talk) Romatschke, RV Large angle deflections of colored particles in strong fields

19. 19 Small fluctuation spectrum ab initio in the Glasma: multiplicity moments to NLO I) Anomalously low viscosity II) Large energy loss of jets in strong fields ? Arnold, Moore; Mueller,Shoshi,Wong; Bödeker,Rummukainen Turbulent isotropization on short time scales ? (talks by Majumder and Müller) III) Explosive generation of P and CP odd transitions via sphalerons (see Warringa’s talk)

20. 20 Another example of a small fluctuation spectrum…

21. 21 Multiplicity to NLO (=O(1) in g and all orders in (g  ) n ) + Gluon pair productionOne loop contribution to classical field Initial value problem with retarded boundary conditions - can be solved on a lattice in real time Gelis, RV (a la Gelis,Kajantie,Lappi for Fermion pair production)

22. 22 NLO and QCD Factorization Gelis,Lappi,RV What small fluctuations go into wave fn. and what go into particle production ? Small x (JIMWLK) evolution of nucleus A -- sum (  S Y) n terms Small x (JIMWLK) evolution of nucleus B ---sum (  S Y) n terms O(  S ) but may grow as

23. 23 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

24. 24 Ridgeology* * Rudy Hwa (see talk) + parallel session Near side peak+ ridge (from talk by J. Putschke,STAR collaboration) Jet spectraRidge spectra p t,assoc,cut inclusive STAR preliminary

25. 25 Two particle correlations in the Glasma: variance at LO Gelis, RV: NPA 779 (2006), 177 Glasma sensitive to long range rapidity correlations: Fourier modes of classical field: O(1/g) Fourier modes of small fluctuation field: O(1) (talk by Gelis)

26. 26 Our take on the Ridge Gelis,Lappi,RV i) Long range rapidity correlations built in at early times because Glasma background field is boost invariant. (These are the “beam” jets.) ii) Rapidity correlations are preserved because matter density dilutes rapidly along the beam direction iii) Opacity effect in : Strong E & B fields destroy azimuthal correlations because survival probability of larger path lengths in radial direction is small ( collimation a la Voloshin/Shuryak ) iv) May explain why features of the ridge persist for both soft and semi-hard associated particles Need detailed models with realistic geometry effects

27. 27 Conclusions I. Ab initio (NLO) calculations of the initial Glasma in HI collisions are becoming available II. Quantifying how the Glasma thermalizes strongly constrains parameters of the (near) perfect fluid III. Deep connections between QCD factorization and turbulent thermalization IV. Possible explanation of interesting structures from jet+medium interactions