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

Abstract.

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 $\Lambda_{\mathrm{QCD}}^3 r^2$.