UV contributions to energy of a static quark-antiquark pair in large ${\beta }_0$ approximation

The total energy of a static quark-antiquark pair $E_{\rm tot}®=2m_{\rm pole}+V_{\rm QCD}®$isknowntobepredictableupto${\cal O}(\Lambda_{\rm QCD}^3 r^2)$and${\cal O}(\frac{\Lambda_{\rm QCD}^3}{\overline{m}^2})$renormalonuncertaintiesinthelarge-$\beta_0$approximation,aftercanceling${\cal O}(\Lambda_{\rm QCD})$ renormalons. We compute the predictable part (genuine UV part) in terms of the $\overline{\mathrm{M}\mathrm{S}}$ mass $\bar{m}$, extending a recently-proposed method which conforms with OPE. In particular the $r$-independent part is determined. The result would help understanding the nature of $E_{\mathrm{t}\mathrm{o}\mathrm{t}}(r)$ in the context of OPE with renormalon subtraction.