1. The Glasma: coherence, evolution, correlations

2. Outline of lectures  Lecture I: The parton model, pQCD and gluon saturation  Lecture II: The Color Glass Condensate. QFT in strong fields, factorization and the Glasma  Lecture III: Glasma graphs: imaging the QCD string at high energies.  The IP-Glasma model: hydrodynamics at RHIC & LHC. The unreasonable effectiveness of hydrodynamics in HIC: Instabilities, the spectrum of initial quantum fluctuations, decoherence, hydrodynamics, B-E condensation & thermalization

3. Traditional picture of heavy ion collisions *@$#! on *@$#! Well known physicist (circa early 1980s)

4. Standard model of HI Collisions Color Glass Condensates Initial Singularity Glasma sQGP - perfect fluid Hadron Gas t Glasma (\Glahs-maa\): Noun: non-equilibrium matter between Color Glass Condensate (CGC)& Quark Gluon Plasma (QGP)

5. Forming a Glasma in the little Bang  Problem: Compute particle production in QCD with strong time dependent sources Gelis, Lappi, RV; arXiv : 0804.2630, 0807.1306, 0810.4829  Solution: for early times (t  1/Q S ) -- n-gluon production computed in A+A to all orders in pert. theory to leading log accuracy

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

7. Multiparticle production for strong time dependent sources: - probability of vacuum-vacuum diagrams with r cuts “combinants” Gelis, RV ; NPA776 (2006 )

8. Observations: I)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. III) However, vacuum-vacuum contributions cancel for inclusive quantitites ( = Σ n p P n / Σ P n ) and one has systematic power counting for these… Power counting LO: 1/g 2, all orders in sources (gρ 1,2 ) n NLO: O(1), all orders in (gρ 1,2 ) n At NLO, large logs : g 2 ln(1/x 1,2 ) – can be resummed to all orders and factorized into evolution of wave functions

9. The Glasma at LO:Yang-Mills eqns. for two nuclei Glasma initial conditions from matching classical CGC wave-fns on light cone Kovner,McLerran,Weigert; Krasnitz, RV; Lappi Lappi,Srednyak,RV (2010) O(1/g 2 ) and all orders in (g  ) n Boost invariant flux tubes of size with || color E & B fields- generate Chern-Simons charge However, this results in very anisotropic (P T >> P L ) pressure for τ ~ 1/Q S

10. RG evolution for 2 nuclei Log divergent contributions crossing nucleus 1 or 2: Gelis,Lappi,RV (2008) and can be computed on the initial Cauchy surface linear operator on initial surface Contributions across both nuclei are finite-no log divergences => factorization

11. Factorization + temporal evolution in the Glasma Glasma factorization => universal “density matrices W”  “matrix element” NLO terms are as large as LO for  S ln(1/x): small x (leading logs) and strong field (gρ) resummation Gelis,Lappi,RV (2008) ε=20-40 GeV/fm 3 for τ=0.3 fm @ RHIC

12. Consequences of the Glasma flux tube picture Compute long range rapidity correlations (the ridge in p+p, p+A and A+A) Compute n-particle distributions, incorporate these along with geometrical fluctuations in event-by-event hydro models Isotropization and thermalization – next lecture

13. Long range rapidity correlations associated  trigger Di-hadron correlations Some notation: Δη-ΔΦ Rapidity: a measure of velocity (denoted by y or η) additive under Lorentz boost Δη – measure of angular separation along beam direction Large Δη means particles are flying off in opposite directions along beam axis

14. Long range rapidity correlations as chronometer Au+Au 200 GeV, 0 - 30% PHOBOS preliminary Long range rapidity correlations are sensitive to Glasma dynamics at early times Dumitru, Gelis, McLerran, RV, arXiv 0804.3858

15. Really long range correlations Au+Au 200 GeV, 0 - 30% PHOBOS preliminary Au+Au 200 GeV, 0 - 30% PHOBOS These structures reflect dynamics of strong gluon fields at times < 3  10 -24 seconds

16. The high-energy collisions of protons in the LHC may be uncovering “a new deep internal structure of the initial protons,” says Frank Wilczek of the Massachusetts Institute of Technology, winner of a Nobel Prize “At these higher energies [of the LHC], one is taking a snapshot of the proton with higher spatial and time resolution than ever before” Scientific American, February (2011)

17. Wei Li, MIT A ridge in high multiplicity pp collisions 17

18. Wei Li, MIT High Multiplicity pp collisions Very high particle density regime Is there anything peculiar happening there? High Multiplicity events are rare in nature 18

19. Wei Li, MIT Relativistic Heavy Ion Collisions 19 Quark Gluon PlasmaHadron GasDetectorPre-collision Initial state ? CMS pp 7TeV, N>110 PHOBOS CuCu 62.4GeV

20. Two particle correlations: CMS results “Discovery”  Ridge: Distinct long range correlation in η collimated around ΔΦ≈ 0 for two hadrons in the intermediate 1 < p T, q T < 3 GeV

21. High multiplicity events in p+p High multiplicity events likely correspond to high occupation numbers (1/α S ) in the proton wave functions for p T ≤ Q S I will emphasize this point further shortly

22. Associated Di-hadron Yield Glasma graphs BFKL Mini-jet Anatomy of long range di-hadron collimation

23. Long range di-hadron correlations Gelis,Lappi,RV (2009) Dusling,Gelis,Lappi,RV, arXiv:0911.2720 LRC of Δy~10 can be studied at the LHC

24. The saturated proton: two particle correlations Correlations are induced by color fluctuations that vary event to event - these are local transversely and have color screening radius ~ 1/Q S However, effective coupling of sources to fields with k T ≤ Q S = 1/g (“saturation”) These graphs (called “Glasma graphs”), which generate long range rapidity correlations, are highly suppressed for Q S << p T Power counting changes for high multiplicity events by α S 8 ! These graphs become competitive with usual pQCD graphs

25. Collimated yield ? From RG evolution of BK equation | p T -k T | ~ |q T -k T | ~ |k T | ~ Q S Q0Q0 Dominant contribution from This gives a collimation for ΔΦ ≈ 0 and π

26. Angular structure from (mini-) Jet radiation G BFKL Mini-jets: O (1) in high multiplicity events - give an angular collimation, albeit only at ΔΦ ≅ π LHC results also test the structure of bremsstrahlung radiation between jets p q

27. Dusling, RV: 1201.2658 1210.3890

28. Quantitative description of pp ridge Dusling,RV, 1201.2658 Try soft and hard fragmentation functions: D 1 = 3(1-x) 2 / x D 2 = 2(1-x) / x Only parameter fit to yield data is K =2.3 Subtracts any pedestal “phi-independent” correlation Dependence on transverse area cancels in ratio…

29. Quantitative description of pp ridge Dusling,RV, 1201.2658, PRL, in press CMS preliminary data Assoc. yield with centrality Assoc. yield with p T Trig

30. What about flow in p+p ? Au+Au 200 GeV, 0 - 30% PHOBOS preliminary Simple radial flow model result: Boosts, bottom to top, β=0,0.1,0.2,0.25,0.3 With increasing flow, the pedestal gets collimated Associated yield reflects the p T dependence of the Glasma pedestal Can accommodate only very small re-scattering / flow contribution

31. Exciting first results on proton lead collisions Key observation: Ridge much bigger than p+p for the same multiplicity ! CMS coll. arXiv:1210.5482, Phys. Lett. B

32. Exciting results on proton lead collisions

33. Systematics of p+Pb data explained Dusling, RV: 1211.3701 Q 0 2 (lead)=N Part Pb * Q 0 2 (proton) # of “wounded” nucleons in Lead nucleus Glasma signal is ~ N part * N track

34. CMS p+Pb data explained Dusling, RV: 1211.3701 Same parameters as in p+p - gives larger ridge when saturation scales are varied

35. Physics underlying the ridge

36. CMS p+Pb data explained Dusling, RV: 1211.3701 Smoking gun for gluon saturation and BFKL dynamics ?

37. ALICE data on the p+Pb ridge ALICE coll. arXiv:1212.2001 Different acceptance (|Δη| < 1.8) than CMS (2 < |η| < 4) and ATLAS (2 < |η| <5). ALICE subtracts away-side “jet” contribution at 40-60% centrality from most central events –this gives dipole shape of correlation Different analysis technique from CMS/ATLAS -- our fit here is with arbitrary normalization

38. Comparison to ATLAS p+Pb ridge ATLAS coll. arXiv: 1212.5198 ATLAS yields in asymmetric p T windows compared to Glasma + BFKL: K BFKL =1 and K glasma =4/3 Glasma graph contributions compared to ATLAS central – ATLAS peripheral

39. IP-Glasma + MUSIC model

40. Can flow in p+A explain the ridge ? In a thermal picture, for same transverse overlap area, ε pp ≈ ε pA when N track pp = N track pA For same energy densities, expect same flow dynamics but pA yield is ~ 6 times larger than pp In CGC picture, ε pA < ε pp for same N track until very large N part Flow explanation unlikely based on this simple argument + questions about applicability to small size systems for large transverse momenta

41. 2-particle Dumitru,Gelis,McLerran,RV Dusling,Fernandez-Fraile,RV n-particle correlations Glasma flux tube picture: two particle correlations proportional to ratio 1/Q S 2 / S T Only certain color combinations of “dimers” give leading contributions …iterating combinatorics for 2, 3, n…gives

42. 2-particle Gelis, Lappi,McLerran Multiplicity distribution: Leading combinatorics of dimers gives the negative binomial distribution k = 1 : Bose-Einstein k = ∞ : Poisson Yang-Mills computation shows picture is robust for 2 part. Corr. and gives ζ ~ 1/3 – 3/2 … O(1) Lappi,Srednyak,RV n-particle correlations

43. Convolution of NBDs describes LHC p+p data Dynamical quantum fluctuations in energy/# of gluons event-by-event Tribedy, RV 1112.2445