The QCD static potential in D<4 dimensions at weak coupling

Abstract

We study the static potential of a color singlet quark-antiquark pair with (fixed) distance r in D=3 and D=2 space-time dimensions at weak coupling (alpha r << 1 and g r << 1, respectively). Using the effective theory pNRQCD we determine the ultrasoft contributions, which cannot be computed in conventional perturbative QCD. We show in detail how the ultrasoft renormalization in pNRQCD is carried out. In three dimensions the precision of our results reaches O(alpha^3 r^2), i.e. NNLO in the multipole expansion, and NNLL in a alpha/DeltaV expansion, where DeltaV ~ alpha ln(alpha r). We even present results up to partly N^4LL order and compare them to existing lattice data. Finally we discuss the relevance of the perturbative calculation in two dimensions, where the exact result is known.

21 pages, 5 figures, 1 table; Corrected sign in the 3D gluon condensate contribution. Significantly improved agreement with lattice. Updated and extended discussion. Added plots

References in corpus (7)

• Three-loop static potential
• Static QCD potential at three-loop order
• The QCD static energy at NNNLL
• The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure
• Continuum limit of string formation in 3-d SU(2) LGT
• Plaquette expectation value and lattice free energy of three-dimensional SU(N) gauge theory
• Static forces in d=2+1 SU(N) gauge theories

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• Disentangling the gravity dual of Yang-Mills theory
• Relativistic corrections to the static energy in terms of Wilson loops at weak coupling
• Heavy quark and gluino potentials to two loops
• The QCD static potential in 2+1 dimensions at weak coupling