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Toward parton equilibration with improved parton interaction matrix elements

This study explores parton equilibration with improved matrix elements and pressure anisotropy dynamics. The exact matrix elements for gg ↔ ggg processes, regulated by μ2, provide insights into isotropization and equilibration mechanisms in high-energy systems. The comparison between the exact and Gunion-Bertsch matrix elements reveals significant differences, impacting the understanding of thermalization processes. The significance of elastic collisions, specific shear viscosity effects, and formation time regularization is discussed, highlighting their roles in equilibration and thermalization phenomena.

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Toward parton equilibration with improved parton interaction matrix elements

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  1. Toward parton equilibration with improved parton interaction matrix elements Bin Zhang Arkansas State University The 11th International Conference on Nucleus-Nucleus Collisions San Antonio, Texas, May 27 – June 1, 2012 • Introduction • Pressure anisotropy and energy density • gg <-> ggg with the exact matrix element • Summary and speculations Work supported by the U.S. National Science Foundation under Grant No. PHY-0970104

  2. Introduction: radiative transport • The reaction rates

  3. Longitudinal to transverse pressure ratio Lines (points): exponential (condensate) initial conditions • competition between expansion and equilibration • common asymptotic evolution • more isotropization with inelastic processes • not sensitive to initial momentum distribution with inelastic processes

  4. Exact matrix element for gg↔ggg Propagators regulated by μ2 When αs=0.47, μ2=10 fm-2, s=4 GeV2, σ22=0.312 fm2, and σ23=0.0523 fm2. σ23/σ22~0.168 (When αs=0.3, μ2=6.38 fm-2, s=4 GeV2, σ22=0.199 fm2, and σ23=0.0504 fm2.)

  5. Exact matrix element vs. Gunion-Bertsch singularity regulated by μ2 Gunion-Bertsch Gunion-Bertsch Gunion-Bertsch f exact f f exact exact φ φ

  6. Exact matrix element for gg↔ggg When αs=0.47, μ2=10 fm-2, I32=6.84 fm2. Estimate with isotropic matrix element gives I32=6.19 fm2. When αs=0.47, μ2=10 fm-2, I32=4.85 fm2. Estimate with isotropic matrix element gives I32=6.19 fm2. E=0.344 GeV 0.728 0.691 0.626 0.682 0.928

  7. Summary and speculations • Elastic collisions may be more important in thermalization than expected. • Specific shear viscosity may be larger than the quantum limit. • Formation time regularization can be approximated by screening mass regularization (replacement of the theta function by a Lorentzian). • Exact and Gunion-Bertsch can have big differences. • Bethe-Heitler limit may be important for bulk matter thermalization (formation time vs. mean free path). • Elastic collisions can also be important for heavy quark equilibration (meson dissociation).

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