The static potential to O(α2) in lattice perturbation theory

Abstract

We present a calculation of Wilson loops, and the static inter-quark potential to O(α 2 ) in lattice perturbation theory. This is carried out with the Wilson, Symanzik-Weisz, and Iwasaki gauge actions and the Wilson, Sheikholeslami-Wohlert, and Kogut-Susskind dynamical fermion action for small Wilson loops, and with the Wilson gauge action and each of the dynamical quark actions in the case of the static potential.

The static potential: lattice versus perturbation theory in a renormalon-based approach

“…Moreover, In Ref. [18] (see also [16,19]), it has been shown that perturbation theory can indeed reproduce the slope of the static potential given 1 There also exists a computation of the running of the Coulomb potential in vNRQCD [8] with the same precision that disagrees with the one obtained in pNRQCD [7]. At this respect, we would like to report on a recent computation [9] of the 4-loop double log term of the Coulomb potential proportional to C 3 A β 0 that agrees with the pNRQCD result and disagrees with the vNRQCD one.…”

“…For his study, he used the static version of the 1S mass and the upsilon expansion [17], which cancels the leading renormalon and relate the 1S mass to the MS mass. Moreover, in [18] (see also [16,19]), it has been shown that perturbation theory can indeed reproduce the slope of the static potential given by lattice simulations at short distances by using force instead of potential as the basic tool without the need to talk about renormalons.…”