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…
QuickTime™ and aTIFF (LZW) decompressor
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
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:
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,
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)