# UV contributions to energy of a static quark-antiquark pair in large $\beta_0$ approximation

## TL;DR

This paper calculates the ultraviolet contributions to the energy of a static quark-antiquark pair within the large-beta_0 approximation, clarifying the UV part's role in the operator product expansion and renormalon cancellation.

## Contribution

It extends a recent method to compute the UV part of the total energy in terms of the MS-bar mass, including the r-independent component, aiding understanding of renormalon effects.

## Key findings

- Computed the genuine UV part of the energy in the large-beta_0 approximation.
- Extended a method consistent with the operator product expansion.
- Determined the r-independent part of the energy.

## Abstract

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.