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

Abstract

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.

Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

“…31 The numerical results presented in this work [principally Eqs. ( 53), ( 58), (60), Table 4] appear to confirm the arguments given above. Namely, the extracted values of α s are closer to each other when the FOPT (and FOPT) and PV evaluation methods are used, while the extracted value of α s becomes significantly larger when the (truncated) CIPT evaluation method is used.…”

“…The main results of the paper are in Eq. (60). For the purpose of additional comparison of different methods (FOPT, PV, CIPT), the results in Eq.…”

“…[29], the coefficients d n 6 The MiniMOM β-function has been evaluated up to four-loops [56,57,59]. In the work [60] it has been shown that the MiniMOM scheme, in the Landau gauge, respects the β-function factorisation property of the conformal symmetry breaking contribution to the generalised Crewther relation. 7 The effective charge (ECH) method [61] gives the estimate (d 4 ) ECH = 275 [16,63].…”

An analysis of Bayesian estimates for missing higher orders in perturbative calculations

“…Various prescriptions for reducing or eliminating scale ambiguity have also been discussed broadly in the literature, e.g., refs. [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2

“…5 Interestingly, it was shown in Ref. [52] that the β-function factorisation of the conformal symmetry breaking contribution to the generalised Crewther relation is preserved in the MM scheme in the Landau gauge. 6 The MM scheme in pQCD sense is known up to 4-loop level.…”