Handbook of perturbative QCD George Sterman, John Smith, John C. Collins, James Whitmore, Raymond Brock, Joey Huston, Jon Pumplin, Wu-Ki Tung, Hendrik Weerts, Chien-Peng Yuan, Stephen Kuhlmann, Sanjib Mishra, Jorge G. Morf´ın, Fredrick Olness, Joseph Owens, Jianwei Qui, Davison E. Soper Handbook of perturbative QCD Version 1.0 The CTEQ Collaboration George Sterman and John Smith Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840 John C. Collins and James Whitmore Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802-6300 Raymond Brock, Joey Huston, Jon Pumplin, Wu-Ki Tung, Hendrik Weerts, and Chien-Peng Yuan Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1116 Stephen Kuhlmann Argonne National Laboratory, Argonne, Illinois 60439-4815 Sanjib Mishra Department of Physics, Harvard University, Cambridge, Massachusetts 02138 Jorge G. Morf´ın Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 Fredrick Olness Department of Physics, Southern Methodist University, Dallas, Texas 75275-0175 Joseph Owens Department of Physics, Florida State University, Tallahassee, Florida 32306-3016 Jianwei Qui Department of Physics, Iowa State University, Ames, Iowa 50011-3160 Davison E. Soper Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403 The elements, theoretical basis, and experimental status of perturbative quantum chromodynamics are pre- sented. Relevant field-theoretic methods are introduced at a nonspecialist level, along with a review of the basic ideas and methods of the parton model. This is followed by an account of the fundamental theorems of quantum chromodynamics, which generalize the parton model. Summaries of the theoretical and exper- imental status of the most important hard-scattering processes are then given, including electron-positron annihilation, deeply inelastic scattering, and hard hadron-hadron scattering, as induced both by electroweak interactions and by quantum chromodynamics directly. In addition, a discussion is presented of the global fitting approach to the determination of parton distributions in nucleons. 2 Contents I. Introduction 12 II. Field Theory Background 16 A. Lagrangian . 16 B. Feynman Rules and Green Functions . 18 C. From Green Functions to Experiment . 20 1. The S-matrix and Cross Sections . 20 2. UV Divergences, Renormalization and Schemes . 22 3. The Renormalization Scale and Experiment . 24 D. Asymptotic Freedom . 25 1. Forces in QCD and QED . 25 2. The Renormalization Group and the Effective Coupling . 29 E. Quark Masses . 31 F. Infrared Safety . 33 III. The Parton Model: Fundamental Cross Sections 34 A. Overview; heuristic justification . 34 B. Lepton-Hadron Cross Sections . 36 1. Deeply inelastic scattering kinematics. 36 2. Cross Sections and Parton Distributions . 40 + C. e e− Annihilation . 45 1. Total cross section . 45 2. Single-hadron inclusive annihilation . 46 3. Jet Cross Sections . 48 D. Drell-Yan Production . 48 E. O(ααs) Processes . 51 F. The Parton Model and Experiment . 52 1. Deeply Inelastic Scattering . 53 a. Scaling: . 53 b. Quarks as Partons: . 53 c. The charge ratio: . 54 d. Quark number sum rules: . 54 2. Electron-positron Annihilation into Hadrons . 54 a. Total cross-section and scaling . 54 b. Two-jet final states as evidence for underlying partons . 55 c. Angular distribution and spin of the parton . 55 3. Lepton-pair Production (Drell-Yan Process) . 55 a. Scaling: . 55 b. Color factor: . 56 3 c. Cross-section ratios: . 56 d. Angular distribution of the leptons: . 56 4. Other Hard Processes . 56 IV. Perturbative QCD: Fundamental Theorems 57 + A. Infrared Safety in e e− Annihilation . 57 1. Total Cross Section . 57 + 2. Other infrared safe quantities in e e− annihilation . 59 B. Factorization Theorems in Deeply Inelastic Scattering . 60 1. Factorization for structure functions . 61 2. Factorization Schemes . 63 3. Evolution . 64 C. Other Factorization Theorems . 69 1. Drell-Yan . 69 2. Single-Particle Inclusive Cross Sections . 71 D. Operator Definitions of Parton Distribution and Fragmentation Functions . 72 1. Quark Distribution Functions . 72 2. Gluon Distribution Functions . 73 3. Fragmentation Functions . 74 + V. e e− Annihilation 75 A. Total Cross Section . 75 + B. e e− Total Cross Section at One Loop . 77 C. Energy-Energy Correlation . 80 D. Jets . 82 E. Calculations . 83 VI. Deeply Inelastic Scattering 85 A. Use of Perturbative Corrections in DIS . 85 B. One-Loop Corrections in DIS . 86 1. MS scheme . 86 2. DIS scheme . 88 C. Two-Loop Corrections . 88 D. Computation of One-Loop DIS Correction . 89 E. Review of DIS Experiments . 92 1. Historical perspective . 92 2. The Experiments . 94 3. Outstanding Issues in DIS . 95 F. Experimental Status of Parton Distributions . 95 1. General Features . 95 a. Quark Densities from ν-H Scattering . 95 4 b. Valence Quark Densities in the Proton . 96 c. Valence Quark Densities in an Isoscalar Target . 96 d. Antiquark Densities in an Isoscalar Target . 98 e. Strange Quark Content of an Isoscalar Nucleon Sea . 98 2. Evolution . 99 a. Measurements of R(x; Q2) versus QCD . 99 b. Evolution of Non-singlet Structure Function . 100 c. Determination of ΛQCD .......................... 102 d. Evolution of Singlet Structure Function . 104 G. Status of DIS Sum Rules . 104 1. Introduction . 104 2. Gross-Llewellyn Smith Sum Rule . 110 3. Adler Sum Rule . 111 4. Gottfried Sum Rule . 113 5. Bjorken Sum Rule . 116 VII. Electroweak-Induced Hard Hadron-Hadron Cross Sections 119 A. Hard-Scattering Corrections in the Drell-Yan Cross Section; O(αs) corrections . 119 B. Drell-Yan at Two Loops . 123 C. Drell-Yan Cross Sections: Experimental Review . 124 1. Massive Photon Production . 125 a. General experimental techniques . 125 b. New quarks . 126 c. Nucleon distributions . 126 d. Pion distributions . 126 e. Scaling . 127 f. The K-factor . 127 2. W and Z Production . 128 a. General experimental techniques . 129 b. Running of αs ............................... 129 D. Direct Photons: Theory . 130 E. Direct Photon Production: Experiment . 132 c. Reconstruction . 133 d. Conversion . 133 e. Profiles . 134 f. Isolation . 134 g. Experiments . 135 5 VIII. QCD-induced Hard Hadron-Hadron Cross Sections 138 A. Jet Production in Hadron Collisions . 138 1. Cone.