The $\{\beta \}$-expansion formalism in perturbative QCD and its extension

Abstract

We discuss the $\{\beta \}$-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ $R$-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the $\{\beta \}$-expansion. We illustrate this feature considering the nonsinglet Adler function $D^{\text{NS}}$ in the third order of perturbation. We propose a generalization of the $\{\beta \}$-expansion for the renormalization group covariant quantities -- the $\{\beta ,\gamma \}$-expansion.

arXiv comment16 pages, 3 figures, a few editorial corrections for JHEP version

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Cited by in corpus (12)

• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• Optimized determination of the polarized Bjorken sum rule in pQCD
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• The $\{\beta \}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O({\alpha }_s^4)$
• On a realization of $\{\beta \}$-expansion in QCD
• Correlators of vector, tensor, and scalar composite vertices of order $O({\alpha }_s^2{\beta }_0)$
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables