Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD

Abstract

It is becoming more important to subtract renormalons efficiently from perturbative calculations, in order to achieve high precision QCD calculations. We propose a new framework ``Dual Space Approach" for renormalon separation, which enables subtraction of multiple renormalons simultaneously. Using a dual transform which suppresses infrared renormalons, we derive a one-parameter integral representation of a general observable. We investigate systematically how renormalons emerge and get canceled in the entire operator product expansion (OPE) of an observable, by applying the expansion-by-regions (EBR) method to this one-parameter integral expression. In particular we investigate in detail OPEs in a solvable model, the 2-dimensional $O(N)$ nonlinear $\sigma$ model, by the dual space approach. A nontrivial mechanism of renormalon cancellation in this model can be understood from an integration identity on which the EBR method is founded. We demonstrate that the dual space approach can be useful by a simulation study imitating the QCD case. Application of this method to QCD calculations is also discussed.

arXiv comment42 pages, 6 figures

References in corpus (36)

• Asymptotic expansion of Feynman integrals near threshold
• Effective field theories for heavy quarkonium
• Renormalons
• 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
• A quark mass definition adequate for threshold problems
• The infrared behaviour of the static potential in perturbative QCD
• B decay and the Upsilon mass
• B decays in the upsilon expansion
• Precision determination of the CKM element Vcb
• Foundation and generalization of the expansion by regions
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• Quarkonia and the Pole Mass
• Determination of alpha_s from the QCD static energy
• Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory
• Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of $|V_{cb}|$
• The bottom-quark mass from non-relativistic sum rules at NNNLO
• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Renormalons and confinement
• The charm/bottom quark mass from heavy quarkonium at N${}^3$LO
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• Surviving the renormalon in heavy quark potential
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Bottom Quark Mass from ${\rm Y}$ Sum Rules to $\mathcal{O}({\alpha }_s^3)$
• Hyperasymptotic approximation to the top, bottom and charm pole mass
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme
• Determination of ${\alpha }_s$ from static QCD potential with renormalon subtraction
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$
• Hyperasymptotic approximation to the plaquette and determination of the gluon condensate
• Nonperturbative Effects from the Resummation of Perturbation Theory
• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation
• On renormalons of static QCD potential at $u=1/2$ and $3/2$
• New method for renormalon subtraction using Fourier transform
• Renormalon subtraction using Fourier transform: Analyses of simplified models