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

TL;DR

This paper investigates the static quark-antiquark potential in 2 and 3 dimensions at weak coupling using pNRQCD, providing high-precision perturbative results and comparisons with lattice data.

Contribution

It advances the calculation of the static potential in lower dimensions by including ultrasoft contributions and extending precision to high orders, with detailed renormalization procedures.

Findings

High-precision results for D=3 static potential up to N^4LL order.

Comparison of perturbative results with existing lattice data in three dimensions.

Discussion of perturbative calculation relevance in two dimensions with known exact results.

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.