The heavy quark potential from Wilson's exact renormalization group

Ulrich Ellwanger; Manfred Hirsch; Axel Weber

doi:doi:10.1007/s100520050105

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2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 1, 563-578

The heavy quark potential
from Wilson's exact renormalization group

Ulrich Ellwanger¹ - Manfred Hirsch^2,3 - Axel Weber^2,3

¹ Laboratoire de Physique Théorique et Hautes Energies Université de Paris XI, bâtiment 211, F-91405 Orsay Cedex, France (e-mail: ellwange@qcd.th.u-psud.fr)
² Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
³ Laboratoire de Physique Théorique et Hautes Energies Université de Paris XI, bâtiment 211, F-91405 Orsay Cedex, France

Received: 28 February 1997 / Revised version: 12 May 1997

Abstract
We perform a calculation of the full momentum dependence of the gluon and ghost propagators in pure SU(3) Yang-Mills theory by integrating Wilson's exact renormalization group equations with respect to an infrared cutoff k. The heavy quark potential in the quenched approximation can be expressed in terms of these propagators. Our results strongly indicate a 1/p⁴-behaviour of the heavy quark potential for $p^2 \to 0$ . We show in general, that effective actions which satisfy Schwinger-Dyson equations, correspond to (quasi-) fixed points of Wilson's exact renormalization group equations.