Asymptotic scaling of the heavy-quark potential in lattice QCD

The scaling behavior of the heavy-quark $q\overline{q}$ potential is studied by measuring Wilson-line operator-operator correlations via extensive simulations on large lattices. By using large size loops (up to 16×12) and extracting the potential at large distance $R\ge 4$ we find that the string tension satisfies the two-loop asymptotic scaling within about 95% accuracy at the coupling $\beta =6.0\mathrm{}$ 6.1, 6.2 and $\alpha$ remains a constant. Thus the scaling of the string tension sets in at around $\beta =6\mathrm{}$. The obtained values $\frac{\sqrt{\sigma }}{{\Lambda }_L}=78\mathrm{}\pm 4$ and $\alpha \simeq 0.54\pm 0.11$ agree well with the potential-model analysis on the $c\overline{c}$ and $b\overline{b}$ systems. Among the existing underlying string theories, our results favor the Neveu-Schwarz string theory.