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

Understand

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.