| Acknowledgments |
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xii | |
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1 | (7) |
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1.1 Factorization and high-energy collisions |
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3 | (3) |
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1.2 Why we trust QCD is correct |
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6 | (1) |
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6 | (1) |
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1.4 Problems and exercises |
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7 | (1) |
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8 | (28) |
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2.1 QCD: statement of the theory |
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9 | (1) |
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10 | (6) |
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2.3 Deeply inelastic scattering |
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16 | (7) |
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23 | (5) |
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28 | (1) |
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29 | (2) |
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2.7 QCD in the full Standard Model |
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31 | (1) |
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2.8 Beyond the Standard Model |
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32 | (1) |
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2.9 Relation between fields and particles |
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33 | (3) |
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34 | (2) |
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36 | (33) |
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36 | (3) |
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39 | (6) |
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3.3 Renormalization counterterms of QCD |
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45 | (3) |
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3.4 Meaning of unit of mass, renormalization scale |
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48 | (3) |
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3.5 Renormalization group |
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51 | (3) |
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3.6 Solution of RG equations |
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54 | (4) |
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3.7 Values of RG coefficients |
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58 | (2) |
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3.8 Symmetries and approximate symmetries of QCD |
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60 | (2) |
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3.9 Dealing with quark masses |
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62 | (2) |
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3.10 CWZ (ACOT) method for heavy quarks |
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64 | (2) |
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3.11 Relating CWZ subschemes with different numbers of active quarks |
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66 | (3) |
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67 | (2) |
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4 Infra-red safety and non-safety |
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69 | (18) |
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4.1 e+e- total cross section |
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69 | (6) |
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4.2 Explicit calculations |
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75 | (6) |
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81 | (3) |
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4.4 Dispersion relation and effective virtuality of final-state quarks and gluons |
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84 | (2) |
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86 | (1) |
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86 | (1) |
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5 Libby-Sterman analysis and power-counting |
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87 | (74) |
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5.1 High-energy asymptotics and mass singularities |
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88 | (3) |
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5.2 Reduced graphs and space-time propagation |
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91 | (1) |
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5.3 Examples of general reduced graphs |
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92 | (13) |
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5.4 One-loop vertex graph |
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105 | (6) |
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5.5 Power-counting for vertex graph |
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111 | (14) |
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5.6 Which reactions have a pinch in the Glauber region? |
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125 | (5) |
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5.7 Coordinates for a PSS |
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130 | (4) |
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134 | (12) |
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5.9 Catalog of leading regions |
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146 | (2) |
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5.10 Power-counting with multiple regions |
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148 | (8) |
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5.11 Determination of Glauber-like regions |
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156 | (5) |
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158 | (3) |
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6 Parton model to parton theory: simple model theories |
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161 | (52) |
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6.1 Field theory formulation of parton model |
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161 | (9) |
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6.2 When is the parton model valid? |
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170 | (4) |
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6.3 Parton densities as operator matrix elements |
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174 | (3) |
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6.4 Consequences of rotation and parity invariance: polarization dependence |
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177 | (2) |
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6.5 Polarization and polarized parton densities in spin-1/2 target |
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179 | (1) |
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6.6 Light-front quantization |
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180 | (5) |
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6.7 Parton densities as number densities |
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185 | (5) |
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6.8 Unintegrated parton densities |
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190 | (1) |
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6.9 Properties of parton densities |
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190 | (11) |
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6.10 Feynman rules for pdfs |
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201 | (1) |
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6.11 Calculational examples |
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202 | (11) |
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210 | (3) |
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7 Parton theory: further development |
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213 | (30) |
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7.1 DIS with weak interactions, neutrino scattering, etc. |
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213 | (4) |
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7.2 Light-front perturbation theory |
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217 | (8) |
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7.3 Light-front wave functions |
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225 | (2) |
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7.4 Light-front quantization in gauge theories |
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227 | (2) |
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7.5 Parton densities in gauge theories |
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229 | (6) |
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7.6 Feynman rules for gauge-invariant parton densities |
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235 | (2) |
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7.7 Interpretation of Wilson lines within parton model |
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237 | (6) |
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241 | (2) |
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8 Factorization for DIS, mostly in simple field theories |
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243 | (41) |
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8.1 Factorization: overall view |
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243 | (2) |
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8.2 Elementary treatment of factorization |
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245 | (6) |
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8.3 Renormalization of parton densities |
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251 | (10) |
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8.4 Renormalization group, and DGLAP equation |
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261 | (1) |
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8.5 Moments and Mellin transform |
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262 | (1) |
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8.6 Sum rules for parton densities and DGLAP kernels, including in QCD |
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263 | (1) |
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8.7 Renormalization calculations: model theory |
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264 | (5) |
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8.8 Successive approximation method |
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269 | (2) |
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8.9 Derivation of factorization by ladder method |
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271 | (5) |
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8.10 Factorization formula for structure functions |
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276 | (4) |
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8.11 Transverse-spin dependence at leading power? |
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280 | (4) |
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282 | (2) |
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9 Corrections to the parton model in QCD |
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284 | (29) |
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284 | (1) |
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9.2 Projections onto structure functions |
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284 | (1) |
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285 | (1) |
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9.4 One-loop renormalization calculations in QCD |
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286 | (7) |
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9.5 One-loop renormalization by subtraction of asymptote |
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293 | (2) |
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9.6 DIS on partonic target |
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295 | (1) |
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9.7 Computation of NLO gluon coefficient function |
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296 | (4) |
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9.8 Choice of renormalization scale μ |
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300 | (1) |
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9.9 NLO quark coefficient |
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301 | (5) |
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9.10 Hard scattering with quark masses |
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306 | (1) |
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9.11 Critique of conventional treatments |
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307 | (2) |
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9.12 Summary of known higher-order corrections |
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309 | (1) |
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310 | (3) |
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312 | (1) |
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10 Factorization and subtractions |
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313 | (85) |
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314 | (6) |
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10.2 Simple example of subtraction method |
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320 | (1) |
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321 | (2) |
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10.4 Region approximator TR for Sudakov form factor |
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323 | (7) |
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10.5 One-loop Sudakov form factor |
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330 | (15) |
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10.6 Rationale for definition of TR |
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345 | (6) |
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10.7 General derivation of region decomposition |
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351 | (8) |
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10.8 Sudakov form factor factorization: first version |
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359 | (15) |
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10.9 Factorization in terms of unsubtracted factors |
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374 | (1) |
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374 | (4) |
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10.11 Sudakov: redefinition of factors |
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378 | (10) |
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10.12 Calculations for Sudakov problem |
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388 | (5) |
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10.13 Deduction of some non-leading logarithms |
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393 | (1) |
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10.14 Comparisons with other work |
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394 | (4) |
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395 | (3) |
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11 DIS and related processes in QCD |
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398 | (28) |
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398 | (1) |
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11.2 Regions and PSSs, with uncut hadronic amplitude |
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399 | (5) |
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11.3 Factorization for DIS |
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404 | (7) |
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11.4 Renormalization of parton densities, DGLAP evolution |
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411 | (1) |
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11.5 DIS with weak interactions |
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412 | (1) |
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11.6 Polarized DIS, especially transverse polarization |
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412 | (1) |
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413 | (2) |
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415 | (1) |
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11.9 Ward identities to convert K gluons to Wilson line |
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416 | (10) |
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425 | (1) |
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12 Fragmentation functions: e+e- annihilation to hadrons, and SIDIS |
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426 | (53) |
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12.1 Structure-function analysis of one-particle inclusive cross section |
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427 | (2) |
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12.2 Statement of factorization etc. for e+e_ → h(p) + X |
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429 | (3) |
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432 | (1) |
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12.4 Introduction to fragmentation functions |
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433 | (6) |
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12.5 Leading regions and issues in a gauge theory |
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439 | (5) |
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12.6 Which gauge to use in a proof? |
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444 | (3) |
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12.7 Unitarity sum over jets/sum over cuts |
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447 | (1) |
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12.8 Factorization for e+e- → h(p) + X in gauge theory |
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448 | (13) |
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12.9 Use of perturbative calculations |
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461 | (1) |
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12.10 One-loop renormalization of fragmentation function |
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461 | (3) |
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12.11 One-loop coefficient functions |
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464 | (1) |
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12.12 Non-perturbative effects and factorization |
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465 | (1) |
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466 | (4) |
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12.14 Semi-inclusive deeply inelastic scattering |
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470 | (5) |
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12.15 Target fragmentation region: fracture functions |
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475 | (4) |
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477 | (2) |
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479 | (61) |
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13.1 Overview of two-particle-inclusive e+e- annihilation |
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479 | (2) |
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13.2 Kinematics, coordinate frames, and structure functions |
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481 | (4) |
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485 | (6) |
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491 | (3) |
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13.5 Initial version of factorization with TMD fragmentation |
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494 | (1) |
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13.6 Factorization and transverse coordinate space |
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495 | (1) |
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13.7 Final version of factorization for e+e- annihilation |
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496 | (5) |
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13.8 Evolution equations for TMD fragmentation functions |
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501 | (1) |
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13.9 Flavor dependence of CS and RG evolution |
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502 | (1) |
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13.10 Analysis of CS kernel K: perturbative and non-perturbative |
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503 | (4) |
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13.11 Relation of TMD to integrated fragmentation function |
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507 | (6) |
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13.12 Correction term for large qhr |
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513 | (1) |
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13.13 Using TMD factorization |
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514 | (5) |
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13.14 NLO calculation of TMD fragmentation function at small bT and at large kT |
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519 | (7) |
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13.15 SIDIS and TMD parton densities |
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526 | (6) |
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13.16 Polarization issues |
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532 | (1) |
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13.17 Implications of time-reversal invariance |
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533 | (7) |
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537 | (3) |
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14 Inclusive processes in hadron-hadron collisions |
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540 | (33) |
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540 | (2) |
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14.2 Drell-Yan process: kinematics etc. |
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542 | (3) |
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14.3 Glauber region example |
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545 | (8) |
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14.4 Factorization for Drell-Yan |
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553 | (9) |
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14.5 TMD pdfs and Drell-Yan process |
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562 | (7) |
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14.6 Calculations with initial-state partons |
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569 | (1) |
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14.7 Production of hadrons |
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570 | (3) |
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571 | (2) |
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15 Introduction to more advanced topics |
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573 | (9) |
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15.1 Light-front wave functions and exclusive scattering at large momentum transfer |
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574 | (1) |
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15.2 Exclusive diffraction: generalized parton densities |
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574 | (1) |
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15.3 Small-x, BFKL, perturbative Regge physics |
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575 | (1) |
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576 | (1) |
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15.5 Methods for efficient high-order calculations |
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577 | (1) |
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15.6 Monte-Carlo event generators |
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577 | (1) |
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578 | (1) |
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579 | (1) |
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15.9 Soft-collinear effective theory (SCET) |
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579 | (1) |
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15.10 Higher twist: power corrections |
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580 | (2) |
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Appendix A Notations, conventions, standard mathematical results |
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582 | (13) |
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582 | (1) |
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A.2 Units, and conversion factors |
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582 | (1) |
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A.3 Acronyms and abbreviations |
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583 | (1) |
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A.4 Vectors, metric, etc. |
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584 | (1) |
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A.5 Renormalization group (RG) |
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584 | (1) |
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A.6 Lorentz, vector, color etc. sub- and superscripts |
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585 | (1) |
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A.7 Polarization and spin |
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585 | (1) |
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586 | (1) |
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A.9 States, cross sections, integrals over particle momentum |
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587 | (1) |
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A.10 Dirac, or gamma, matrices |
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587 | (1) |
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588 | (1) |
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A.12 Dimensional regularization and MS: basics |
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589 | (1) |
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A.13 Dimensional regularization: standard integrals |
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590 | (1) |
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A.14 Properties of Γ function |
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591 | (1) |
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A.15 Plus distributions, etc. |
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591 | (1) |
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592 | (1) |
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A.17 Orders of magnitude, estimation, etc. |
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592 | (3) |
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Appendix B Light-front coordinates, rapidity, etc. |
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595 | (5) |
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595 | (1) |
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596 | (1) |
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596 | (2) |
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598 | (1) |
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B.5 Rapidity distributions in high-energy collisions |
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598 | (2) |
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Appendix C Summary of primary results |
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600 | (3) |
| References |
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603 | (14) |
| Index |
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617 | |
Lisainfo e-raamatute kohta