Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation

Abstract

We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee's method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-${\beta }_0$ approximation. Here, we introduce an "ambiguity function," which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-${\beta }_0$ approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.

arXiv comment43 pages, 15 figures, version to appear in JHEP, minor modifications to v2

References in corpus (32)

• Potential NRQCD: an effective theory for heavy quarkonium
• Renormalons
• Five-Loop Running of the QCD coupling constant
• The static potential in QCD to two loops
• The five-loop beta function of Yang-Mills theory with fermions
• A quark mass definition adequate for threshold problems
• Naive nonabelianization and resummation of fermion bubble chains
• The static quark-antiquark potential in QCD to three loops
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• Three-loop static potential
• The infrared behaviour of the static potential in perturbative QCD
• The static potential in QCD - a full Two-Loop Calculation
• Static QCD potential at three-loop order
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Ultrasoft Effects in Heavy-Quarkonium Physics
• Fermionic contributions to the three-loop static potential
• Quarkonia and the Pole Mass
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Renormalons and confinement
• Analytic three-loop static potential
• QCD potential as a "Coulomb-plus-linear" potential
• Renormalons Beyond One-Loop
• Surviving the renormalon in heavy quark potential
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• 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
• Renormalon-free definition of the gluon condensate within the large-${\beta }_0$ approximation
• On renormalons of static QCD potential at $u=1/2$ and $3/2$
• UV contribution and power dependence on ${\Lambda }_{\mathrm{QCD}}$ of Adler function

Cited by in corpus (8)

• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme
• Bjorken sum rule with hyperasymptotic precision
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• Renormalon subtraction using Fourier transform: Analyses of simplified models
• Renormalons in static QCD potential: review and some updates
• Determination of HQET nonperturbative matrix elements with renormalon subtraction using Fourier transform