Wilson expansion of QCD popagators at three loops: operators of dimension two and three

Abstract

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A 2 , m 2 , m A 2 , ψ ψ and m 3 . We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.

High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm

“…and, taking advantage of the ms Wilson coefficients for the gluon and ghost OPE expansions at the O(α 4 )-order [43], one can obtain in the appropriate renormalization scheme [35] R (α, α 0 ) = 1 + 1.03735α + 1.07203α 2 + 1.59654α…”

Strong Running Coupling atτandZ0Mass Scales from Lattice QCD

“…Thus, we can apply the two estimates of Λ MS , that can be found in Tab. I, to run the coupling down to the scale of τ mass, below the bottom quark mass threshold, and compare the result with the estimate from τ decays [1], α ms (m 2 τ ) = 0.334 (14). This will produce, with the 1-σ error propagation, the two following results at the τ -mass scale: α MS (m 2 τ ) = 0.337(8) and α MS (m 2 τ ) = 0.342(10).…”

Testing the operator product expansion Wilson coefficient forA2from lattice QCD with a dynamical charm

“…[40]. For our purposes, the running with momentum, p, for the OPE nonperturbative correction inside the bracket of Eq.…”

“…[41] and at the four-loop level in Ref. [40]. This RG equation is obtained just by applying the logarithm derivative on the renormalization momentum, , to the two hand sides of Eq.…”