Determination of the QCD coupling from the static energy and the free energy

Abstract

1 The lattice observables (gluon action density, and sea quark condensates) contributing to the Equation of State have divergent, additive contributions, which depend only on the lattice spacing. Renormalization group invariant observables are obtained by subtracting the T = 0 observables from the T > 0 observables at each lattice spacing.

Strong coupling constant and heavy quark masses in (2+1)-flavor QCD

“…The T = 0 NPC data with r/a < √ 8 are well-aligned with the fit excluding these data, while the T = 0 TLC data with r/a < √ 8 cannot be consistently described by a continuum result for any value of α s (M Z ). (right) The T > 0 NPC data[5] in different r/a windows are fully compatible with the same continuum result.…”

“…The error budget is discussed in detail in Ref. [5]. All estimates of the perturbative uncertainty are dramatically reduced when the comparison is restricted to the smaller maximal distance r, while the central value hardly depends on the fit range for r 0.45 r 1 .…”

“…The line represents the threeloop result with resummed leading ultrasoft logarithms, Eq. (3) in Ref [5],. corresponding to the central value α s (M Z ) = 0.1167 of the analysis of the T = 0 data with r/a ≥ √ 8 (gray bullets).…”

“…The nonperturbative lattice and the perturbative continuum results for E QCD (r) multiplied by the distance, rE(r). (left) The T = 0 data[5] are NPC (colored bullets) or TLC (black crosses and gray bullets). The colors indicate different lattice spacings of the NPC data.…”

Precise determination of αs from relativistic quarkonium sum rules

“…The question is, of course, by how much the perturbative error grows, and if it would still make the method eligible for a precise determination of the strong coupling. Another approach to exclude the continuum from the 0.110 0.112 0.114 0.116 0.118 0.120 0.122 [77][78][79]; lattice QCD [11,12,76,80,81] and static energy potential [82] (both use lattice input, in dark blue); Electroweak precision observables fits [83] (black); Deep Inelastic Scattering [84] and global PDF fits [85,86] (light blue); and hadronic τ decays [87,88] and e + e − → hadrons [89] (gray). The current world average [47] is shown as a translucent orange band.…”