Two-loop QCD vertices and three-loop MOM β functions

Chetyrkin, K.G.; Seidensticker, T.

doi:10.1016/s0370-2693(00)01217-x

Cited by 52 publications

(49 citation statements)

References 33 publications

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“…(E.13) of the Ref. [46] and reads 15) where the special functions K µ and K µ are given in Fig. 3; notice that, as happens for H Therefore, at least in principle, all form factors of the quark-gluon vertex can be determined by "solving" it.…”

Section: B Transverse Ward Identitymentioning

confidence: 99%

“…There is an additional issue that complicates the extraction of pertinent nonperturbative information on the quark-gluon vertex by means of traditional methods, which will be of e (p), which relates the photon-electron vertex with the electron propagator S e , but it is substantially more complicated, because it involves, in addition to 1 In perturbation theory, a complete study has been carried out at the one-loop level in arbitrary gauges, dimensions and kinematics [14], whereas at the two-and three-loop order only partial results for specific gauges and kinematics exist [15,16].…”

Section: Introductionmentioning

confidence: 99%

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New method for determining the quark-gluon vertex

et al. 2014

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We present a novel non-perturbative approach for calculating the form factors of the quark-gluon vertex in terms of an unknown three-point function, in the Landau gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the approximate calculation of the components of the aforementioned (fully-dressed) three-point function, using lattice data as input for the gluon propagators appearing in its diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding qualitative agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.

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Section: B Transverse Ward Identitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New method for determining the quark-gluon vertex

et al. 2014

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“…However, in theoretical and phenomenological QCD applications the gauge-dependent MOM-like schemes are used as well [87][88][89][90][91][92]. Among the number of MOM subtractions schemes one of the most applicable at present is the miniMOM (mMOM) scheme, which was originally formulated in ref.…”

Section: The Qed Generalized Crewther Relation In the Ms Mom And Os mentioning

confidence: 99%

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Garkusha

Kataev

Molokoedov

2018

J. High Energ. Phys.

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The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O(a 4 s ) level of perturbation theory. It is known that in the gauge-invariant renormalization MS-scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the MS-scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O(a 3 s ) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = −3, −1 and ξ = 0. In the O(a 4 s ) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = −3 at the O(a 3 s ) approximation. It is demonstrated that if factorization property for the MS-like 1 Affiliation from 2011 till 2015.Open Access, c The Authors. Article funded by SCOAP 3 .https://doi.org/10.1007/JHEP02(2018)161 JHEP02(2018)161schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

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“…The Ward identity implies that Z p and g 1 p have, in particular, the same perturbative p scale dependence. From the calculations of Chetyrkin et al [26,27], we may express, for example, the perturbative running of Z at large p as a function of the running MOM p. This is our main choice throughout this paper, although we discuss the effect of substituting an expansion in MS p. More precisely, we will always choose to use the definition of MOM p by the symmetric three-gluon vertex. The advantage of quarks is that we can reach an accuracy of four loops in the renormalization group (RG) expansion, because we do not need MOM 3 (for symmetric MOM p), since the dimension of the fermion is 0 at lowest order in the Landau gauge.…”

Section: B Mom Renormalization; Radiative Correctionsmentioning

confidence: 99%

“…This is possible in the Landau gauge to the order of four loops included, thanks to the papers of Chetyrkin and collaborators, Refs. [26,27].…”

Section: Appendix A: Perturbative Expansion To Four Loops In the Fullmentioning

confidence: 99%

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
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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.

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Two-loop QCD vertices and three-loop MOM β functions

Cited by 52 publications

References 33 publications

New method for determining the quark-gluon vertex

New method for determining the quark-gluon vertex

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
View full text Add to dashboard Cite

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Two-loop QCD vertices and three-loop MOM β functions

Cited by 52 publications

References 33 publications

New method for determining the quark-gluon vertex

New method for determining the quark-gluon vertex

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)Boucaud1, Soto2, Leroy3 et al. 2006Phys. Rev. D390190View full textAdd to dashboardCite

Contact Info

Product

Resources

About

Artifacts and⟨A2⟩power corrections: ReexaminingZψ(p2)
Boucaud
¹
,
Soto
²
,
Leroy
³

et al. 2006
Phys. Rev. D
39
0
19
0
View full text Add to dashboard Cite