Superasymptotic and hyperasymptotic approximation to the operator product expansion

Abstract

Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the splitting is achieved and the organization of the different terms is done along an super/hyper-asymptotic expansion. As a test we apply the methods to the static potential in the large ${\beta }_0$ approximation. We see the superasymptotic and hyperasymptotic structure of the observable in full glory.

arXiv comment60 pages, 11 figures, 2 Tables. Minor changes to meet journal version. Conclusions unchanged

References in corpus (37)

• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• Non-perturbative quark mass renormalization in quenched lattice QCD
• A quark mass definition adequate for threshold problems
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• QCD phenomenology of static sources and gluonic excitations at short distances
• Quarkonia and the Pole Mass
• On the ultimate uncertainty of the top quark pole mass
• On The Difficulty of Computing Higher-Twist Corrections
• More on ambiguities in the pole mass
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate
• Renormalons and confinement
• A Study of Ultraviolet Renormalon Ambiguities in the Determination of $\as$ from $\tau$ Decay
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• R-evolution: Improving perturbative QCD
• The charm/bottom quark mass from heavy quarkonium at N${}^3$LO
• QCD potential as a "Coulomb-plus-linear" potential
• Numerical Stochastic Perturbation Theory for full QCD
• Surviving the renormalon in heavy quark potential
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• The strong coupling from $e^{+}{e}^{-}\to$ hadrons below charm
• Relations between Heavy-light Meson and Quark Masses
• Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
• Mass of the bottom quark from Upsilon(1S) at NNNLO: an update
• Subtracting IR Renormalons from Wilson Coefficients: Uniqueness and power dependences on ${\Lambda }_{\mathrm{QCD}}$
• Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach
• QCD perturbation theory at large orders with large renormalization scales in the large ${\beta }_0$ limit
• Analytic structure in the coupling constant plane in perturbative QCD
• Constraining renormalon effects in lattice determination of heavy quark mass

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