Testing perturbation theory on the nf=0 static quark potential

Abstract

The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling ${\alpha }_{qq}(\mu =1/r)=(C_f{)}^{-1}{r}^{2}F(r)$. Since the Lambda-parameter of the $\text{nf}=0$ theory is known from previous work, the perturbative prediction contains no free parameter. It is confronted with recent non-perturbative results. For $\alpha <0.3$ where the truncation error of the perturbative expression is naively estimated to be moderate, it is really quite accurate and large ``non-perturbative terms'' are excluded.

Comments: Added comment on known alpha^4 log(alpha) term (page 8), References and acknowledgement