alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory

Abstract

The determination of ${\alpha }_s$ from hadronic $\tau$ decays is revisited, with a special emphasis on the question of higher-order perturbative corrections and different possibilities of resumming the perturbative series with the renormalisation group: fixed-order (FOPT) vs. contour-improved perturbation theory (CIPT). The difference between these approaches has evolved into a systematic effect that does not go away as higher orders in the perturbative expansion are added. We attempt to clarify under which circumstances one or the other approach provides a better approximation to the true result. To this end, we propose to describe the Adler function series by a model that includes the exactly known coefficients and theoretical constraints on the large-order behaviour originating from the operator product expansion and the renormalisation group. Within this framework we find that while CIPT is unable to account for the fully resummed series, FOPT smoothly approaches the Borel sum, before the expected divergent behaviour sets in at even higher orders. Employing FOPT up to the fifth order to determine ${\alpha }_s$ in the $\MSb$ scheme, we obtain ${\alpha }_s(M_{\tau })=0.320{}_{-0.007}^{+0.012}$, corresponding to ${\alpha }_s(M_Z)=0.1185{}_{-0.0009}^{+0.0014}$. Improving this result by including yet higher orders from our model yields ${\alpha }_s(M_{\tau })=0.316\pm 0.006$, which after evolution leads to ${\alpha }_s(M_Z)=0.1180\pm 0.0008$. Our results are lower than previous values obtained from $\tau$ decays.

42 pages, 9 figures; appendix on Adler function in the complex plane added. Version to appear in JHEP

Cited by in corpus (113)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Review of lattice results concerning low energy particle physics
• The 2009 World Average of ${\alpha }_s$
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• Precision Tau Physics
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• The strong coupling and its running to four loops in a minimal MOM scheme
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• An updated determination of α_s from tau decays
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Duality between QCD Perturbative Series and Power Corrections
• World Summary of ${\alpha }_s$ (2012)
• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions
• K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• A new determination of α_s from hadronic τ decays
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• QCD Running Couplings and Effective Charges
• K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays
• Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane
• Possible duality violations in tau decay and their impact on the determination of alpha_s
• Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays
• Taming Landau singularities in QCD perturbation theory: The analytic approach 2.0
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• Expansion functions in perturbative QCD and the determination of ${\alpha }_s(M_{\tau }^2)$
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• The strong coupling from an improved $\tau$ vector isovector spectral function
• Semileptonic tau decays beyond the Standard Model
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Violation of Quark-Hadron Duality and Spectral Chiral Moments in QCD
• Determination of ${\alpha }_s(M_{\tau }^2)$ from Improved Fixed Order Perturbation Theory
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• The strong coupling from hadronic $\tau$ decays: a critical appraisal
• The strong coupling from $e^{+}{e}^{-}\to$ hadrons below charm
• Modified Contour-Improved Perturbation Theory
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• R(s) and hadronic tau-Decays in Order alpha_s^4: technical aspects
• Expansions of $\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior
• On the Difference between FOPT and CIPT for Hadronic Tau Decays
• Calculation of binding energies and masses of quarkonia in analytic QCD models
• Renormalon-motivated evaluation of QCD observables
• Low-energy constants and condensates from the tau hadronic spectral functions
• Precision physics with inclusive QCD processes
• Pole mass renormalon and its ramifications
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Constraints on the $\omega \pi$ form factor from analyticity and unitarity
• Absence of even-integer $\zeta$-function values in Euclidean physical quantities in QCD
• 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
• REvolver: Automated running and matching of couplings and masses in QCD
• Duality violations in tau hadronic spectral moments
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Testing the Concept of Quark-Hadron Duality with the ALEPH $\tau$ Decay Data
• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• Spacelike pion form factor from analytic continuation and the onset of perturbative QCD
• QCD Effective Coupling in the Infrared Region
• Lattice-motivated holomorphic nearly perturbative QCD
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• QCD Description of Hadronic Tau Decays
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Renormalons in integrated spectral function moments and ${\alpha }_s$ extractions
• The Mass of the Higgs Boson in the Standard Electroweak Model
• A Mixed Tau-Electroproduction Sum Rule for V_us
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Status of the Hadronic tau Decay Determination of |V_{us}|
• Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
• A critical look at V_us determinations from hadronic tau decay data
• Evidence against naive truncations of the OPE from $e^{+}{e}^{-}\to$ hadrons below charm
• What two models may teach us about duality violations in QCD
• Optimal renormalization and the extraction of the strange quark mass from moments of the $\tau$-decay spectral function
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Mathematical Aspects of the Asymptotic Expansion in Contour Improved Perturbation Theory for Hadronic Tau Decays
• Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior
• Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD
• Dispersive approach to QCD: tau lepton hadronic decay in vector and axial-vector channels
• Functional-analysis based tool for testing quark-hadron duality
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Determination of ${\alpha }_s(M_{\tau }^2)$: a conformal mapping approach
• On the difference between Fixed-Order and Contour-Improved Perturbation Theory
• Anomalous magnetic moment of the muon, a hybrid approach
• Hunting for QCD Instantons at the LHC in Events with Large Rapidity Gaps
• TAU2012 Summary
• Higher-order behaviour of two-point current correlators
• Vacuum quark condensate, chiral Lagrangian, and Bose-Einstein statistics
• Renormalization group improved $m_s$ and $|V_{us}|$ determination from hadronic $\tau$ decays
• 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
• The scalar gluonium correlator: large-beta_0 and beyond
• Scheme variations of the QCD coupling
• Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
• Dispersive approach to QCD and hadronic contributions to electroweak observables
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
• Recent progress in hadronic tau decays
• Recent Progress on Tau Lepton Physics
• Hadronic tau decays and the strong coupling
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Lattice Input on the Inclusive $\tau$ Decay $V_{us}$ Puzzle
• Chemical sensing with graphene: A quantum field theory perspective
• Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate
• From hadronic tau decays to the chiral couplings L_10 and C_87
• ${\alpha }_s$ analyses from hadronic tau decays with OPAL and ALEPH data
• Charged-Lepton Flavour Physics
• alpha_s and the tau hadronic width
• Evaluation of the three-flavor quark-disconnected contribution to the muon anomalous magnetic moment from experimental data
• Issues in determining alpha_s from hadronic tau decay and electroproduction data
• Perturbative expansion of tau hadronic spectral function moments
• alpha_s from tau decays revisited