Renormalization of quark propagators from twisted-mass lattice QCD atNf=2

Abstract

We present results concerning the non-perturbative evaluation of the renormalisation constant for the quark field, Z q , from lattice simulations with twisted mass quarks and three values of the lattice spacing. We use the RI'-MOM scheme. Z q has very large lattice spacing artefacts ; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalisation constants. We recall and develop the non-perturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice spacing artefacts scale indeed as a 2 p 2 .We then study the running of Z q with particular attention to the non-perturbative effects, presumably dominated by the dimension-two gluon condensate A 2 in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units confirming that it is a continuum effect. It gives a ∼ 4% contribution at 2 GeV.Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties.Finally combining all our results and using the known Wilson coefficient of A 2 we find g 2 (µ 2 ) A 2 µ 2 CM = 2.01(11) +0.61 −0.73 GeV 2 at µ = 10 GeV, in fair agreement within uncertainties with the value indepently extracted from the strong coupling constant. We convert the non-perturbative part of Z q from RI'-MOM to MS. Our result for the quark field renormalisation constant in the MS scheme is Z MS pert q ((2 GeV) 2 , g 2 bare ) = 0.750(3)(7) − 0.313(20) (g 2 bare − 1.5) for the perturbative contribution and Z MS non−perturbative q ((2 GeV) 2 , g 2 bare ) = 0.781(6)(21)− 0.313(20) (g 2 bare − 1.5) when the non-perturbative contribution is included.

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

“…All together, these results appear to be fairly consistency. A similar consistency has also been found when comparing the condensate extracted from the lattice quark propagator and the Taylor coupling with N f ¼ 2 dynamical flavors [24,36]. Still, despite this consistency and the rather convincing estimate of à QCD obtained with the good agreement of the OPE formula and the lattice results for the Taylor coupling with N f ¼ 2 þ 1 þ 1, the actual nature of the unavoidable nonperturbative corrections and the condensates involved is a controversial matter.…”

“…The rhs of Eq. (3) stands for the definition of c WMS 2 in the ''Wilson MS'' scheme 3 (MS) [36], after the introduction of c MOM 0 ðp 2 ; 2 Þ ¼ À pert ðp 2 ; " À1 Þ À pert ð 2 ; " À1 Þ ; (5) which allows one to recast Eq. (1) to read…”

Alpha, Lambda and Gluon condensate: Precision sudies with dynamical charm

“…However our previous studies in quenched approximation suggested that such universality (even including the three-gluon vertex) is indeed compatible with the numerical data (N f =0) [20,27,28,6,29,7]. This has been also supported by the calculations with N f =2 dynamical flavours [19,30]. Now we will address this question in the N f =2+1+1 case, to clarify the nature itself of the unavoidable nonperturbative corrections and the involved condensates.…”

“…As we did in ref. [17,18,30] for the Taylor coupling and the vector quark propagator, the gluon propagator renormalization constant Z Latt 3 in MOM scheme can be written as…”

Three-gluon running coupling from lattice QCD at N f = 2 + 1 + 1: a consistency check of the OPE approach

“…For instance, the study of the coupling defined from the asymmetric ( MOM) three-gluon vertex and estimated from quenched lattice data revealed the main role of nonperturbative power corrections to account for its running [16]. Then, in a vast series of papers [17,18,[22][23][24][25][26][27][28][29][30], some of us have exhaustively proven that Wilson's Operator Product Expansion (OPE) provides a general framework to include non-perturbative contributions, and that its application to QCD couplings for several renormalization schemes allows a coherent and simple explanation of the running obtained from the lattice for momenta as…”