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Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD

Steven S. Gubser

TL;DR

This work assesses heavy-quark drag in a strongly coupled quark-gluon plasma by comparing drag predictions from ${\\cal N}=4$ SYM to QCD. It proposes two physically motivated matching strategies: normalize the 't Hooft coupling by equating the static quark–antiquark force from AdS/CFT with lattice QCD results, and compare the theories at fixed energy density rather than fixed temperature. Implementing these prescriptions yields an estimated charm relaxation time of about ${t_D \\\approx 2.1\\ \mathrm{fm}/\\mathrm{c}}$ at ${T_{QCD}=250\\ \mathrm{MeV}}$, with sizable theoretical uncertainties from non-conformality, finite-$N$ effects, and possible running of the coupling. The results illustrate how holographic drag calculations can be anchored to QCD phenomenology, while flagging the need for more realistic modeling of running coupling and stringy corrections to sharpen quantitative predictions.

Abstract

Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled N=4 super-Yang-Mills theory have appeared recently in hep-th/0605158, hep-ph/0605199, and hep-th/0605182. I compare the strength of this effect between N=4 gauge theory and QCD, using the static force between external quarks to normalize the 't Hooft coupling. Comparing N=4 and QCD at fixed energy density then leads to a relaxation time of roughly 2 fm/c for charm quarks moving through a quark-gluon plasma at T=250 MeV. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.

Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD

TL;DR

This work assesses heavy-quark drag in a strongly coupled quark-gluon plasma by comparing drag predictions from SYM to QCD. It proposes two physically motivated matching strategies: normalize the 't Hooft coupling by equating the static quark–antiquark force from AdS/CFT with lattice QCD results, and compare the theories at fixed energy density rather than fixed temperature. Implementing these prescriptions yields an estimated charm relaxation time of about at , with sizable theoretical uncertainties from non-conformality, finite- effects, and possible running of the coupling. The results illustrate how holographic drag calculations can be anchored to QCD phenomenology, while flagging the need for more realistic modeling of running coupling and stringy corrections to sharpen quantitative predictions.

Abstract

Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled N=4 super-Yang-Mills theory have appeared recently in hep-th/0605158, hep-ph/0605199, and hep-th/0605182. I compare the strength of this effect between N=4 gauge theory and QCD, using the static force between external quarks to normalize the 't Hooft coupling. Comparing N=4 and QCD at fixed energy density then leads to a relaxation time of roughly 2 fm/c for charm quarks moving through a quark-gluon plasma at T=250 MeV. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.

Paper Structure

This paper contains 4 sections, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Normalizing against the static Coulomb force
  3. Discussion
  4. Conclusions

Figures (1)

  • Figure 1: Comparisons of the static force between quark and anti-quark between ${\cal N}=4$ super-Yang-Mills and QCD for two different values of $T_{\rm SYM}$. The radius $r$, in ${\rm fm}$, is plotted on a log scale. The thick black curve shows $\alpha_{\rm SYM}$ as defined by (\ref{['aYMdef']}) for $g_{YM}^2 N = 5.5$. The thin upper curve is for $g_{YM}^2 N = 8$, and the thin lower curve is for $g_{YM}^2 N = 3.5$. The dots are from lattice simulations Kaczmarek:2005ui and are shown without error bars. The red dots (highest on average) are for $T/T_c = 1.23$; the green dots are for $T/T_c = 1.37$; and the blue dots (lowest on average) are for $T/T_c = 1.5$. The dashed grey curve shows the zero-temperature $\alpha_{q\bar{q}}(r)$ derived from (\ref{['CornellPotential']}).