Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT

Abstract

Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width ${\Gamma }_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^{+}{e}^{-}$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of $R_S$ and $D_V$ using one- and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.

34 pages, 7 figures, 7 tables. Version 4: Fig. 4 (left panel) corrected; some typos with Kroneccker symbols in Eqs. (D14) and (D18) corrected

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Cited by in corpus (22)

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• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Fractional Analytic QCD beyond Leading Order
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• The $\{\beta \}$-expansion formalism in perturbative QCD and its extension
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• 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
• Perturbative QCD in acceptable schemes with holomorphic coupling
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• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
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