**31**: 187-196

https://doi.org/10.1140/epjc/s2003-01319-9

theoretical physics

## Comparing the QCD potential in perturbative QCD and lattice QCD at large distances

^{1}
Theory Group, KEK, 305-0801, Tsukuba, Ibaraki, Japan

^{2}
Department of Physics, Tohoku University, 980-8578, Sendai, Japan

We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine *E*
_{tot}(*r*) = 2 *m*
_{pole} + *V*
_{QCD}(*r*) by re-expressing it in the $\overline{\mathrm {MS}}$ mass $\overline{m} \equiv m^{\raisebox{-1pt}{$\scriptstyle\overline{\mathrm{MS}}$}}(m^{\raisebox{-1pt}{$\scriptstyle\overline{\mathrm{MS}}$}})$ and by choosing specific prescriptions for fixing the scale μ (dependent on *r* and $\overline{m}$). By adjusting $\overline{m}$ so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to $3 r_0\simeq 7.5 {\mathrm {GeV}}^{-1}$ (*r*
_{0} is the Sommer scale) within the uncertainty of order $\Lambda_{\mathrm{QCD}}^3 r^2$.

*© Springer-Verlag, 2003*