The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\overline{MS}$-based scheme

Abstract

We apply the 't Hooft $\overline{MS}$-based scheme to study the scheme-dependence of the QCD generalization of Crewther relation for the product of the normalised non-singlet perturbative contributions to the $e^{+}{e}^{-}$-annihilation Adler function and to the Bjorken sum rule of the polarized lepton-nucleon deep-inelastic scattering process. We prove that after the transformations from the pure $\overline{MS}$-scheme to the 't Hooft scheme the characteristic $\overline{MS}$-scheme theoretical property of this relation, namely the factorization of the $\beta$-function in its conformal symmetry breaking part, disappears. Another "non-comfortable" theoretical consequence of the application of this prescription in $\mathcal{N}=1$ SUSY QED model is mentioned. It is shown, that within the 't Hooft scheme the expansions of Green functions in terms of the Lambert function is simplified in high orders of perturbation theory. This may be considered as the attractive feature of the 't Hooft scheme, which manifest itself in high-order perturbative phenomenological applications.

LateX, 10 pages, Title a bit modified, comments on the conservation of vector current in the 't Hooft scheme added, 1 extra reference added, accepted for publication in Phys. Lett.B

References in corpus (4)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• Simple analytic QCD model with perturbative QCD behavior at high momenta
• Is it possible to check urgently the 5-loop analytical results for the $e^{+}{e}^{-}$-annihilation Adler function ?

Cited by in corpus (12)

• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Gluon Propagator in Fractional Analytic Perturbation Theory
• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Evaluations of low-energy physical quantities in QCD with IR freezing of the coupling
• On applications of Mathematica Package "FAPT" in QCD