Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)

Abstract

The next-to-leading-order (NLO) term in the operator product expansion (OPE) of the quark propagator vector part Z and the vertex function g 1 of the vector current in the Landau gauge should be dominated by the same hA 2 i condensate as in the gluon propagator. On the other hand, the perturbative part has been calculated to a very high precision thanks to Chetyrkin and collaborators. We test this on the lattice, with both clover and overlap fermion actions at 6:0, 6.4, 6.6, 6.8. Elucidation of discretization artifacts appears to be absolutely crucial. First hypercubic artifacts are eliminated by a powerful method, which gives results notably different from the standard democratic method. Then, the presence of unexpected, very large, nonperturbative, O4 symmetric discretization artifacts, increasing towards small momenta, is demonstrated by considering Z MOM V , which should be constant in the absence of such artifacts. They impede in general the analysis of OPE. However, in two special cases with overlap action -(1) for Z ; (2) for g 1 , but only at large p 2 -we are able to identify the hA 2 i condensate; it agrees with the one resulting from gluonic Green functions. We conclude that the OPE analysis of quark and gluon Green function has reached a quite consistent status, and that the power corrections have been correctly identified. A practical consequence of the whole analysis is that the renormalization constant Z ( Z ÿ1 2 of the momentum-subtraction (MOM) scheme) may differ sizably from the one given by democratic selection methods. More generally, the values of the renormalization constants may be seriously affected by the differences in the treatment of the various types of artifacts, and by the subtraction of power corrections.

QCD effective charges from lattice data

“…Then, in order to check if the α(µ 2 ) values found through the above procedure are compatible with what one would expect within the MOM scheme that we use, we compare them with the corresponding four-loop perturbative calculation, presented in [76,77]. The result of this comparison is shown in figure 6; the yellow band is obtained by varying the Λ QCD , appearing in the expression derived in [76,77], in the range between 350 − 450 MeV. As we can see, the best adjustment for the values of α(µ 2 ) occurs for Λ QCD = 410 MeV.…”

Gluon mass generation in the presence of dynamical quarks

“…Notice that both sets of data will be renormalized at the scale ¼ 4:3 GeV, which is the last available point in the ultraviolet. At this scale, the expected value of the (quenched) strong effective charge is s ¼ g 2 =4 ¼ 0:22 [39,40]. (iii) The function Yðk 2 Þ represents a crucial ingredient of Eq.…”

Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume

“…One may suspect that it is connected with the ''amputation'' of external lines, i.e. for instance the tree approximation is exactly 5 ; nevertheless, this is not a sufficient reason, for the analogous vector vertex is found to be still spoiled by large artefacts [6,7].…”

“…the quark propagator in the various configurations, are the same as already used in [6,7] to study Z c ðp 2 Þ. We have at hand simulations at N f ¼ 0 with the Wilson gauge action and the SW clover action in Landau (i.e.…”

“…The central object will be the quark mass function, in the chiral limit, calculated, along the line described above, through the residue of the Goldstone boson in the pseudoscalar vertex. Thus the present paper completes the study of the papers [6,7] devoted to the vector part of the propagator, Z c . For an extensive study of the quark propagator, one can refer also to the papers of the Adelaide group, see, for instance, our reference below [8].…”