Asymptotic scaling of the gluon propagator on the lattice -: art. no. 114508

We pursue the study of the high energy behavior of the gluon propagator on the lattice in the Landau gauge in the flavorless case (n(f) = 0) It was Shown in a preceding paper that the gluon propagator did not reach three-loop asymptotic scaling at an energy scale as high as 5 GeV. Our present high statistics analysis includes also a simulation at beta = 6.8 (a similar or equal to 0.03 fm), which allows us to reach mu similar or equal to 10 GeV. Special care has been devoted to the finite lattice-spacing artifacts as well as to the finite-volume effects, the latter being acute at beta = 6.8 where the volume is bounded by technical limits. Our main conclusion is strong evidence that the gluon propagator has reached three-loop asymptotic scaling, at mu ranging from 5.6-9.5 GeV. We buttress up this conclusion on several demanding criteria of asymptoticity, including scheme independence. Our fit in the 5.6 GeV to 9.5 GeV window yields Lambda<(MS)over bar> = 319 +/- 14(-20)(+10) MeV, in good agreement with our previous result Lambda(<(MS)over bar>) = 295 +/- 20 MeV, obtained from the three-gluon vertex, but it is significantly above the Schrodinger functional method estimate: 238 +/- 19 MeV. The latter difference is not understood. Confirming our previous paper, we show that a fourth loop is necessary to fit the whole (2.8-9.5) GeV energy window.