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Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update

Alex Krasnitz, Yasushi Nara, Raju Venugopalan

TL;DR

This note corrects an energy-normalization error in the authors' earlier classical gluodynamics results, bringing their energy predictions into agreement with Lappi's independent SU(3) computation. After the fix, the gluon number results remain consistent while the energy per unit rapidity is halved, aligning the two approaches and refining the gluon spectrum scaling with Λ_s. The corrected results place quantitative bounds on RHIC initial-state parameters, constraining initial energy density and transverse energy per particle, and clarifying the relationship between Λ_s and the saturation scale Q_s. Overall, the convergence of the two calculations strengthens the use of classical gluodynamics to inform early-time dynamics and limits the freedom of subsequent final-state evolution models.

Abstract

We comment on the relation of our previous work on the classical gluodynamics of high energy nuclear collisions to recent work by Lappi (hep-ph/0303076). While our results for the non-perturbative number liberation coefficient agree, those for the energy disagree by a factor of 2. This discrepancy can be traced to an overall normalization error in our non-perturbative formula for the energy. When corrected for, all previous results are in excellent agreement with those of Lappi. The implications of the results of these two independent computations for RHIC phenomenology are noted.

Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update

TL;DR

This note corrects an energy-normalization error in the authors' earlier classical gluodynamics results, bringing their energy predictions into agreement with Lappi's independent SU(3) computation. After the fix, the gluon number results remain consistent while the energy per unit rapidity is halved, aligning the two approaches and refining the gluon spectrum scaling with Λ_s. The corrected results place quantitative bounds on RHIC initial-state parameters, constraining initial energy density and transverse energy per particle, and clarifying the relationship between Λ_s and the saturation scale Q_s. Overall, the convergence of the two calculations strengthens the use of classical gluodynamics to inform early-time dynamics and limits the freedom of subsequent final-state evolution models.

Abstract

We comment on the relation of our previous work on the classical gluodynamics of high energy nuclear collisions to recent work by Lappi (hep-ph/0303076). While our results for the non-perturbative number liberation coefficient agree, those for the energy disagree by a factor of 2. This discrepancy can be traced to an overall normalization error in our non-perturbative formula for the energy. When corrected for, all previous results are in excellent agreement with those of Lappi. The implications of the results of these two independent computations for RHIC phenomenology are noted.

Paper Structure

This paper contains 4 sections, 31 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Normalization of Classical Effective Lagrangean
  3. Corrected Results
  4. Numerical Gluodynamics and RHIC Phenomenology

Figures (2)

  • Figure 1: Comparison of gluon transverse momentum distributions per unit area as a function of $k_{T}/\Lambda_s$. KNV I (circles): the number defined as in Eq. (\ref{['eq:gn1']}), with $k_T$ taken to mean the lattice wave number along one of the principal directions. KNV II (squares) and Lappi (solid line): the number defined as in Eq. (\ref{['eq:gn3']}), with an average over the entire Brillouin zone and with $k_T$ taken to mean the frequency $\omega({\vec{k}}_T)$.
  • Figure 2: Gluon occupation number defined in Eq .(\ref{['glue']}), computed using Eq. (\ref{['eq:gn1']}).