The total energy of a static quark-antiquark pair $E_{ \rm tot}(r)=2m_{ \rm pole}+V_{ \rm QCD}(r)$ is known to be predictable up to ${ \cal O}(\Lambda_{ \rm QCD}^3 r^2)$ and ${ \cal O}(\frac{ \Lambda_{ \rm QCD}^3}{ \overline{ m}^2})$ renormalon uncertainties in the large-$\beta_0$ approximation, after canceling ${ \cal O}(\Lambda_{ \rm QCD})$ renormalons. We compute the predictable part (genuine UV part) in terms of the $\overline{ \rm MS}$ mass $\overline{ m}$, 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 $E_{ \rm tot}(r)$ in the context of OPE with renormalon subtraction.
Categories: hep-ph