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.

arXiv comment34 pages, 7 figures, 7 tables. Version 4: Fig. 4 (left panel) corrected; some typos with Kroneccker symbols in Eqs. (D14) and (D18) corrected

References in corpus (50)

• The four-loop beta-function in Quantum Chromodynamics
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• Charm and Bottom Quark Masses: an Update
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules
• Correlator of the quark scalar currents and Γ_{tot}(H --> hadrons) at O(α_s^3) in pQCD
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Short Distance Mass of a Heavy Quark at Order α_s^3
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• Renormalization group analysis of the tau-lepton decay within QCD
• The Determination of alpha_s from Tau Decays Revisited
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Determination of ${\alpha }_s$ and heavy quark masses from recent measurements of $R(s)$
• Pion form factor in QCD: From nonlocal condensates to NLO analytic perturbation theory
• Analytic Perturbation Theory in analyzing some QCD observables
• Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density
• Heavy Quarkonium Spectrum at $\mathcal{O}({\alpha }_s^5{m}_q)$ and Bottom/Top Quark Mass Determination
• Ten years of the Analytic Perturbation Theory in QCD
• Analytic coupling and Sudakov effects in exclusive processes: pion and ${\gamma }^{\ast }\gamma \to {\pi }^0$ form factors
• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• Fractional Analytic Perturbation Theory in Minkowski space and application to Higgs boson decay into a b\bar{b} pair
• Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence
• Various versions of analytic QCD and skeleton-motivated evaluation of observables
• Pion form factors with improved infrared factorization
• Global Fractional Analytic Perturbation Theory in QCD with Selected Applications
• Generalization of the BLM procedure and its scales in any order of pQCD
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• On the role of power expansions in quantum field theory
• Estimations of Order alpha_s^3 and alpha_s^4 Corrections to Mass-Dependent Observables
• Analyticity and power corrections in hard-scattering hadronic functions
• Analytic Perturbation Theory: A New Approach to the Analytic Continuation of the Strong Coupling Constant ${\alpha }_S$ into the Timelike Region
• Renorm-group, Causality and Non-power Perturbation Expansion in QFT
• Analytic Approach to Perturbative QCD
• Optimized Lambda-Parametrization for the QCD Running Coupling Constant in Spacelike and Timelike Regions
• Analyticity properties of three-point functions in QCD beyond leading order
• Mass Dependent ${\alpha }_S$ Evolution and the Light Gluino Existence
• A novel series solution to the renormalization group equation in QCD
• Spectral moments of two-point correlators in perturbation theory and beyond
• Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
• Pion form factor analysis using NLO analytic perturbation theory
• Practical techniques of analytic perturbation theory of QCD
• Resummation in (F)APT
• Explicit expressions for Euclidean and Minkowskian QCD observables in analytic perturbation theory
• Higgs boson decay into bottom quarks and uncertainties of perturbative QCD predictions
• Perturbative logarithms and power corrections in QCD hadronic functions. A unifying approach
• Analyticity of QCD observables beyond leading-order perturbation theory

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