Classical Initial Conditions for Ultrarelativistic Heavy Ion Collisions

TL;DR

The paper derives an analytic, gauge-consistent description of the gluon distribution immediately after ultrarelativistic heavy ion collisions within the McLerran-Venugopalan (MV) quasi-classical framework, incorporating all multiple rescatterings through classical Yang-Mills dynamics. It demonstrates that the produced gluon spectrum is finite in the soft momentum limit due to saturation effects, with a typical transverse momentum of order the saturation scale $Q_s$. The total produced gluon number is proportional to the initial gluon content of the nuclei with a coefficient $c=2\ln 2$, aligning with prior numerical results and Mueller’s expectation. By analyzing both proton-nucleus and nucleus-nucleus collisions in covariant and light-cone gauges, the work provides a robust, analytic initial condition for the subsequent evolution toward possible thermalization, and connects $Q_s$ to RHIC data for phenomenological estimates. These results underpin a perturbative, yet saturated, description of early-time QCD matter in heavy ion collisions.

Abstract

We construct an analytical expression for the distribution of gluons in the state immediately following a heavy ion collision in the quasi-classical limit of QCD given by McLerran-Venugopalan model. The resulting gluon number distribution function includes the effects of all multiple rescatterings of gluons with the nucleons of both colliding nuclei. The typical transverse momentum k of the produced gluons is shown to be of the order of the saturation scale of the nuclei Qs, as predicted by Mueller. We analyze the properties of the obtained distribution and demonstrate that due to multiple rescatterings it remains finite (up to logarithms of k) in the soft transverse momentum limit of k << Qs unlike the usual perturbative initial conditions given by collinear factorization. We calculate the total number of produced gluons and show that it is proportional to the total number of gluons inside the nuclear wave function before the collision with the proportionality coefficient c = 2 ln2.

Figures (11)

• Figure 1: Non-Abelian Weizsäcker-Williams field of a large nucleus, as derived in mejklwme2.
• Figure 2: A collision of two ultrarelativistic nuclei at high energies.
• Figure 3: Diagrams contributing to the classical gluon field in covariant gauge at order $g^3$.
• Figure 4: $A_+ = 0$ light cone gauge diagrams: A contributes to the classical gluon field while B does not.
• Figure 5: Covariant gauge (or more accurately $A_- = 0$ gauge) gluon production diagrams for proton--nucleus collision as considered in meM. Multiple rescatterings in the nucleus determine the interactions in this gauge.