Yang-Mills Radiation in Ultra-relativistic Nuclear Collisions

TL;DR

The paper demonstrates that classical Yang-Mills radiation in the McLerran-Venugopalan framework reproduces the gluon bremsstrahlung distribution at leading order and smoothly connects to the conventional mini-jet distribution via a scale set by the initial parton density, $k_⊥^2 \sim χ$. It clarifies how the density parameter $χ$ accrues from both valence quarks and, dominantly, hard gluons, and it derives a practical expression tying YM radiation to standard pQCD quantities through DGLAP evolution and the GLR formalism. By evaluating $χ$ with GRV95 nucleon structure functions, the authors identify a perturbative-classical overlap that grows with energy, predicting that at LHC energies the classical source approaches $k_⊥\sim 1$ GeV, while RHIC energies remain largely nonperturbative in the beam-jet regime. The work provides a calculable bridge between nonperturbative YM dynamics and perturbative QCD in ultra-relativistic nuclear collisions, offering a framework to set initial conditions for quark-gluon plasma evolution. It also delineates the limits of applicability for the classical description and highlights the continuity between gluon bremsstrahlung and mini-jet production across a broad $k_⊥$ range.

Abstract

The classical Yang-Mills radiation computed in the McLerran-Venugopalan model is shown to be equivalent to the gluon bremsstrahlung distribution to lowest order in pQCD. The classical distribution is also shown to match smoothly onto the conventional pQCD mini-jet distribution at a scale characteristic of the initial parton transverse density of the system. The atomic number and energy dependence of that scale is computed from available structure function information. The limits of applicability of the classical Yang-Mills description of nuclear collisions at RHIC and LHC energies are discussed.

Figures (2)

• Figure 1: The GRV95 NLOgrv95 and BFKL-likeesk parametrizations of the gluon structure function, $xG(x,Q^2)$, for $Q^2=7,20$ GeV$^2$ are compared to preliminary ZEUS "data"zeus from HERA.
• Figure 2: The classical Yang-Mills scale, $Q_{YM}$, from (\ref{['mus']}) is shown for $A=200$ nuclei at collider energies $\surd s=0.2,6.5,100$ ATeV as a function of the reference scale, $Q$, used to evaluate the GRV95grv95 structure functions. Upper curves and lower curves for each energy correspond to taking the lower cutoff scale $x_0=x_\perp,2x_\perp$, respectively. The bottom two dashed curves give the valence quark contributions at $\surd s=0.2,100$ ATeV..