Production of gluons in the classical field model for heavy ion collisions

TL;DR

The paper investigates gluon production in ultrarelativistic heavy-ion collisions using a 2+1D classical Yang-Mills framework with MV-model initial conditions, computed on a lattice. It defines and analyzes gluon energy and multiplicity via equal-time field correlators, revealing a strong-field saturation regime where infrared sensitivities diminish, and a weak-field regime where IR effects dominate. The authors relate their results to RHIC phenomenology, highlighting potential tensions between initial-energy estimates and final-state observations, and they explore extensions to finite nuclei and saturation-inspired initial conditions. They conclude that while the classical-field approach captures essential initial features, further work—such as JIMWLK evolution and 3+1D studies—is needed to draw robust phenomenological conclusions for RHIC and LHC.

Abstract

The initial stages of relativistic heavy ion collisions are studied numerically in the framework of a 2+1 dimensional classical Yang-Mills theory. We calculate the energy and number densities and momentum spectra of the produced gluons. The model is also applied to non central collisions. The numerical results are discussed in the light of RHIC measurements of energy and multiplicity and other theoretical calculations. Some problems of the present approach are pointed out.

Figures (11)

• Figure 1: The functions (\ref{['eq:omega']}). The circles are $\omega(\tilde{k})$ determined from the transverse fields $E^i$ and $A_i$, the solid line is $\omega(\tilde{k})$ determined from $\pi$ and $\phi$. The maximum value of $\tilde{k} a$ is $2\sqrt{2}$.
• Figure 2: The functions $f_E$ and $f_N$ as defined by Eqs. (\ref{['eq:deffe']}), (\ref{['eq:deffn']}) vs. $\sqrt{g^4 \mu^2 \pi R_A^2}$. Computed on a $256^2$-lattice.
• Figure 3: The functions $f_E$ and $f_N$ defined by Eqs. (\ref{['eq:deffe']}), (\ref{['eq:deffn']}) for constant $\sqrt{g^4 \mu^2 \pi R_A^2}$ and with different lattice spacings. The horizontal axis is $g^2\mu a$, so the continuum ($a \to 0$) limit is obtained by extrapolating each set of points to the $g^2 \mu a =0$-axis on the left.
• Figure 4: Total energy per unit rapidity as a function of time for $\mu = 0.5 \ \textrm{GeV}$. The three curves give an error estimate from 5 trajectories on a $512^2$-lattice.
• Figure 5: Energy in different field components from the same simulations as in Fig. \ref{['fig:toten']}.