Static QCD Potential at Three-Loop Order

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

Figure 1

$V_{\mathrm{QCD}}(r)=[V_{\mathrm{QCD}}(r){]}_{\mathrm{PT}}+[V_{\mathrm{QCD}}(r){]}_{\mathrm{US}}$ up to $\mathcal{O}({\alpha }_s^4)$ and $\mathcal{O}({\alpha }_s^4\log {\alpha }_S)$. (a) In the toponium region, three 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 [15, 30]. We set $n_l=0$. The distance region corresponds roughly to the size of ${\rm Y}(1S)$ state.