Speaker
Description
We report our analysis for the static energy in (2+1+1)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly 1fm, allowing us to perform a simultaneous determination of the lattice scales r1 and r0 as well as the string tension, σ. For the smallest three lattice spacings we also determine the scale r2. While our results for r0/r1 and r0 √σ agree with published (2+1)-flavor results, our result for r1/r2 differs significantly from the value obtained in the (2+1)-flavor case, which is most likely due to the effect of the charm quark. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published (2+1)-flavor QCD results at similar lattice spacing. We find that for r > 0.2fm our results on the static energy agree with the (2+1)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. The perturbative expression features decoupling at large distances, an effective running with four massless quarks at very short distances, and finite charm mass effects at distances comparable with the inverse of the charm mass. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.
