Renormalons

Abstract

A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We first summarize what is known about ultraviolet and infrared renormalons from an analysis of Feynman diagrams. Because infrared renormalons probe large distances, they are closely connected with non-perturbative power corrections in asymptotically free theories such as QCD. We discuss this aspect of the renormalon phenomenon in various contexts, and in particular the successes and failures of renormalon-inspired models of power corrections to hard processes in QCD.

168 pages, LaTeX, 23 figures, rmpbib.sty file required and included. v2: minor rearrangements, bibliographical style changed

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• Achieving effective renormalization scale and scheme independence via the Principle of Observable Effective Matching
• The resummed quark form factor in dimensional regularization
• Revisiting the Bottom Quark Forward-Backward Asymmetry $A_{\mathrm{FB}}$ in Electron-Positron Collisions
• Confinement as Analytic Continuation Beyond Infinity
• Renormalon free part of an ultrasoft correction to the static QCD potential
• Anomalous dimensions of four-quark operators and renormalon structure of mesonic two-point correlators
• Appearance and disappearance of thermal renormalons
• Exponentially Modified QCD Coupling
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Phenomenology of B -> pi pi, pi K Decays at O(alpha^2 beta_0) in QCD Factorization
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• QCD sum rule analysis of the charmonium system: The charm quark mass
• On the ambiguity of field correlators represented by asymptotic perturbation expansions
• Off-shell Suppression of Renormalons in Non-relativistic QCD Boundstates
• Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC
• The heavy quark potential in pNRQCD
• Power corrections to the process ${\gamma }^{\ast }\gamma \to \pi \pi$ in the running coupling method
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• Quark-Antiquark Potential and Generalized Borel Transform
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Estimate of 4-loop Pole-MSbar Mass Relation from Static QCD Potential
• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
• Interplay between perturbative and non-perturbative effects with the ARES method
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Probing the Sivers asymmetries through $J/\psi$ photoproduction in ${\mathrm{p}}^{\uparrow }\mathrm{p}$ collision with forward proton tagging
• Non-perturbative tests of continuum HQET through small-volume two-flavour QCD
• Improved separation of soft and hard components in multiple Coulomb scattering
• Using an Effective Charges Method to extract Lambda-MS-bar from event shape moments in e+e- annihilation
• Recent progress in hadronic tau decays
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• New determination of $|V_{\mathrm{cb}}|$ using the three-loop QCD corrections for the $B\to D^{\ast }$ semi-leptonic decays
• Infrared Renormalons in Supersymmetric Theories
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model
• Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• Linear power corrections to single top production and decay at the LHC in the narrow width approximation
• The constraints on the non-singlet polarised parton densities from the infrared-renormalon model
• The value of QCD coupling constant and power corrections in the structure function F2 measurements
• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
• On-shell Matrix Elements of the EMT Trace in Gauge Theories and Heavy Quark Masses
• $H\to \gamma \gamma$ to all orders in ${\alpha }_s$ in the large-${\beta }_0$ limit of QCD
• alpha_s in DIS scheme
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• QCD, from its inception to its stubbornly unsolved problems
• Flavor dependence of normalization constant for an infrared renormalon
• Quark-antiquark static energy from a restricted Fourier transform
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator
• Progress in computing inclusive B decay spectra
• Nonperturbative contributions to the quark form factor at high energy
• On the relation between pole and running heavy quark masses beyond the four-loop approximation
• Renormalon subtraction using Fourier transform: Analyses of simplified models
• Perturbative study of large $N$ principal chiral model with twisted reduction
• Nonperturbative definition of the pole mass and short distance expansion of the heavy quark potential in QCD
• Power Corrections in QCD
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Gross-Llewellyn Smith sum rule from lattice QCD
• Perturbative QCD analysis of near-to-planar three jet events
• Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections
• Summary of Working Group 3 of the Neutrino Factory '02 Workshop
• Theoretical description of the plaquette with exponential accuracy
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• Power Corrections in Flavour-Singlet Deep Inelastic Scattering
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness
• On the Light Massive Flavor Dependence of the Top Quark Mass
• Feynman integrals at large loop order and the $\log$-$\Gamma$ distribution
• Confinement, Chiral Symmetry Breaking, and Axial Anomaly from Domain Formation at Intermediate Resolution
• A reanalysis of event shape distributions in electron-positron annihilation
• Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
• Gluon Mass Generation from Renormalons and Resurgence
• Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD
• On the Relationship between Large Order Graphs and Instantons for the Double Well Oscillator
• Renormalons as dilatation modes in the functional space
• Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate
• On the ambiguity of functions represented by divergent power series
• Applications of QCD
• Computation of the one-loop spectral QCD running coupling using covariant spectral regularization
• Background field method in the large $N_f$ expansion of scalar QED
• A Computational Companion to Transient de Sitter and Quasi de Sitter States in SO(32) and E_8 X E_8 Heterotic String Theories I: Formalisms
• Infrared Renormalons in Collider Processes
• Anomalous scaling of linear power corrections
• Monte Carlo Event Generators for Future Lepton Colliders
• Higher-twist mechanism and inclusive gluon production in pion-proton collisions
• Renormalons and Analytic Properties of the βfunction
• Heavy top renormalon contribution to fermion propagators
• alpha_s and the tau hadronic width
• Soft end-point and mass corrections to the eta' g*g* vertex function
• Renormalon effect of quasi-PDF in gradient flow formalism
• Properties of the Free Energy Density Using the Principle of Maximum Conformality
• Renormalisation
• The Beauty of Lattice Perturbation Theory: The Role of Lattice Perturbation Theory in B Physics
• The nature of power corrections in large ${\beta }_0$ approximation
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• Convergent perturbative series via finite path integral limits: application to energy at strong coupling of the anharmonic oscillator
• Trans-series from condensates in the non-linear sigma model
• Borel resummation with low order perturbations in QCD
• Perturbative expansion of tau hadronic spectral function moments
• A new determination of higher-order QCD corrections to hadronic $\tau$ decays
• Charm and bottom quark masses from QCD moment sum rules
• Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series