Static quark-antiquark free energy and the running coupling at finite temperature

O. Kaczmarek, F. Karsch, F. Zantow, and P. Petreczky

Phys. Rev. D 70, 074505 – Published 12 October 2004; Erratum Phys. Rev. D 72, 059903 (2005)

Abstract

We analyze the free energy of a static quark-antiquark pair in quenched QCD at short and large distances. From this we deduce running couplings, $g^{2}$ ( $r$ , $T$ ), and determine the length scale that separates at high temperature the short distance perturbative regime from the large distance nonperturbative regime in the QCD plasma phase. Ambiguities in the definition of a coupling beyond the perturbative regime are discussed in their relation to phenomenological considerations on heavy quark bound states in the quark gluon plasma. Our analysis suggests that it is more appropriate to characterize the nonperturbative properties of the QCD plasma phase close to $T_{c}$ in terms remnants of the confinement part of the QCD force rather than a strong Coulombic force.

Received 30 June 2004
Publisher error corrected 8 September 2005

DOI:https://doi.org/10.1103/PhysRevD.70.074505

Corrections

8 September 2005

Erratum

Publisher’s Note: Static quark-antiquark free energy and the running coupling at finite temperature [Phys. Rev. DPRVDAQ0556-2821 70, 074505 (2004)]

O. Kaczmarek, F. Karsch, F. Zantow, and P. Petreczky

Phys. Rev. D 72, 059903 (2005)

Authors & Affiliations

O. Kaczmarek, F. Karsch, and F. Zantow

Fakultät für Physik, Universität Bielefeld, P. O. Box 100131, D-33501 Bielefeld, Germany

P. Petreczky^*

Physics Department, Brookhaven National Laboratory, Upton, New York 11973 USA

^*Goldhaber Fellow

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Vol. 70, Iss. 7 — 1 October 2004

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Images

Figure 1
Heavy quark free energies in the singlet channel calculated for several values of the temperature above $T_{c}$ (a) and the short distance part of the singlet free energy at $T / T_{c} = 1.5$ (b). The dashed line shows $V_{s t r i n g} (r)$ defined in Eq. (13) and the solid line is the perturbative result of Ref. 10 for $V_{q \bar{q}} (r)$ . This has been matched smoothly to $V_{s t r i n g} (r)$ at $r ≃ 0.1 f m$ . Physical units have been obtained by using $\sqrt{σ} = 420 M e V$ .Reuse & Permissions
Figure 2
The running coupling in the $q q$ -scheme determined on lattices of size $32^{3} \times N_{τ}$ with $N_{τ} = 4$ (open symbols) and 8 (filled symbols) from derivatives the short distance part of the singlet free energy ( $T = 0$ : from the force) at different temperatures. The relation of different symbols to the values of the temperature are as in Fig. 1a. The various lines are explained in the text.Reuse & Permissions
Figure 3
The running coupling in the $V$ -scheme determined on lattices of size $32^{3} \times N_{τ}$ with $N_{τ} = 4$ (open symbols) and 8 (filled symbols) from the short distance part of the singlet free energy ( $T = 0$ : from the potential) at different temperatures. The relation of different symbols to the values of the temperature are as in Fig. 1a. The dashed (solid) lines for $α_{q q} (α_{V})$ represent the zero temperature results of Ref. 10 which are continued to shorter distances using our new results.Reuse & Permissions
Figure 4
The location of the maximum in $α_{q q} (r, T)$ at fixed temperature versus temperature in units of the deconfinement temperature. Open (filled) symbols correspond to calculations on lattices with temporal extent $N_{τ} = 4$ and 8, respectively. The solid line corresponds to $r_{s c r e e n} = 0.48 f m \cdot T_{c} / T$ .Reuse & Permissions
Figure 5
The singlet free energy versus $r T$ for several temperatures above $T_{c}$ obtained from calculations on lattices with temporal extent $N_{τ} = 4$ (open symbols) and $N_{τ} = 8$ (filled symbols).Reuse & Permissions
Figure 6
The temperature dependent running coupling determined from the large distance behavior of the singlet free energy on lattices with temporal extent $N_{τ} = 4$ (open symbols) and $N_{τ} = 8$ (filled symbols). The upper figure shows $α (T) \equiv g^{2} (T) / 4 π$ (dots) and the value $α_{q q} (r_{s c r e e n}, T)$ (squares) determined from the short distance behavior of the singlet free energy (see Fig. 3). The figure in the middle shows $\tilde{α} (T) \equiv {\tilde{g}}^{2} (T) / 4 π$ and characterizes the temperature dependence of the screening mass. The lower figure gives the ratio of both fit parameters. The solid lines with the dotted error band are discussed in the text.Reuse & Permissions

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