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Quarks, Partons and Quantum Chromodynamics

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Quarks, Partons and Quantum Chromodynamics Quarks, partons and Quantum Chromodynamics A course in the phenomenology of the quark-parton model and Quantum Chromodynamics 1 Jiˇr´ıCh´yla Institute of Physics, Academy of Sciences of the Czech Republic Abstract The elements of the quark-parton model and its incorporation within the framework of perturbative Quantum Chromodynamics are laid out. The development of the basic concept of quarks as fundamental constituents of matter is traced in considerable detail, emphasizing the interplay of experimental observations and their theoretical interpretation. The relation of quarks to partons, invented by Feynman to explain striking phenomena in deep inelastic scattering of electrons on nucleons, is explained. This is followed by the introduction into the phenomenology of the parton model, which provides the basic means of communication between experimentalists and theorists. No systematic exposition of the formalism of quantized fields is given, but the essential differences of Quantum Chromodynamics and the more familiar Quantum Electrodynamics are pointed out. The ideas of asymptotic freedom and quark confinement are introduced and the central role played in their derivation by the color degree of freedom are analyzed. Considerable attention is paid to the physical interpretation of ultraviolet and infrared singularities in QCD, which lead to crucial concepts of the “running” coupling constant and the jet, respectively. Basic equations of QCD–improved quark–parton model are derived and the main features of their solutions dis- cussed. It is argued that the “pictures” taken by modern detectors provide a compelling evidence for the interpretation of jets as traces of underlying quark–gluon dynamics. Finally, the role of jets as tools in searching for new phenomena is illustrated on several examples of recent important discoveries. 1Available at http://www-hep.fzu.cz/ chyla/lectures/text.pdf 1 Contents 1 Introduction 7 1.1Whataretheselecturesallabout?................................. 7 1.2Rutherfordexperiment........................................ 8 1.3Bohrmodelofatom......................................... 10 1.4Scatteringexperimentandtheconceptofcross-section...................... 10 1.5Scatteringinnonrelativisticclassicalphysics............................ 12 1.6 Scattering in nonrelativistic quantum physics . 14 1.7Scatteringonboundsystems.................................... 15 1.8Exercises............................................... 16 2 Elements of groups and algebras 17 2.1Definitionsandbasicfacts...................................... 17 2.2Liegroupsandalgebras....................................... 19 2.3SU(2)groupandalgebra....................................... 21 2.4ApplicationofSU(2)group:theisospin.............................. 23 2.5WeightsandrootsofcompactLiealgebras............................. 25 2.6SimplerootsofsimpleLiealgebras................................. 28 2.7ExamplesoffurtherimportantmultipletsofSU(3)........................ 32 2.7.1 Sextet............................................. 33 2.7.2 Octet............................................. 33 2.7.3 Decuplet............................................ 34 2.7.4 Otherproductsandmultiplets............................... 34 2.8Exercises............................................... 34 3 The road to quarks 36 3.1Whatarethenucleimadeof,whatforcesholdthemtogether?................. 36 3.1.1 Electronswithinnuclei.................................... 36 3.1.2 Firstglimpseofnuclearforce................................ 37 3.1.3 Birthofthe“new”quantummechanics.......................... 38 3.1.4 Pauliandneutrinohypothesis................................ 38 3.1.5 1932-34: three years that changed all . 40 3.1.6 1935-1938: final touches . 42 3.2 1938-1947: decade of uncertainty . 43 3.3 1947-1955: strange discovery and its consequences . 43 3.4 1956-1960: paving the eightfold way . 47 3.5 1961-1964: from resonances to quarks . 50 4 Quark Model 54 4.1 January 1964: birth of the quark model . 54 4.2Quarkswithflavorandspin:theSU(6)symmetry........................ 56 4.3Spinstructureofthebaryons.................................... 61 4.4TheZweigrule............................................ 62 4.5ProblemsandpuzzlesoftheQuarkModel............................. 62 4.6 Color to the rescue: Quasinuclear colored model of hadrons . 64 2 4.7Thearrivalofcharm......................................... 66 4.8Tobeornottobe?.......................................... 71 4.9Loneatthetop............................................ 73 4.10Exercises............................................... 74 5 Elements of the parton model 75 5.1Kinematics.............................................. 75 5.2Dynamics............................................... 76 5.3*Cross–sectionsofvirtualphotons................................. 81 5.4Electronsastoolsforinvestigatingnuclearstructure....................... 83 5.5Probingthestructureofprotonbyelasticepscattering..................... 84 5.6 What does the deep inelastic scattering of electrons tell us about the structure of nucleons? . 85 5.7Emergenceofthepartonmodel................................... 90 5.8Partondistributionfunctionsandtheirbasicproperties..................... 93 5.9Partonmodelinneutrinointeractions............................... 96 5.10Polarizednucleonstructurefunctions................................100 5.11 Space–time picture of DIS and hadronization . 101 5.12 Deep inelastic scattering at small x .................................103 5.13Exercises...............................................103 6 Parton model in other processes 106 6.1 Electron-positron annihilations into hadrons at high energies . 106 6.2Drell-Yanproductionofheavydileptonpairs...........................109 6.3Exercises...............................................111 7 Basics of Quantum Chromodynamics 112 7.1Theriseandfallofquantumfieldtheory..............................112 7.2Anditsremarkableresurrection...................................114 7.3Maxwellequationsinthecovariantform..............................116 7.4Commentsonthebasicideaandconceptsofgaugetheories...................117 7.5Elementarycalculations.......................................123 7.5.1 Quark-quarkscattering...................................123 7.5.2 Quark-gluonscattering....................................124 7.5.3 Gluon-gluonscattering....................................125 7.5.4 Comparison of different parton subprocesses . 126 7.6Exercises...............................................127 8 Ultraviolet renormalization – basic ideas and techniques 128 8.1 *Infinities in perturbative calculations . 128 8.2*RenormalizationinQED......................................129 8.2.1 Electricchargerenormalization...............................129 8.2.2 *Photonwavefunctionrenormalization..........................137 8.2.3 *Renormalization of the electron mass . 138 8.2.4 *Vertexrenormalization...................................141 8.3 Elements of dimensional regularization . 142 8.3.1 Asimpleexample......................................142 8.3.2 Feynmanparametrization..................................146 8.3.3 Momentumintegralsandrelatedformulae.........................146 8.3.4 DimensionalregularizationinQEDandQCD.......................147 8.3.5 *Renormalization at one loop level and the technique of counterterms . 149 8.4*RenormalizationinQCD......................................150 8.4.1 *Higher orders, IR fixed points and consistency of perturbation theory. 153 8.4.2 Quark mass thresholds in the running αs .........................155 8.4.3 *Summation of QCD perturbation expansions . 157 8.5Exercises...............................................162 3 9 Mass singularities and jets 164 9.1*Masssingularitiesinperturbationtheory.............................164 9.2*Kinoshita–Lee–Nauenbergtheorem................................167 9.3*Introductionintothetheoryofjets................................169 9.3.1 Jetalgorithms........................................170 9.3.2 Jetsofpartonsvsjetsofhadrons..............................171 9.4Exercises...............................................172 10 QCD improved quark-parton model 173 10.1Generalframework..........................................173 10.2Partonswithinpartons........................................175 10.2.1Equivalentphotonapproximation..............................175 10.2.2BranchingfunctionsinQCD................................178 10.2.3 *Multigluon emission and Sudakov formfactors of partons . 179 10.3Partonswithinhadrons.......................................181 10.3.1 Evolution equations at the leading order . 181 10.3.2Momentsofstructurefunctionsandsumrules.......................184 10.3.3 Extraction of the gluon distribution function from scaling violations . 185 10.3.4 *Evolution equations at the next-to-leading order . 186 10.3.5 *Hard scattering and the factorization theorem . 188 10.4Briefsurveyofmethodsofsolvingtheevolutionequations....................189 10.5Exercises...............................................191 11 Particle interactions as seen in modern detectors 193 11.1TheH1experimentatDESY....................................193 11.1.1 Manifestation of the jet–like structure of final states in DIS . 195 11.1.2Photoproductionofjets...................................197 11.1.3 Photoproduction of the J/ψ particle............................198 11.1.4Arealljetsalike?.......................................199 11.2TopquarkdiscoveryatFermilab..................................199 11.3Arequarkscomposite?........................................199
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