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The Standard Model in the Making : Precision Study of the Electroweak Interactions - Dima Bardin

The Standard Model in the Making

Precision Study of the Electroweak Interactions


Published: 1st October 1999
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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 processesp. 1
QED Lagrangian, U (1) invariance and Feynman rulesp. 1
The processes e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -], e[superscript +]e[superscript -]p. 2
The Born cross-sectionsp. 4
Polarized fermionsp. 6
A list of QED one-loop diagramsp. 9
Photonic self-energyp. 10
Fermionic self-energyp. 10
QED vertexp. 11
QED box diagramsp. 15
Renormalization in QEDp. 17
The basic approach to renormalizationp. 17
On-shell versus MS renormalization in QEDp. 23
Parameter renormalization and the S-matrix: the GMS frameworkp. 32
Renormalization and scale behaviourp. 35
Gauge dependence and renormalizationp. 39
The dispersion relation for hadronic vacuum polarizationp. 41
One-loop corrections and bremsstrahlung in e[superscript +]e[superscript -] [right arrow] ffp. 42
Soft bremsstrahlungp. 43
The treatment of infrared divergencesp. 44
Hard bremsstrahlungp. 49
Final state QED corrections with realistic cutsp. 51
Large logarithmic corrections in QEDp. 55
Kinematics and cross-section for a 2 [right arrow] 2 processp. 56
The structure function approachp. 57
The flux-function or radiator approachp. 61
Initial state bremsstrahlung correctionsp. 65
The angular distributionp. 65
The integrated angular distributionp. 67
Initial-final interference correctionsp. 68
The inclusion of resonancesp. 71
General introductionp. 71
Radiative corrections for the spin 1 resonant statep. 71
General basis and notationp. 71
Initial state radiative corrections to narrow resonancesp. 73
Folding with the energy resolution functionp. 74
Determination of the width in the presence of radiative correctionsp. 78
Parameters for a resonance with [Gamma] [double greater-than sign] [sigma subscript E]p. 79
More on radiative corrections for a resonancep. 81
Soft photon approximationp. 81
Leading QED corrections around a resonancep. 85
The mixed and non-QED box diagramsp. 86
The box and soft photon corrections. Cancellation of infrared divergencesp. 89
Forward-backward asymmetryp. 91
An inventory of QED corrections for a resonancep. 91
Vacuum polarization and vertex correctionsp. 92
Bremsstrahlung correctionsp. 92
YFS exponentiationp. 96
Bhabha scattering in the presence of a resonancep. 98
Helicity formalismp. 101
Polarization for spin = 1/2 particlesp. 102
The example of e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript - gamma]p. 105
The Minimal Standard Model Lagrangianp. 109
Electroweak Lagrangian and Feynman rulesp. 109
Lagrangian buildingp. 109
Tadpolesp. 119
The QCD Lagrangian and running parametersp. 120
The QCD Lagrangianp. 120
The MS scheme and the running parametersp. 121
The four-loop improvementp. 125
Appendix: Feynman rules for verticesp. 126
Muon decayp. 132
Introduction: muon lifetimep. 132
Bremsstrahlung in muon decayp. 133
Virtual QED correctionsp. 137
Total QED correctionsp. 139
Two-loop QED correctionsp. 140
The Minimal Standard Model at one-loopp. 141
Scalar integrals, vectorial and tensorial reductionp. 141
One-point integrals, A-functionsp. 141
Two-point integrals, B-functionsp. 143
Derivatives of B-functionsp. 147
Three-point integrals, C-functionsp. 149
Four-point integrals, D-functionsp. 158
a, b, c[superscript (j)], d[superscript (j)]-functionsp. 166
Two-point scalar functions for complex p[superscript 2]p. 175
Bosonic self-energies and related topicsp. 175
Vector-vector self-energiesp. 177
Scalar-scalar self-energiesp. 181
Scalar-vector transitionsp. 187
A summary of resultsp. 189
Self-energy diagrams in the unitary gaugep. 196
A summary of results in the unitary gaugep. 199
Ward identities for self-energies and transitionsp. 200
Appendix: total self-energies in the R[subscript xi] gaugep. 203
Appendix: auxiliary functions for self-energy diagramsp. 208
[xi] = 1 gaugep. 208
R[subscript xi] gaugep. 209
Unitary gaugep. 212
Appendix: Bosonic self-energies and transitionsp. 213
Fermion self-energy in the Standard Modelp. 221
Fermionic self-energies in the [xi] = 1 gaugep. 222
Fermionic self-energies in the R[subscript xi] gaugep. 223
Fermionic self-energies in the unitary gaugep. 224
Fermion wave-function renormalizationp. 224
The b-quark wave-function renormalizationp. 229
The Standard Model Vff verticesp. 231
Vff vertices in the 't Hooft-Feynman gauge and in the massless limitp. 232
The m[subscript t]-dependent part in [xi] = 1p. 238
The Hbb vertex in [xi] = 1p. 239
Q[superscript 2] = 0 limit of [xi] = 1 vertex correctionsp. 241
Infrared-divergent form factorsp. 241
The Vff vertices in the R[subscript xi] and unitary gaugesp. 242
[gamma]ff-diagramsp. 244
Zff-diagramsp. 247
Wff-diagramsp. 249
Hff-diagramsp. 253
Limiting cases: Q[superscript 2] [right arrow] 0p. 255
Taylor expansions for Q[superscript 2] [right arrow] 0p. 255
[gamma]ff diagramsp. 256
Zff-diagramsp. 257
Wff-diagramsp. 257
Appendix: the Standard Model vertices: V,S [right arrow] f[subscript 1]f[subscript 2]p. 258
(Z, A) verticesp. 258
W verticesp. 259
H verticesp. 260
Box diagrams for f[subscript 1]f[subscript 2] [right arrow] f[subscript 3]f[subscript 4]p. 261
General definitionsp. 261
Calculation of a box diagram in the [xi] = 1 gaugep. 263
A library of boxes for NC-processesp. 267
A library of boxes for CC processesp. 272
Appendix: Box diagrams for e[superscript +]e[superscript -] [right arrow] ffp. 276
One-loop renormalization in the Standard Modelp. 277
Introductionp. 277
Preludep. 279
The OMS schemesp. 279
The GMS schemep. 285
Vector boson wave-function renormalizationp. 286
Fermion wave-function renormalizationp. 290
Equivalence to the OMS schemep. 292
Renormalization with unstable particlesp. 293
Fermion-loop approximation: massless fermionsp. 294
Fermion-loop approximation: finite top massp. 295
Running couplingsp. 295
Transition to the line-shape frameworkp. 300
One-loop renormalization of the electric chargep. 302
Electric charge renormalization: the [xi] = 1 gaugep. 302
Electric charge renormalization: the R[subscript xi] gaugep. 306
The OMS scheme in the unitary gaugep. 308
Muon decayp. 309
Muon decay: the [xi] = 1 gaugep. 310
Muon decay: the R[subscript xi] gaugep. 314
Towards a choice of the input parameter setp. 315
One-loop in the GMS frameworkp. 317
Renormalization equations and their solutionp. 319
The Z-propagatorp. 321
Large effects in radiative correctionsp. 322
Dyson re-summed propagatorsp. 325
Re-summation of large corrections: basicsp. 328
Re-summation: improvementsp. 331
The W massp. 339
What to use for M[subscript w] in loopsp. 341
M[subscript w] and the LEP2 IPSp. 344
Vector boson propagators in the t-channelp. 345
The observable [Delta]rp. 347
The observable [Delta]r in the unitary gaugep. 349
The gauge invariance of [Delta]r and its calculation in the [xi] = 1 gaugep. 353
Re-summation of large correctionsp. 353
[Delta]r in the standard MS schemep. 355
One-loop renormalization and CKM mixingp. 358
Gauge parameter dependence: the building blocksp. 361
Tadpoles, M[subscript H], renormalization and all thatp. 367
[Delta]r and screening theoremp. 370
One-loop neutral current amplitudesp. 372
The partial widths of the Z bosonp. 372
The partial widths of Z in the GMS approachp. 373
The partial widths of Z in the OMS approachp. 380
The process e[superscript +]e[superscript -] [right arrow] ffp. 389
The Born amplitude and diagramsp. 390
The amplitude in the GMS approachp. 391
The amplitude in the OMS approachp. 397
Higher-order electroweak and QCD correctionsp. 408
Higher-order correctionsp. 408
Two-loop, heavy-top correctionsp. 408
Two-loop leading correction for Zbb vertexp. 410
Mixed two-loop, QCD-weak correctionsp. 410
Two-loop self-energiesp. 411
Mixed QCD corrections in the OMS schemep. 413
Mixed two-loop effects in the Z [right arrow] bb vertexp. 414
More on QCD corrections to [Delta rho]p. 415
Light quark production and QCD radiationp. 416
Sub-leading two-loop heavy-top correctionsp. 417
Implementation of two-loop EW corrections within GMS approachp. 420
Implementation of two-loop EW corrections within the OMS approachp. 422
Assessment of the theoretical precisionp. 425
Parametric uncertaintiesp. 425
Theoretical uncertaintiesp. 426
Appendix: The two-loop, sub-leading ingredientsp. 430
Appendix: Auxiliary functions for sub-leading correctionsp. 433
Applications for LEP1/SLC phenomenologyp. 435
The pseudo-observablesp. 435
Pseudo-observables and experimental datap. 440
Fitting the experimental datap. 441
Realistic observablesp. 444
The final state radiation of pairs in e[superscript +]e[superscript -] annihilationp. 448
Hadron radiationp. 451
A summary of corrections to Z decay into l[superscript +]l[superscript -]p. 454
The initial state radiation of pairsp. 455
One-loop corrected partial widths of the W bosonp. 459
The partial widths of W in the GMS approachp. 459
QED corrections: the massless approachp. 460
QCD correctionsp. 468
The partial widths of W in the OMS approachp. 469
One-loop corrections to the W decay amplitude in the unitary gaugep. 469
The gauge invariance of the W decay amplitudep. 471
The OMS W width in one-loop approximationp. 472
One-loop corrected H partial widthsp. 474
Introductionp. 474
The H fermionic partial widths in the GMS approachp. 475
QED correctionsp. 475
Full electroweak corrections in the GMS schemep. 478
The H fermionic partial widths in the OMS approachp. 481
One-loop corrections to the H decay amplitudep. 481
The OMS H width in the one-loop approximationp. 483
The decay H [right arrow] ttp. 484
QCD correctionsp. 485
The H partial width into ZZp. 489
The H partial widths into [gamma gamma](gg)p. 493
A summary of results for the MSM Higgs bosonp. 495
QCD corrections for two-fermion productionp. 496
QCD and the Z decayp. 496
QCD radiator functionsp. 500
Dimensional regularization and [gamma subscript 5]p. 501
An inventory of QCD radiator functionsp. 503
The cross-section e[superscript +]e[superscript -] [right arrow] ff and QCDp. 505
QCD corrections for the forward-backward asymmetryp. 506
Production of on-shell vector (scalar) bosonsp. 509
Introductionp. 509
Born processes, e[superscript +]e[superscript -] [right arrow] W[superscript +]W[superscript -], ZZ, [gamma]Z, [gamma gamma], HZp. 511
Lowest order Ward identitiesp. 513
Lowest order helicity amplitudesp. 513
Narrow width approximationp. 516
One-loop corrections for e[superscript +]e[superscript -] [right arrow] VVp. 518
Introductionp. 518
Triple gauge boson couplingsp. 518
Ward identities for trilinear couplingsp. 520
Properties of the operatorsp. 522
The trilinear couplings made explicitp. 524
Renormalization: all the ingredientsp. 527
The wave-function of a vector bosonp. 527
Treatment of internal fermion propagatorsp. 528
Complete and over-complete basesp. 530
Renormalization of the annihilation diagramsp. 534
Renormalization at [characters not reproducible] ([alpha])p. 535
The Complete Loop frameworkp. 536
Renormalization: back to the GMS schemep. 540
Renormalization of the conversion diagramsp. 545
Off-shell [gamma](Z) e[superscript +]e[superscript -] and Wev verticesp. 545
A digression: e[superscript +]e[superscript -] [right arrow] H[gamma]p. 553
The off-shell e[superscript +]e[superscript -] H vertexp. 556
Renormalization: e[superscript +]e[superscript -] [right arrow] HZp. 557
High-energy limit of vertex correctionsp. 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] WWp. 564
Infrared limit of virtual corrections in e[superscript +]e[superscript -] [right arrow] WWp. 569
The infrared limit of vertex diagramsp. 570
The infrared limit of the box diagramsp. 572
Appendix: complete collection of bosonic verticesp. 576
Appendix: Infrared limit of box diagramsp. 583
The annihilation e[superscript +]e[superscript -] [right arrow] ff away from the Z-resonancep. 587
Introductionp. 587
Pair production away from the Z-resonancep. 588
Realistic distributions away from the Z-resonancep. 591
Four-fermion production in e[superscript +]e[superscript -] annihilationp. 597
Introductionp. 597
A classification of four-fermion processesp. 597
Observables in four-fermion productionp. 601
The fully extrapolated setupp. 601
The deterministic approachp. 608
Gauge invariance and the width of a vector bosonp. 617
More Ward identitiesp. 623
The Fermion-Loop scheme and its applicationsp. 627
A determination of the W boson massp. 633
Introductionp. 633
Semi-leptonic channel lv [right arrow] qqp. 635
Fully-hadronic channel qq [right arrow] qqp. 638
The CKM matrixp. 643
Phenomenology of the MSM Higgs bosonp. 644
Introductionp. 644
The strategy of the calculationp. 647
Theoretical uncertaintiesp. 648
The Higgs signal and its backgroundp. 650
Numerical results and commentsp. 652
Appendix: some useful formulasp. 662
Bibliographp. 669
Indexp. 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