Preface ..................................................... ix
1 Introduction: basics of QCD perturbation theory .............. 1
1.1 The QCD Lagrangian ...................................... 1
1.2 A review of Feynman rules for QCD ....................... 3
1.2.1 QCD Feynman rules ................................ 6
1.3 Rules of light cone perturbation theory ................. 7
1.3.1 QCD LCPT rules .................................. 10
1.3.2 Light cone wave function ........................ 12
1.4 Sample LCPT calculations ............................... 14
1.4.1 LCPT "cross-check" .............................. 14
1.4.2 A sample light cone wave function ............... 17
1.5 Asymptotic freedom ..................................... 19
2 Deep inelastic scattering ................................... 22
2.1 Kinematics, cross section, and structure functions ..... 22
2.2 Parton model and Bjorken scaling ....................... 27
2.2.1 Warm-up: DIS on a single free quark ............. 27
2.2.2 Full calculation: DIS on a proton ............... 29
2.3 Space-time structure of DIS processes .................. 38
2.4 Violation of Bjorken scaling; the Dokshitzer-Gribov-
Lipatov-Altarelli-Parisi evolution equation ............ 43
2.4.1 Parton distributions ............................ 43
2.4.2 Evolution for quark distribution ................ 45
2.4.3 The DGLAP evolution equations ................... 53
2.4.4 Gluon-gluon splitting function .................. 56
2.4.5 General solution of the DGLAP equations ......... 60
2.4.6 Double logarithmic approximation ................ 63
Further reading ............................................. 72
Exercises ................................................... 72
3 Energy evolution and leading logarithm-1/x approximation
in QCD ...................................................... 74
3.1 Paradigm shift ......................................... 74
3.2 Two-gluon exchange: the Low-Nussinov pomeron ........... 76
3.3 The Balitsky-Fadin-Kuraev-Lipatov evolution equation ... 82
3.3.1 Effective emission vertex ....................... 83
3.3.2 Virtual corrections and reggeized gluons ........ 88
3.3.3 The BFKL equation ............................... 92
3.3.4 Solution of the BFKL equation ................... 95
3.3.5 Bootstrap property of the BFKL equation* ....... 103
3.3.6 Problems of BFKL evolution: unitarity and
diffusion ...................................... 107
3.4 The nonlinear Gribov-Levin-Ryskin and Mueller-Qiu
evolution equation .................................... 112
3.4.1 The physical picture of parton saturation ...... 112
3.4.2 The GLR-MQ equation ............................ 115
Further reading ............................................ 121
Exercises .................................................. 121
4 Dipole approach to high parton density QCD ................. 123
4.1 Dipole picture of DIS ................................. 123
4.2 Glauber-Gribov-Mueller multiple-rescatterings
formula ............................................... 129
4.2.1 Scattering on one nuclйon ...................... 130
4.2.2 Scattering on many nuclйons .................... 133
4.2.3 Saturation picture from the GGM formula ........ 139
4.3 Mueller' s dipole model ............................... 141
4.3.1 Dipole wave function and generating
functional ..................................... 141
4.3.2 The BFKL equation in transverse coordinate
space .......................................... 153
4.3.3 The general solution of the coordinate-space
BFKL equation .................................. 159
4.4 The Balitsky-Kovchegov equation ....................... 163
4.5 Solution of the Balitsky-Kovchegov equation ........... 172
4.5.1 Solution outside the saturation region;
extended geometric scaling ..................... 172
4.5.2 Solution inside the saturation region;
geometric scaling .............................. 176
4.5.3 Semiclassical solution ......................... 178
4.5.4 Traveling wave solution ........................ 181
4.5.5 Numerical solutions ............................ 184
4.5.6 Map of high energy QCD ......................... 188
4.6 The Bartels-Kwiecinski-Praszalowicz equation .......... 189
4.7 The odderon ........................................... 192
Further reading ............................................ 195
Exercises .................................................. 196
5 Classical gluon fields and the color glass condensate ...... 198
5.1 Strong classical gluon fields: the McLerran-
Venugopalan model ..................................... 198
5.1.1 The key idea of the approach ................... 198
5.1.2 Classical gluon field of a single nucleus ...... 200
5.1.3 Classical gluon distribution ................... 205
5.2 The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-
Kovner evolution equation ............................. 215
5.2.1 The color glass condensate (CGC) ............... 215
5.2.2 Derivation of JIMWLK evolution ................. 216
5.2.3 Obtaining BK from JIMWLK and the Balitsky
hierarchy ...................................... 224
Further reading ............................................ 226
Exercises .................................................. 226
6 Corrections to nonlinear evolution equations ............... 228
6.1 Why we need higher-order corrections .................. 228
6.2 Running-coupling corrections to the BFKL, BK, and
JIMWLK evolutions ..................................... 229
6.2.1 An outline of the running-coupling
calculation .................................... 230
6.2.2 Impact of running coupling on small-x
evolution ...................................... 235
6.2.3 Nonperturbative effects and renormalons ........ 240
6.3 The next-to-leading order BFKL and BK equations ....... 242
6.3.1 Short summary of NLO calculations .............. 243
6.3.2 Renormalization-group-improved NLO approach .... 245
Further reading ............................................ 248
Exercises .................................................. 249
7 Diffraction at high energy ................................. 250
7.1 General concepts ...................................... 250
7.1.1 Diffraction in optics .......................... 250
7.1.2 Elastic scattering and inelastic diffraction ... 253
7.2 Diffractive dissociation in DIS ....................... 255
7.2.1 Low-mass diffraction ........................... 256
7.2.2 Nonlinear evolution equation for high-mass
diffraction .................................... 262
Further reading ............................................ 270
Exercises .................................................. 271
8 Particle production in high energy QCD ..................... 272
8.1 Gluon production at the lowest order .................. 272
8.2 Gluon production in DIS and pA collisions ............. 274
8.2.1 Quasi-classical gluon production ............... 274
8.2.2 Including nonlinear evolution .................. 284
8.3 Gluon production in nucleus-nucleus collisions ........ 290
Further reading ............................................ 291
Exercises .................................................. 292
9 Instead of conclusions ..................................... 293
9.1 Comparison with experimental data ..................... 293
9.1.1 Deep inelastic scattering ..................... 294
9.1.2 Proton(deuteron)-nucleus collisions ............ 295
9.1.3 Proton-proton and heavy ion collisions ......... 297
9.2 Unsolved theoretical problems .......................... 303
Further reading ............................................ 306
Appendix A: Reference formulas ................................ 307
A.l Dirac matrix element tables ........................... 307
A.2 Some useful integrals ................................. 307
A.3 Another useful integral ............................... 310
Appendix B: Dispersion relations, analyticity, and
unitarity of the scattering amplitude ...................... 312
B.l Crossing symmetry and dispersion relations ............ 312
B.2 Unitarity and the Froissart-Martin bound .............. 316
References ................................................. 319
Index ...................................................... 336
|
