Renormalisation

Abstract

We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of gauge theories such as QCD summarising the current state of the art. We introduce the renormalisation scale setting problem in QCD and we give an illustration of the possible optimisation procedures currently in use.

28 pages, 10 figures, invited contribution to the Encyclopedia of Particle Physics

References in corpus (55)

• The four-loop beta-function in Quantum Chromodynamics
• Renormalons
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Light-Front Holographic QCD and Emerging Confinement
• The static potential in QCD to two loops
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• The static quark-antiquark potential in QCD to three loops
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Three-loop static potential
• Static QCD potential at three-loop order
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Commensurate Scale Relations in Quantum Chromodynamics
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• On the running coupling constant in QCD
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The Large Quark Mass Expansion of Gamma (Z^0 -> hadrons) and Gamma(tau^- -> nu_tau + hadrons) in the Order alpha_s^3
• The Renormalization Scale-Setting Problem in QCD
• Studies of Hadronic Event Structure in e+e- Annihilation from 30 GeV to 209 GeV with the L3 Detector
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Fermionic contributions to the three-loop static potential
• Can the QCD running coupling have a causal analyticity structure?
• A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP
• Five-loop renormalisation of QCD in covariant gauges
• Is there a Landau Pole Problem in QED?
• Measurement of alpha_s(M_Z^2) from Hadronic Event Observables at the Z^0 Resonance
• The Generalized Crewther Relation in QCD and its Experimental Consequences
• Complete renormalization of QCD at five loops
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
• Disentangling running coupling and conformal effects in QCD
• Aspects of SU(N_c) Gauge Theories in the Limit of Small Number of Colors
• Angular Distributions of Massive Quarks and Leptons Close to Threshold
• Conformal Window 2.0: The Large $N_f$ Safe Story
• Hot Conformal Gauge Theories
• Renormalization of the Vector Current in QED
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Relating Physical Observables in QCD without Scale-Scheme Ambiguity
• PMC${}_{\infty }$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
• Novel Method for the Precise Determination of the QCD Running Coupling from Event Shapes Distributions in Electron-Positron Annihilation
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Renormalization Scheme Dependence in a QCD Cross Section
• Minimal prescription corrected spectra in heavy quark decays
• Renormalization Scheme Dependence and the Renormalization Group Beta Function
• Thrust Distribution for 3-Jet Production from $e^{+}{e}^{-}$ Annihilation within the QCD Conformal Window and in QED
• Renormalization Scale Setting for Heavy Quark Pair Production in $e^{+}{e}^{-}$ Annihilation near the Threshold Region
• Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• A reanalysis of event shape distributions in electron-positron annihilation