The Renormalization Group Improvement of the QCD Static Potentials

Abstract

We resum the leading ultrasoft logs of the singlet and octet static QCD potentials within potential NRQCD. We then obtain the complete three-loop renormalization group improvement of the singlet QCD static potential. The discrepancies between the perturbative evaluation and the lattice results at short distances are slightly reduced.

Figures (1)

• Figure 1: We plot $\alpha_{V_s}$ versus $r$ (GeV) for a range of energies relevant to a comparison with lattice simulations and also to the study of the $\Upsilon(1S)$ system ($n_f=4$, $\Lambda_{\rm QCD}^{{\rm three\,loops}}=0.28$ GeV). The solid line corresponds to $\alpha^{{\rm (2\,loops)}}_{V_s}$, the dotted line to $\alpha_{V_s}^{{\rm(2\, loops)}}$ plus the single leading-log correction computed in Ref. short, the dot-dashed line to Eq. (\ref{['solals']}) and the dashed line to Eq. (\ref{['sol']}). We have fixed $\nu=\alpha_{\rm s}(r)/r$.