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

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

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…

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

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/

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Violations of boost invariance => exploding sphalerons! ( Kharzeev, Krasnitz, RV ; Shuryak ; Arnold, Moore) (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)

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 D computations of Lappi Summary and Outlook

 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)

EXTRA BACKUP SLIDES

Dispersion relation: Just as for a Debye screening mass

Compute components of the Energy-Momentum Tensor

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