Hyperasymptotic approximation to the plaquette and determination of the gluon condensate

Abstract

We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $⟨G^2{⟩}_{\mathrm{PV}}(n_f=0)=3.15(18)r_0^{-4}$.

20 pages, 9 figure. To meet journal version

References in corpus (4)

• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Conformal mapping of the Borel plane: going beyond perturbative QCD
• The non-perturbative part of the plaquette in quenched QCD
• Renormalon Subtraction from the Average Plaquette and the Gluon Condensate

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• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Bjorken sum rule with hyperasymptotic precision
• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• Theoretical description of the plaquette with exponential accuracy
• Exotic bottomonium hadronic transitions