1. Thermalization of the Quark-Gluon Plasma and Dynamical Formation of Bose Condensate NN2012 @ San Antonio MAY.31 th, 2012 Jinfeng Liao Indiana University, Physics Dept. & CEEM RIKEN BNL Research Center

2. Outline The Pre-Equilibrium Matter in Heavy Ion Collisions Important Features: Overpopulation & Uni-Scale A Kinetic Approach: Dynamical BEC & Separation of Scales Discussions References: Blaizot, Gelis, JL, McLerran, Venugopalan, Nucl. Phys. A873, 68 (2012); Blaizot, JL, McLerran, to appear; Chiu, Hemmick, Khachatryan, Leonidov, JL, McLerran, arXiv:1202.3679 [nucl-th].

3. “Little Bang” in the Laboratories Currently ongoing heavy ion collisions programs: RHIC (BNL), since 2000; LHC (CERN), since 2010. RHIC Event (from STAR) LHC Event (from ALICE) Beautiful “little bang” delivered ! T~10^12 K : The hottest matter today! Furthermore: strongly interacting !

4. Hot QCD Matter: Nearly Perfect Fluid Created matter’s explosion appears nearly ideal  strongly coupled Song, Bass, Heinz, Hirano, Shen, 2010 “Coupling-ometer” via transport properties e.g. shear viscosity 0 (infinitely viscous) Infinity (eta/s=1/4pi) (quantum limit?)

5. Hot QCD Matter: Strong Jet Quenching Jet-medium interaction is very strong  color-opaque matter! (high Pt yield (Raa), di-hadron correlation,…… ) Gyulassy, Wang; ……

6. Just After the “Little Bang”??? Heavy ion physics modeling (hydro, jet, …) implies a thermalized QGP already around 1 fm/c  fast thermalization, or strong re-scattering  Strongly interacting matter from the very beginning, but how? t = 0t = 1fm/c The energy/momentum scale, ~1 GeV, is still high here  A.F. says the coupling should be small/moderate ?! However, the (phase-space) density is so high that it coherently amplifies interaction  More is different !  crucial for early time evolution!

7. The Pre-Equilibrium Matter Pre-equilibrium matter (We focus on this!) Strong constraint from the initial condition: saturation Strong constraint from Hydro modeling and empirical data: fast “thermalization” ~ fm/c (to the extent of justifying hydro as effective description)

8. Before the collision: saturation Right after the collision Strong longitudinal expansion  anisotropy; Instabilities play an important role: Isotropization of energy-momentum tensor; rapid growth toward large occupation of soft modes; on the time scale ~ 1/Qs. The Pre-Pre-Equilibrium

9. A High Density Gluon System We consider a high density gluon system, starting at a time Some idealization concerning real heavy ion collisions: very large transversely; very high energy, i.e. large Qs and small coupling Energy scale Our starting point

10. Far from Equilibrium… The initial gluon system is far from equilibrium ! (Plotted here: f(p) ) Equilibrium Distribution (with the same Energy density) Initial gluon distribution Saturation Scale Qs ~ 1 GeV or larger, weakly coupled Thermalization: how the initial distribution evolves toward the equilibrium?

11. Three Important Features of the Initial System  Very high phase space density f ~ 1/alpha_s  Strong overpopulation  Only one scale that characterizes the distribution

12. Amplified Scattering The initial gluon system is highly occupied  change the power-counting e.g. for the collision integral in kinetic evolution Coherent amplification of scattering  Fast thermalization from overpopulation?!

13. Kinetic Evolution With 2  2 gluon scattering & small-angle approximation (Blaizot, JL, McLerran, to appear) For highly occupied initial condition: coupling constant disappears in the scales! In contrast, for thermalized BE distribution: (BE as fixed point)

14. OVERPOPULATION We consider a high density gluon system, starting at a time Overpopulation parameter: For our initial gluon system: In contrast, for equilibrated QGP: For the given amount of energy, there are initially way too many gluons !

15. OVERPOPULATION For the given amount of initial energy, our gluon system has too many gluons  Actually a “cold” dense system of gluons initially  can NOT equilibrate to a BE distribution by default (assuming elastic dominance) Does building up a chemical potential help? NO! The maximum gluons that can be accommodated by a Bose-Einstein distribution with \mu:

16. OVERPOPULATION Overpopulation  Bose-Einstein condensation for equilibrium state All the extra gluons get absorbed into zero momentum mode.

17. Bose-Einstein Condensation from Overpopulation Initial overpopulation + Energy & Number conservation  BEC !! Atomic BEC: for given number of atoms, reduce energy (cooling) toward overpopulation Dynamical formation of BEC at the early stage after heavy ion collisions: born to have too many gluons for the available energy, really fascinating ! (Caveat: assuming elastic process dominance on certain time scale; discuss later…)

18. Initially Uni-Scale There is ONLY ONE SCALE initially, i.e. the Qs This distribution is highly un-desired thermodynamically, i.e. by examining the entropy: Thermalization  maximization of entropy  More beneficial to distribute the gluons to wider region in p-space with f ~ 1

19. Separation of Scales There is ONLY ONE SCALE initially, We introduce two scales --- momentum cutoff scale & the saturated scale Toward thermalization, the two scales must be separated! By how much? Again, for a very weakly coupled equilibrated QGP Thermalization must be accompanied by specific separation of the two scales:

20. Recap of the Scenario A highly overpopulated gluon system evolving toward equilibrium: High occupancy  coherent amplification of scattering, ~O(1) effect despite coupling Strong overpopulation  dynamical BEC formation Initial uni-scale  separation of the two scales by coupling \alpha_s NEXT: analytic analysis of scaling solutions ; ultimately nuermically solving the equation

21. Kinetic Approach & Approximate Scaling Solution Blaizot, JL, McLerran, to appear.

22. The “Static Box” Problem A schematic scaling distribution characterized by the two evolving scales: Time evolution of the distribution, i.e. of the two scales  need two conditions Essential points here: Energy is conserved, but not gluon number  absorption into condensate Collision time scale (from transport equation) ~ \tau for scaling solutions

23. Thermalization in The “Static Box” Two conditions fixing the time evolution: The scaling solution: Upon thermalization: separation of scales; entropy production; eliminating over-pop.

24. Thermalization in The “Static Box” Two conditions fixing the time evolution: The scaling solution: Upon thermalization: separation of scales; entropy production; eliminating over-pop.

25. Condensate in The “Static Box” Condensate dominates the number density: While gluons dominate the energy density A robust, though transient ultimately, Bose-Einstein condensate can be dynamically formed and maintained during the thermalization!

26. Evidence of BEC from Scalar Field Theory Computation From: Epelbaum & Gelis

27. Evidence of BEC from Scalar Field Theory Computation From: Berges & Sexty

28. Effect of Longitudinal Expansion Assuming boost-invariance and studying mid-rapidity Further assuming certain fixed anisotropy

29. Effect of Longitudinal Expansion Two conditions fixing the time evolution: The scaling solution: Upon thermalization: separation of scales; entropy production; eliminating over-pop.

30. Condensate in Expanding Case NOTE: anisotropic expansion reduces overpopulation Condensate still can exist and dominate density: Energy carried by condensate is subleading: The more isotropic the expansion is, the stronger the condensation will be. Would be great to test in scalar/gauge field simulations aand kinetic computation.

31. Summary: a Scenario for the First-Fermi/c after Little Bang  The pre-equilibrium matter starts with high gluon density and one scale.  Elastic scattering is coherently enhanced despite the small coupling, therefore leading to strongly interacting matter even at early time and driving the thermalization.  Strong overpopulation enforces the system toward BEC.  Separation of scales must happen toward thermalization.  Expansion may proceed with asymmetry  anisotropic hydro?

32. Post Summary: EM Production in the Pre-Equilibrium Matter Chiu, Hemmick, Khachatryan, Leonidov, JL, McLerran, arXiv:1202.3679 [nucl-th]. There should be additional EM emission from the pre-equilibrium stage We derived fitting formula motivated by our thermalization scenario. PHOTONS DILEPTONS There are important contributions to EM production from the pre-equilibrium matter !