The aim of this book is to give a comprehensive exposition of the foundations of the Standard Model and to outline their applicability to high energy phenomena. It provides an easily accessible introduction to all aspects of renormalization, the mathematical tool that has paved the way for a calculable theory of the fundamental interactions. The theory is clearly developed from the renormalizability of the Standard Model and guidance is given as to its applications to high energy phenomena. The book includes all the details needed to derive the results and collects in one place all relevant formulae, recipes and prescriptions which are needed to construct the theoretical predictions and compare them with the experimental results. This makes the book unique in its field.
' No other book offers a complete, exhaustive and authoritative description of the electroweak theory predictions for p[recision tests.All calculations are described in detail and the results are reported explicitly...the expostion is clear and only a basic knowledge of quantum field theory is assumed.Thus, the book qualifies as a complete reference handbook for this domain of contemporary physics. Those interested in the overall physical picture and the main implications of precision tests can find more-readable reviews elsewhere.However this work will be invaluable for professional theorists looking for state-of-the-art reviews' CERN Courier
Pure QED processes | p. 1 |
QED Lagrangian, U (1) invariance and Feynman rules | p. 1 |
The processes e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -], e[superscript +]e[superscript -] | p. 2 |
The Born cross-sections | p. 4 |
Polarized fermions | p. 6 |
A list of QED one-loop diagrams | p. 9 |
Photonic self-energy | p. 10 |
Fermionic self-energy | p. 10 |
QED vertex | p. 11 |
QED box diagrams | p. 15 |
Renormalization in QED | p. 17 |
The basic approach to renormalization | p. 17 |
On-shell versus MS renormalization in QED | p. 23 |
Parameter renormalization and the S-matrix: the GMS framework | p. 32 |
Renormalization and scale behaviour | p. 35 |
Gauge dependence and renormalization | p. 39 |
The dispersion relation for hadronic vacuum polarization | p. 41 |
One-loop corrections and bremsstrahlung in e[superscript +]e[superscript -] [right arrow] ff | p. 42 |
Soft bremsstrahlung | p. 43 |
The treatment of infrared divergences | p. 44 |
Hard bremsstrahlung | p. 49 |
Final state QED corrections with realistic cuts | p. 51 |
Large logarithmic corrections in QED | p. 55 |
Kinematics and cross-section for a 2 [right arrow] 2 process | p. 56 |
The structure function approach | p. 57 |
The flux-function or radiator approach | p. 61 |
Initial state bremsstrahlung corrections | p. 65 |
The angular distribution | p. 65 |
The integrated angular distribution | p. 67 |
Initial-final interference corrections | p. 68 |
The inclusion of resonances | p. 71 |
General introduction | p. 71 |
Radiative corrections for the spin 1 resonant state | p. 71 |
General basis and notation | p. 71 |
Initial state radiative corrections to narrow resonances | p. 73 |
Folding with the energy resolution function | p. 74 |
Determination of the width in the presence of radiative corrections | p. 78 |
Parameters for a resonance with [Gamma] [double greater-than sign] [sigma subscript E] | p. 79 |
More on radiative corrections for a resonance | p. 81 |
Soft photon approximation | p. 81 |
Leading QED corrections around a resonance | p. 85 |
The mixed and non-QED box diagrams | p. 86 |
The box and soft photon corrections. Cancellation of infrared divergences | p. 89 |
Forward-backward asymmetry | p. 91 |
An inventory of QED corrections for a resonance | p. 91 |
Vacuum polarization and vertex corrections | p. 92 |
Bremsstrahlung corrections | p. 92 |
YFS exponentiation | p. 96 |
Bhabha scattering in the presence of a resonance | p. 98 |
Helicity formalism | p. 101 |
Polarization for spin = 1/2 particles | p. 102 |
The example of e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript - gamma] | p. 105 |
The Minimal Standard Model Lagrangian | p. 109 |
Electroweak Lagrangian and Feynman rules | p. 109 |
Lagrangian building | p. 109 |
Tadpoles | p. 119 |
The QCD Lagrangian and running parameters | p. 120 |
The QCD Lagrangian | p. 120 |
The MS scheme and the running parameters | p. 121 |
The four-loop improvement | p. 125 |
Appendix: Feynman rules for vertices | p. 126 |
Muon decay | p. 132 |
Introduction: muon lifetime | p. 132 |
Bremsstrahlung in muon decay | p. 133 |
Virtual QED corrections | p. 137 |
Total QED corrections | p. 139 |
Two-loop QED corrections | p. 140 |
The Minimal Standard Model at one-loop | p. 141 |
Scalar integrals, vectorial and tensorial reduction | p. 141 |
One-point integrals, A-functions | p. 141 |
Two-point integrals, B-functions | p. 143 |
Derivatives of B-functions | p. 147 |
Three-point integrals, C-functions | p. 149 |
Four-point integrals, D-functions | p. 158 |
a, b, c[superscript (j)], d[superscript (j)]-functions | p. 166 |
Two-point scalar functions for complex p[superscript 2] | p. 175 |
Bosonic self-energies and related topics | p. 175 |
Vector-vector self-energies | p. 177 |
Scalar-scalar self-energies | p. 181 |
Scalar-vector transitions | p. 187 |
A summary of results | p. 189 |
Self-energy diagrams in the unitary gauge | p. 196 |
A summary of results in the unitary gauge | p. 199 |
Ward identities for self-energies and transitions | p. 200 |
Appendix: total self-energies in the R[subscript xi] gauge | p. 203 |
Appendix: auxiliary functions for self-energy diagrams | p. 208 |
[xi] = 1 gauge | p. 208 |
R[subscript xi] gauge | p. 209 |
Unitary gauge | p. 212 |
Appendix: Bosonic self-energies and transitions | p. 213 |
Fermion self-energy in the Standard Model | p. 221 |
Fermionic self-energies in the [xi] = 1 gauge | p. 222 |
Fermionic self-energies in the R[subscript xi] gauge | p. 223 |
Fermionic self-energies in the unitary gauge | p. 224 |
Fermion wave-function renormalization | p. 224 |
The b-quark wave-function renormalization | p. 229 |
The Standard Model Vff vertices | p. 231 |
Vff vertices in the 't Hooft-Feynman gauge and in the massless limit | p. 232 |
The m[subscript t]-dependent part in [xi] = 1 | p. 238 |
The Hbb vertex in [xi] = 1 | p. 239 |
Q[superscript 2] = 0 limit of [xi] = 1 vertex corrections | p. 241 |
Infrared-divergent form factors | p. 241 |
The Vff vertices in the R[subscript xi] and unitary gauges | p. 242 |
[gamma]ff-diagrams | p. 244 |
Zff-diagrams | p. 247 |
Wff-diagrams | p. 249 |
Hff-diagrams | p. 253 |
Limiting cases: Q[superscript 2] [right arrow] 0 | p. 255 |
Taylor expansions for Q[superscript 2] [right arrow] 0 | p. 255 |
[gamma]ff diagrams | p. 256 |
Zff-diagrams | p. 257 |
Wff-diagrams | p. 257 |
Appendix: the Standard Model vertices: V,S [right arrow] f[subscript 1]f[subscript 2] | p. 258 |
(Z, A) vertices | p. 258 |
W vertices | p. 259 |
H vertices | p. 260 |
Box diagrams for f[subscript 1]f[subscript 2] [right arrow] f[subscript 3]f[subscript 4] | p. 261 |
General definitions | p. 261 |
Calculation of a box diagram in the [xi] = 1 gauge | p. 263 |
A library of boxes for NC-processes | p. 267 |
A library of boxes for CC processes | p. 272 |
Appendix: Box diagrams for e[superscript +]e[superscript -] [right arrow] ff | p. 276 |
One-loop renormalization in the Standard Model | p. 277 |
Introduction | p. 277 |
Prelude | p. 279 |
The OMS schemes | p. 279 |
The GMS scheme | p. 285 |
Vector boson wave-function renormalization | p. 286 |
Fermion wave-function renormalization | p. 290 |
Equivalence to the OMS scheme | p. 292 |
Renormalization with unstable particles | p. 293 |
Fermion-loop approximation: massless fermions | p. 294 |
Fermion-loop approximation: finite top mass | p. 295 |
Running couplings | p. 295 |
Transition to the line-shape framework | p. 300 |
One-loop renormalization of the electric charge | p. 302 |
Electric charge renormalization: the [xi] = 1 gauge | p. 302 |
Electric charge renormalization: the R[subscript xi] gauge | p. 306 |
The OMS scheme in the unitary gauge | p. 308 |
Muon decay | p. 309 |
Muon decay: the [xi] = 1 gauge | p. 310 |
Muon decay: the R[subscript xi] gauge | p. 314 |
Towards a choice of the input parameter set | p. 315 |
One-loop in the GMS framework | p. 317 |
Renormalization equations and their solution | p. 319 |
The Z-propagator | p. 321 |
Large effects in radiative corrections | p. 322 |
Dyson re-summed propagators | p. 325 |
Re-summation of large corrections: basics | p. 328 |
Re-summation: improvements | p. 331 |
The W mass | p. 339 |
What to use for M[subscript w] in loops | p. 341 |
M[subscript w] and the LEP2 IPS | p. 344 |
Vector boson propagators in the t-channel | p. 345 |
The observable [Delta]r | p. 347 |
The observable [Delta]r in the unitary gauge | p. 349 |
The gauge invariance of [Delta]r and its calculation in the [xi] = 1 gauge | p. 353 |
Re-summation of large corrections | p. 353 |
[Delta]r in the standard MS scheme | p. 355 |
One-loop renormalization and CKM mixing | p. 358 |
Gauge parameter dependence: the building blocks | p. 361 |
Tadpoles, M[subscript H], renormalization and all that | p. 367 |
[Delta]r and screening theorem | p. 370 |
One-loop neutral current amplitudes | p. 372 |
The partial widths of the Z boson | p. 372 |
The partial widths of Z in the GMS approach | p. 373 |
The partial widths of Z in the OMS approach | p. 380 |
The process e[superscript +]e[superscript -] [right arrow] ff | p. 389 |
The Born amplitude and diagrams | p. 390 |
The amplitude in the GMS approach | p. 391 |
The amplitude in the OMS approach | p. 397 |
Higher-order electroweak and QCD corrections | p. 408 |
Higher-order corrections | p. 408 |
Two-loop, heavy-top corrections | p. 408 |
Two-loop leading correction for Zbb vertex | p. 410 |
Mixed two-loop, QCD-weak corrections | p. 410 |
Two-loop self-energies | p. 411 |
Mixed QCD corrections in the OMS scheme | p. 413 |
Mixed two-loop effects in the Z [right arrow] bb vertex | p. 414 |
More on QCD corrections to [Delta rho] | p. 415 |
Light quark production and QCD radiation | p. 416 |
Sub-leading two-loop heavy-top corrections | p. 417 |
Implementation of two-loop EW corrections within GMS approach | p. 420 |
Implementation of two-loop EW corrections within the OMS approach | p. 422 |
Assessment of the theoretical precision | p. 425 |
Parametric uncertainties | p. 425 |
Theoretical uncertainties | p. 426 |
Appendix: The two-loop, sub-leading ingredients | p. 430 |
Appendix: Auxiliary functions for sub-leading corrections | p. 433 |
Applications for LEP1/SLC phenomenology | p. 435 |
The pseudo-observables | p. 435 |
Pseudo-observables and experimental data | p. 440 |
Fitting the experimental data | p. 441 |
Realistic observables | p. 444 |
The final state radiation of pairs in e[superscript +]e[superscript -] annihilation | p. 448 |
Hadron radiation | p. 451 |
A summary of corrections to Z decay into l[superscript +]l[superscript -] | p. 454 |
The initial state radiation of pairs | p. 455 |
One-loop corrected partial widths of the W boson | p. 459 |
The partial widths of W in the GMS approach | p. 459 |
QED corrections: the massless approach | p. 460 |
QCD corrections | p. 468 |
The partial widths of W in the OMS approach | p. 469 |
One-loop corrections to the W decay amplitude in the unitary gauge | p. 469 |
The gauge invariance of the W decay amplitude | p. 471 |
The OMS W width in one-loop approximation | p. 472 |
One-loop corrected H partial widths | p. 474 |
Introduction | p. 474 |
The H fermionic partial widths in the GMS approach | p. 475 |
QED corrections | p. 475 |
Full electroweak corrections in the GMS scheme | p. 478 |
The H fermionic partial widths in the OMS approach | p. 481 |
One-loop corrections to the H decay amplitude | p. 481 |
The OMS H width in the one-loop approximation | p. 483 |
The decay H [right arrow] tt | p. 484 |
QCD corrections | p. 485 |
The H partial width into ZZ | p. 489 |
The H partial widths into [gamma gamma](gg) | p. 493 |
A summary of results for the MSM Higgs boson | p. 495 |
QCD corrections for two-fermion production | p. 496 |
QCD and the Z decay | p. 496 |
QCD radiator functions | p. 500 |
Dimensional regularization and [gamma subscript 5] | p. 501 |
An inventory of QCD radiator functions | p. 503 |
The cross-section e[superscript +]e[superscript -] [right arrow] ff and QCD | p. 505 |
QCD corrections for the forward-backward asymmetry | p. 506 |
Production of on-shell vector (scalar) bosons | p. 509 |
Introduction | p. 509 |
Born processes, e[superscript +]e[superscript -] [right arrow] W[superscript +]W[superscript -], ZZ, [gamma]Z, [gamma gamma], HZ | p. 511 |
Lowest order Ward identities | p. 513 |
Lowest order helicity amplitudes | p. 513 |
Narrow width approximation | p. 516 |
One-loop corrections for e[superscript +]e[superscript -] [right arrow] VV | p. 518 |
Introduction | p. 518 |
Triple gauge boson couplings | p. 518 |
Ward identities for trilinear couplings | p. 520 |
Properties of the operators | p. 522 |
The trilinear couplings made explicit | p. 524 |
Renormalization: all the ingredients | p. 527 |
The wave-function of a vector boson | p. 527 |
Treatment of internal fermion propagators | p. 528 |
Complete and over-complete bases | p. 530 |
Renormalization of the annihilation diagrams | p. 534 |
Renormalization at [characters not reproducible] ([alpha]) | p. 535 |
The Complete Loop framework | p. 536 |
Renormalization: back to the GMS scheme | p. 540 |
Renormalization of the conversion diagrams | p. 545 |
Off-shell [gamma](Z) e[superscript +]e[superscript -] and Wev vertices | p. 545 |
A digression: e[superscript +]e[superscript -] [right arrow] H[gamma] | p. 553 |
The off-shell e[superscript +]e[superscript -] H vertex | p. 556 |
Renormalization: e[superscript +]e[superscript -] [right arrow] HZ | p. 557 |
High-energy limit of vertex corrections | p. 559 |
Box diagrams for e[superscript +]e[superscript -] [right arrow] W[superscript +]W[superscript -] | p. 562 |
Soft bremsstrahlung for e[superscript +]e[superscript -] [right arrow] WW | p. 564 |
Infrared limit of virtual corrections in e[superscript +]e[superscript -] [right arrow] WW | p. 569 |
The infrared limit of vertex diagrams | p. 570 |
The infrared limit of the box diagrams | p. 572 |
Appendix: complete collection of bosonic vertices | p. 576 |
Appendix: Infrared limit of box diagrams | p. 583 |
The annihilation e[superscript +]e[superscript -] [right arrow] ff away from the Z-resonance | p. 587 |
Introduction | p. 587 |
Pair production away from the Z-resonance | p. 588 |
Realistic distributions away from the Z-resonance | p. 591 |
Four-fermion production in e[superscript +]e[superscript -] annihilation | p. 597 |
Introduction | p. 597 |
A classification of four-fermion processes | p. 597 |
Observables in four-fermion production | p. 601 |
The fully extrapolated setup | p. 601 |
The deterministic approach | p. 608 |
Gauge invariance and the width of a vector boson | p. 617 |
More Ward identities | p. 623 |
The Fermion-Loop scheme and its applications | p. 627 |
A determination of the W boson mass | p. 633 |
Introduction | p. 633 |
Semi-leptonic channel lv [right arrow] qq | p. 635 |
Fully-hadronic channel qq [right arrow] qq | p. 638 |
The CKM matrix | p. 643 |
Phenomenology of the MSM Higgs boson | p. 644 |
Introduction | p. 644 |
The strategy of the calculation | p. 647 |
Theoretical uncertainties | p. 648 |
The Higgs signal and its background | p. 650 |
Numerical results and comments | p. 652 |
Appendix: some useful formulas | p. 662 |
Bibliograph | p. 669 |
Index | p. 678 |
Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780198502807
ISBN-10: 019850280X
Series: International Series of Monographs on Physics
Audience:
Professional
Format:
Hardcover
Language:
English
Number Of Pages: 702
Published: 1st October 1999
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.8 x 17.8
x 4.6
Weight (kg): 1.4