Static QCD potential at three-loop order

TL;DR

This paper computes the purely gluonic contribution to the static QCD potential at three-loop order and completes computation of the static potential at this order.

Abstract

We compute the purely gluonic contribution to the static QCD potential at three--loop order. This completes the computation of the static potential at this order.

Figures (1)

• Figure 1: $V_{\rm QCD}(r)=[V_{\rm QCD}(r)]_{\rm PT}+[ V_{\rm QCD}(r) ]_{\rm US}$ up to ${\cal O}(\alpha_s^4)$ and ${\cal O}(\alpha_s^4\log\alpha_S)$: (a) In the toponium region 3 lines, corresponding to $\mu=25$, 50 and 100 GeV, are plotted with $n_l=5$; (b) Comparison with the lattice computations in the quenched approximation Takahashi:2002bwNecco:2001xg. We set $n_l=0$. The distance region corresponds roughly to the size of $\Upsilon(1S)$ state.