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/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

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…

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are needed to see this picture.

HEAVY ION COLLISIONS IN THE CGC FRAMEWORK

Color charge distributionof 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, RVhep-ph/0601209

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=1b) 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, 192302 (2001)

Predictions for Au+Au multiplicity at RHIC

Krasnitz, RV

Eskola, QM 2001

Successful KLN phenomenology for multiplicities at RHICKharzeev,Levin,Nardi

Glasma = Melting CGC to QGPL. 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 energyloss ? 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) 062302

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, YaffeRomatschke, 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)

150

1 1150

(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 productionin 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

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

Dispersionrelation:

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 transverseconfigurations:

Generate Gaussian randomfunction in \eta

This construction explicitly satisfies Gauss’ Law