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

Abstract

The total energy of a static quark-antiquark pair $E_{\mathrm{tot}}(r)=2m_{\mathrm{pole}}+V_{\mathrm{QCD}}(r)$ is known to be predictable up to $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^3{r}^2)$ and $\mathcal{O}(\frac{{\Lambda }_{\mathrm{QCD}}^3}{{\overline{m}}^2})$ renormalon uncertainties in the large-${\beta }_0$ approximation, after canceling $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ renormalons. We compute the predictable part (genuine UV part) in terms of the $\overline{\mathrm{MS}}$ 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 $E_{\mathrm{tot}}(r)$ in the context of OPE with renormalon subtraction.

Comments: Version to appear in Physics Letters B, modification of the expression of delta_{G,0} is added; other modifications are minor, 10 pages, 4 figures