Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants

Abstract

Perturbative QCD corrections to hadronic $\tau$ decays and $e^{+}{e}^{-}$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong coupling, ${\alpha }_s$, from these processes suffer from an ambiguity related to the treatment of unknown higher orders in the perturbative series. In this work, we exploit the method of Padé approximants and its convergence theorems to extract information about higher-order corrections to the Adler function in a systematic way. First, the method is tested in the large-${\beta }_0$ limit of QCD, where the perturbative series is known to all orders. We devise strategies to accelerate the convergence of the method employing renormalization scheme variations and the so-called D-log Padé approximants. The success of these strategies can be understood in terms of the analytic structure of the series in the Borel plane. We then apply the method to full QCD and obtain reliable model-independent predictions for the higher-order coefficients of the Adler function. For the six-, seven-, and eight-loop coefficients we find $c_{5,1}=277\pm 51$, $c_{6,1}=3460\pm 690$, and $c_{7,1}=(2.02\pm 0.72)\times 10^4$, respectively, with errors to be understood as lower and upper bounds. Our model-independent reconstruction of the perturbative QCD corrections to the $\tau$ hadronic width strongly favours the use of fixed-order perturbation theory (FOPT) for the renormalization-scale setting.

arXiv comment40 pages, 8 figures. Five references added. Minor changes. To appear in Journal of High Energy Physics

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Cited by in corpus (35)

• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• The strong coupling from an improved $\tau$ vector isovector spectral function
• Semileptonic tau decays beyond the Standard Model
• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Extending the Predictive Power of Perturbative QCD
• Renormalon-motivated evaluation of QCD observables
• Precision physics with inclusive QCD processes
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Conformal mapping of the Borel plane: going beyond perturbative QCD
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Renormalons in integrated spectral function moments and ${\alpha }_s$ extractions
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• 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
• Renormalons beyond the Borel plane
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Higher-order behaviour of two-point current correlators
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Conformal mappings in perturbative QCD
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
• $H\to \gamma \gamma$ to all orders in ${\alpha }_s$ in the large-${\beta }_0$ limit of QCD
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants
• Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination
• Evaluation of the three-flavor quark-disconnected contribution to the muon anomalous magnetic moment from experimental data
• A new determination of higher-order QCD corrections to hadronic $\tau$ decays