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We investigate the $u=1/2$ [$\mathcal{O}(\Lambda_{\rm QCD})$] and $u=3/2$[$\mathcal{O}(\Lambda_{\rm QCD}^3)$] renormalons in the static QCD potential inposition space and momentum space using the OPE of the potential-NRQCDeffective field theory. This is an old problem and we provide a formalformulation to analyze it. In particular we present detailed examinations ofthe $u=3/2$ renormalons. We clarify how the $u=3/2$ renormalon is suppressed inthe momentum-space potential in relation with the Wilson coefficient $V_A(r)$.We also point out that it is not straightforward to subtract the IR renormalonand IR divergences simultaneously in the multipole expansion. Numericalanalyses are given, which clarify the current status of our knowledge on theperturbative series. The analysis gives a positive reasoning to the method forsubtracting renormalons used in recent $\alpha_s(M_Z)$ determination from theQCD potential.

On renormalons of static QCD potential at $u=1/2$ and $3/2$