THE THEORY OF QUARK AND GLUON INTERACTIONS

By ELIZABETH CLARK

THE RATIONALE FOR QCD PERTURBATIVE EXPANSIONS; S-MATRIX AND GREEN’S FUNCTIONS; WICK’S THEOREM PATH INTEGRAL FORMULATION OF FIELD THEORY GAUGE INVARIANCE CANONICAL QUANTIZATION; GAUGE FIXING; COVARIANT GAUGES UNITARITY; LORENTZ GAUGES; GHOSTS; PHYSICAL GAUGES I COVARIANT GAUGES II PHYSICAL GAUGES THE BECCHI–ROUET–STORA TRANSFORMATIONS FUNCTIONAL FORMALISM FOR QCD GAUGE INVARIANCE INTEGRATION OF FERMIONS I GAUGE INVARIANCE GHOSTS II INTEGRATION OF FERMIONS FEYNMAN RULES IN THE PATH INTEGRAL FORMALISM THE BACKGROUND FIELD METHOD GLOBAL SYMMETRIES OF THE QCD LAGRANGIAN: CONSERVED CURRENTS REGULARIZATION (DIMENSIONAL) RENORMALIZATION: GENERALITIES RENORMALIZATION OF QCD (ONE LOOP) I µ-RENORMALIZATION II THE MINIMAL SUBTRACTION SCHEME III RENORMALIZATION IN THE BACKGROUND FIELD FORMALISM THE RENORMALIZATION GROUP THE CALLAN–SYMANZIK EQUATION RENORMALIZATION OF COMPOSITE OPERATORS THE RUNNING COUPLING CONSTANT AND THE RUNNING MASS IN QCD: ASYMPTOTIC FREEDOM HEAVY AND LIGHT QUARKS: THE DECOUPLING THEOREM E?ECTIVE NF, ? THE OPERATOR PRODUCT EXPANSION (OPE) AT SHORT DISTANCES NONPERTURBATIVE E?ECTS IN QUARK AND GLUON PROPAGATORS I SHORT DISTANCE EXPANSION II NONPERTURBATIVE E?ECTS IN QUARK AND GLUON PROPAGATORS 3 10 E?ECTIVE THEORIES FOR HEAVY QUARKS I THE FUNCTIONAL INTEGRATION METHOD II THE FOLDY–WOUTHUSEN METHOD III DISCUSSION; A SAMPLE CALCULATION; RADIATIVE CORRECTIONS E+E?ANNIHILATION INTO HADRONS ? AND Z DECAYS INVOLVING HADRONS I ? DECAY II Z DECAY KINEMATICS OF DEEP INELASTIC SCATTERING THE PARTON MODEL I KINEMATICS STRUCTURE FUNCTIONS II THE PARTON MODEL LIGHT CONE EXPANSION OF PRODUCTS OF CURRENTS THE OPE FOR DEEP INELASTIC SCATTERING IN QCD MOMENTS RENORMALIZATION GROUP ANALYSIS: THE QCD EQUATIONS FOR THE MOMENTS QCD EQUATIONS FOR THE MOMENTS TO SECOND AND HIGHER ORDERS I NONSINGLET II LONGITUDINAL STRUCTURE FUNCTION III SINGLET IV COMPARISON WITH EXPERIMENT THE ALTARELLI–PARISI, OR DGLAP, METHOD GENERAL CONSEQUENCES OF QCD FOR STRUCTURE FUNCTIONS I SUM RULES III THE LIMIT X ?0, NONSINGLET IV THE LIMIT X ?0, SINGLET V THE BFKL POMERON 4 10 TARGET MASS CORRECTIONS 4 11 NONPERTURBATIVE E?ECTS IN E+E?ANNIHILATIONS AND HIGHER TWISTS IN DEEP INELASTIC SCATTERING 4 12 MORE ABOUT COMPARISON OF DIS CALCULATIONS WITH EXPERIMENT I PARAMETRIZATIONS II EXACT RECONSTRUCTION III STRUCTURE FUNCTIONS AT SMALL X IV STRUCTURE FUNCTIONS AT SMALL X AND SMALL Q2 OZI FORBIDDEN DECAYS DRELL–YAN PROCESSES I PARTONIC FORMULATION II RADIATIVE QCD CORRECTIONS III THE K FACTOR JETS: GENERALITIES JETS IN E+E?ANNIHILATIONS I TWO JET EVENTS II THREE JET EVENTS III MULTIJET EVENTS IV GLUON JETS IN QUARKONIUM DECAYS JETS IN HADRON PHYSICS THE SVZ SUM RULES EXCLUSIVE PROCESSES OTHER PROCESSES THAT CAN BE DESCRIBED WITH PERTURBATIVE QCD I DEEP INELASTIC SCATTERING ON ?, K, ? TARGETS II STRONG INTERACTION CORRECTIONS TO WEAK AND ELECTROMAGNETIC DECAYS OF HADRONS GENERALITIES THE QUARK MODEL OF HADRONS POLE MASS AND THE SCHR¨ODINGER EQUATION CORRECTIONS I CON?NEMENT POLE MASS RELATION WITH THE MS MASS II THE SCHR¨ODINGER EQUATION LADDERS III THE STATIC POTENTIAL; RADIATIVE CORRECTIONS IV THE PNRQCD METHOD RELATIVISTIC, RADIATIVE AND NONPERTURBATIVE CORRECTIONS TO HEAVY QUARKONIUM EVALUATION OF LOWEST LYING ¯CC AND ¯BB STATES I COULOMB POTENTIAL AND RELATIVISTIC CORRECTIONS II ONE AND TWO LOOP RADIATIVE CORRECTIONS TO THE COULOMBIC POTENTIAL MIXED RADIATIVE–RELATIVISTIC CORRECTIONS III NONPERTURBATIVE CORRECTIONS IV QCD ANALYSIS OF LOWEST LYING ¯CC AND ¯BB STATES HIGHER EXCITED ¯CC AND ¯BB STATES CON?NEMENT FORCES E?ECTIVE POTENTIALS THE CONSTITUENT QUARK MODEL BAG MODELS I INTRODUCTION BOGOLIUBOV’S MODEL II THE MIT BAG MASS TERMS AND INVARIANCES: CHIRAL INVARIANCE WIGNER–WEYL AND NAMBU–GOLDSTONE REALIZATIONS OF SYMMETRIES PCAC AND LIGHT QUARK MASS RATIOS BOUNDS AND ESTIMATES OF LIGHT QUARK MASSES THE DECAY ?0 ???; THE AXIAL ANOMALY THE U(1) PROBLEM THE GLUON ANOMALY THE ? PARAMETER; THE QCD VACUUM; THE E?ECT OF MASSLESS QUARKS; SOLUTION TO THE U(1) PROBLEM CHIRAL LAGRANGIANS I THE ? MODEL II EXPONENTIAL FORMULATION CONNECTION WITH PCAC, AND A FIRST APPLICATION 7 10 CHIRAL PERTURBATION THEORY: GENERAL FORMULATION I GAUGE EXTENSION OF CHIRAL INVARIANCE II E?ECTIVE LAGRANGIANS IN THE CHIRAL LIMIT III FINITE PION MASS CORRECTIONS IV RENORMALIZED E?ECTIVE THEORY 7 11 COMPARISON OF CHIRAL PERTURBATION THEORY WITH EXPERIMENT 7 12 THE ACCURACY OF CHIRAL PERTURBATION THEORY CALCULATIONS THE WKB APPROXIMATION IN THE PATH INTEGRAL FORMALISM; TUNNELLING EUCLIDEAN QCD INSTANTONS CONNECTION WITH THE TOPOLOGICAL QUANTUM NUMBER AND THE QCD VACUUM QUARKS (AND GLUONS) ON AN EUCLIDEAN LATTICE GLUONS (AND QUARKS) ON THE LATTICE PATHS AND LOOPS THE WILSON ACTION I ABELIAN GAUGE THEORIES II QCD THE WILSON ACTION FEYNMAN RULES ON THE LATTICE RENORMALIZATION GROUP CONNECTION WITH THE CONTINUUM PARAMETERS I FEYNMAN RULES II RENORMALIZATION, AND RENORMALIZATION GROUP THE WILSON LOOP STRONG COUPLING CON?NEMENT OBSERVABLE CONSEQUENCES OF LATTICE QCD I GENERAL I WILSON LOOP; STRING TENSION; CONNECTION BETWEEN LONG AND SHORT DISTANCES II HADRONIZATION OF JETS III LOCALITY OF THE QCD VACUUM LONG DISTANCE BEHAVIOUR OF INVARIANT PROPAGATORS CONSTITUENT QUARK MASS OBSERVABLE CONSEQUENCES OF LATTICE QCD II HADRON AND QUARK MASSES; DECAY CONSTANTS I NON-GOLDSTONE HADRONS II PION PHYSICS ON THE LATTICE THE FUNCTIONS ?, ?M THE CHARACTER OF THE QCD PERTURBATIVE SERIES RENORMALIZATION SCHEME DEPENDENCE OF CALCULATIONS AND PARAMETERS RENORMALONS SATURATION I TRUNCATION AND RENORMALIZATION E?ECTS II RENORMALONS III SATURATION IV THE LIMIT OF ACCURACY OF QCD CALCULATIONS COUPLING CONSTANTS: ?, ?S, ? I THE PARAMETER ? II ? AND ?S QUARK MASSES CONDENSATES I QUARK CONDENSATES, ?¯QQ? REFERENCES