1. Multi-particle production in HI Collisions at high energies Raju Venugopalan Brookhaven National Laboratory Hard Probes, June 9th-16th, 2006

2. Talk based on:  Multiparticle production to NLO: F. Gelis & RV, hep-ph/0601209; hep-ph/0605246  Plasma Instabilities: P. Romatschke & RV, PRL 96: 062302 (2006); hep-ph/0605045  Work in preparation with S. Jeon, F. Gelis, T. Lappi & P. Romatschke Useful discussions with K. Kajantie, D. Kharzeev, L. McLerran, A. Mueller

3. Outline of Talk  How can one systematically compute multi-particle production at early times in HI collisions ? - perturbative VS non-perturbative, strong coupling VS weak coupling  I) Particle production to LO in the coupling (but all orders in strong color currents) - bulk features of multiplicity distribution  II) Particle production to NLO in the coupling (albeit, ditto, all orders in strong color currents) -plasma instabilities, energy loss, thermalization…

4. HEAVY ION COLLISIONS IN THE CGC FRAMEWORK Color charge distribution of light cone sources Field of produced gluons

5. All such diagrams of Order O(1/g) Nucleus-Nucleus Collisions…leading order graphs Inclusive multiplicity to leading order in requires 2 -> n Feynman graphs - completely non-perturbative problem even for small g ! F. Gelis, RV hep-ph/0601209

6. How do we systematically compute multi-particle production to leading order in g and beyond ? Problem can be formulated as a quantum field theory with strong time dependent external sources

7. Keeping track of the g’s : Order of a generic diagram is given by For vacuum diagrams with # of external legs n_E=0,  Arbitrary # n_J of sources all contribute at same order =>“Tree level” LO diagrams of order => NLO graphs of order

8. In standard field theory, For theory with time dependent sources, Vacuum-Vacuum diagrams:

9. From unitarity, a)No simple counting of g’s for P_n even for n=1 b)P_n not Poissonian c)However, simple power counting for average mult.

10. I) Leading order: O (1 / g^2) Obtained by solving classical equations - result known to all orders in (gj)^n but leading order in g! Krasnitz, RV; Krasnitz, Nara, RV; Lappi

11. from solving Yang-Mills Equations for two nuclei Kovner,McLerran,Weigert Boost invariance => 2+1 -D dynamics

12. z Before collision: Random Electric & Magnetic (non-Abelian) Weizacker-Williams fields in the plane of the fast moving nucleus

13. Longitudinal E and B fields created right after the collision - non-zero Chern-Simons charge generated Kharzeev,Krasnitz,RV; Lappi, McLerran After collision:

14. Gluon Multiplicity # dists. are infrared finite Krasnitz + RV, PRL 87, 192302 (2001)

15. Predictions for Au+Au multiplicity at RHIC Krasnitz, RV Eskola, QM 2001

16. Successful KLN phenomenology for multiplicities at RHIC Kharzeev,Levin, Nardi

17. Glasma = Melting CGC to QGP L. McLerran, T. Ludlam, Physics Today

18. II) Next-to-leading order: O ( g^0 ) + Very similar to Schwinger mechanism in QED for non-perturbative production of e^+ - e^- pairs Analogous computation for chromo-electric background Nayak (+ Van Nieuwenhuizen + Cooper) - important for thermalization ? Kharzeev, Tuchin

19. Remarkably, both terms can be computed by solving small fluctuations EOM with retarded boundary conditions- NLO calculations feasible in HI collisions! Gelis & RV Ramifications ?

20. In QCD, for example, 2 + Relation to energy loss ? Gyulassy-Wang, BDMPS-Z-SW, DGLV, AMY Would include both radiative and collisional contributions at early times

21. Pair production: solve Dirac equation in background field of two nuclei… Gelis,Kajantie,Lappi PRL 2005 Ratio of quarks to glue roughly consistent with a chemically equilibrated QGP

22. Relation to instabilities - violations of boost invariance ? Boost invariance is never realized: a) Nuclei always have a finite width at finite energies b) Small x quantum fluctuations cause violations of boost invariance that are of order unity over FIRST TRY: Perform 3+1-D numerical simulations of Yang-Mills equations for Glasma exploding into the vacuum- SIMILAR TO PART OF NLO COMPUTATION Romatsche + RV

23. Weibel instability even for very small violations of boost invariance (3+1 -D YM dynamics) Romatschke, RV PRL 96 (2006) 062302 For an expanding system,

24. ~ 2 * prediction from HTL kinetic theory Growth rate proportional to plasmon mass…

25. Instability saturates at late times-possible non-Abelian saturation of modes ?

26. Distribution of unstable modes also similar to kinetic theory Arnold, Lenaghan, Moore, Yaffe Romatschke, Strickland, Rebhan

27. Very rapid growth in max. frequency when modes of transverse magnetic field become large - “bending” effect ?

28. Growth in longitudinal pressure… Decrease in transverse pressure… Right trends observed but too little too late… also confirmed in HTL study - Romatschke-Rebhan Statuatory Note: Effects at same order not included in this exploratory study

29. Violations of boost invariance => exploding sphalerons! ( Kharzeev, Krasnitz, RV ; Shuryak ; Arnold, Moore) 150 1 1 (Very) preliminary results for very small & very large Violations of boost invariance (Lappi, RV) - possible relevance for metastable P and CP odd states (Kharzeev, Pisarski, Tytgat)

30. Outlined an algorithm exists to systematically compute particle production in AA collisions to NLO Pieces of this algorithm exist:  Pair production computation of Gelis, Lappi and Kajantie very similar  Likewise, the 3+1-D computation of Romatschke and RV + 3+1-D computations of Lappi Summary and Outlook

31.  Result should include  All LO and NLO small x evolution effects  NLO contributions to particle production  Very relevant for studies of energy loss, thermalization, topological charge, at early times  Relation to kinetic theory formulation at late times in progress (Gelis, Jeon, RV, in preparation)

32. EXTRA BACKUP SLIDES

33. Dispersion relation: Just as for a Debye screening mass

34. Compute components of the Energy-Momentum Tensor

35. Construct model of initial conditions with fluctuations: i) ii) Method: Generate random transverse configurations: Generate Gaussian random function in \eta This construction explicitly satisfies Gauss’ Law