The standard model in the making : precision study of the electroweak interactions / Dima Bardin and Giampiero Passarino.

Format:

Book

Author/Creator:

Bardin, D.

Contributor:

Passarino, G. (Giampiero)

Rosengarten Family Fund.

Series:

International series of monographs on physics (Oxford, England) ; 104.

The international series of monographs on physics ; 104

Language:

English

Subjects (All):

Standard model (Nuclear physics).

Electroweak interactions.

Physical Description:

xv, 685 pages : illustrations ; 24 cm.

Place of Publication:

Oxford : Clarendon Press ; Oxford ; New York : Oxford University Press, 1999.

Summary:

The standard model in particle physics unifies the theories of electromagnetic and weak interactions. Much work has been over the last decade, and this book describes some of the leading experimental tests of the model. It is unique in collecting in one volume all of the formulas, recipes, and prescriptions necessary for testing the theory and will be an invaluable tool as experiments move into higher energies. It aims to give a comprehensive exposition of the foundations of the Standard Model and its applications to high energy phenomena.

Contents:

1 Pure QED processes 1

1.1 QED Lagrangian, U (1) invariance and Feynman rules 1

1.2 The processes e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -], e[superscript +]e[superscript -] 2

1.2.1 The Born cross-sections 4

1.2.2 Polarized fermions 6

1.3 A list of QED one-loop diagrams 9

1.3.1 Photonic self-energy 10

1.3.2 Fermionic self-energy 10

1.3.3 QED vertex 11

1.3.4 QED box diagrams 15

1.4 Renormalization in QED 17

1.4.1 The basic approach to renormalization 17

1.4.2 On-shell versus MS renormalization in QED 23

1.4.3 Parameter renormalization and the S-matrix: the GMS framework 32

1.4.4 Renormalization and scale behaviour 35

1.4.5 Gauge dependence and renormalization 39

1.5 The dispersion relation for hadronic vacuum polarization 41

1.6 One-loop corrections and bremsstrahlung in e[superscript +]e[superscript -] [right arrow] ff 42

1.6.1 Soft bremsstrahlung 43

1.6.2 The treatment of infrared divergences 44

1.6.3 Hard bremsstrahlung 49

1.6.4 Final state QED corrections with realistic cuts 51

1.7 Large logarithmic corrections in QED 55

1.7.1 Kinematics and cross-section for a 2 [right arrow] 2 process 56

1.7.2 The structure function approach 57

1.7.3 The flux-function or radiator approach 61

1.8 Initial state bremsstrahlung corrections 65

1.8.1 The angular distribution 65

1.8.2 The integrated angular distribution 67

1.9 Initial-final interference corrections 68

2 The inclusion of resonances 71

2.2 Radiative corrections for the spin 1 resonant state 71

2.2.1 General basis and notation 71

2.2.2 Initial state radiative corrections to narrow resonances 73

2.2.3 Folding with the energy resolution function 74

2.2.4 Determination of the width in the presence of radiative corrections 78

2.2.5 Parameters for a resonance with [Gamma] [double greater-than sign] [sigma subscript E] 79

2.3 More on radiative corrections for a resonance 81

2.3.1 Soft photon approximation 81

2.3.2 Leading QED corrections around a resonance 85

2.3.3 The mixed and non-QED box diagrams 86

2.3.4 The box and soft photon corrections. Cancellation of infrared divergences 89

2.3.5 Forward-backward asymmetry 91

2.4 An inventory of QED corrections for a resonance 91

2.4.1 Vacuum polarization and vertex corrections 92

2.4.2 Bremsstrahlung corrections 92

2.4.3 YFS exponentiation 96

2.5 Bhabha scattering in the presence of a resonance 98

2.6 Helicity formalism 101

2.6.1 Polarization for spin = 1/2 particles 102

2.6.2 The example of e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript - gamma] 105

3 The Minimal Standard Model Lagrangian 109

3.1 Electroweak Lagrangian and Feynman rules 109

3.1.1 Lagrangian building 109

3.1.2 Tadpoles 119

3.2 The QCD Lagrangian and running parameters 120

3.2.1 The QCD Lagrangian 120

3.2.2 The MS scheme and the running parameters 121

3.2.3 The four-loop improvement 125

3.3 Appendix: Feynman rules for vertices 126

4 Muon decay 132

4.1 Introduction: muon lifetime 132

4.2 Bremsstrahlung in muon decay 133

4.3 Virtual QED corrections 137

4.4 Total QED corrections 139

4.5 Two-loop QED corrections 140

5 The Minimal Standard Model at one-loop 141

5.1 Scalar integrals, vectorial and tensorial reduction 141

5.1.1 One-point integrals, A-functions 141

5.1.2 Two-point integrals, B-functions 143

5.1.3 Derivatives of B-functions 147

5.1.4 Three-point integrals, C-functions 149

5.1.5 Four-point integrals, D-functions 158

5.1.6 a, b, c[superscript (j)], d[superscript (j)]-functions 166

5.1.7 Two-point scalar functions for complex p[superscript 2] 175

5.2 Bosonic self-energies and related topics 175

5.2.1 Vector-vector self-energies 177

5.2.2 Scalar-scalar self-energies 181

5.2.3 Scalar-vector transitions 187

5.2.4 A summary of results 189

5.2.5 Self-energy diagrams in the unitary gauge 196

5.2.6 A summary of results in the unitary gauge 199

5.3 Ward identities for self-energies and transitions 200

5.4 Appendix: total self-energies in the R[subscript xi] gauge 203

5.5 Appendix: auxiliary functions for self-energy diagrams 208

5.5.1 [xi] = 1 gauge 208

5.5.2 R[subscript xi] gauge 209

5.5.3 Unitary gauge 212

5.6 Appendix: Bosonic self-energies and transitions 213

5.7 Fermion self-energy in the Standard Model 221

5.7.1 Fermionic self-energies in the [xi] = 1 gauge 222

5.7.2 Fermionic self-energies in the R[subscript xi] gauge 223

5.7.3 Fermionic self-energies in the unitary gauge 224

5.7.4 Fermion wave-function renormalization 224

5.7.5 The b-quark wave-function renormalization 229

5.8 The Standard Model Vff vertices 231

5.8.1 Vff vertices in the 't Hooft-Feynman gauge and in the massless limit 232

5.8.2 The m[subscript t]-dependent part in [xi] = 1 238

5.8.3 The Hbb vertex in [xi] = 1 239

5.8.4 Q[superscript 2] = 0 limit of [xi] = 1 vertex corrections 241

5.8.5 Infrared-divergent form factors 241

5.9 The Vff vertices in the R[subscript xi] and unitary gauges 242

5.9.1 [gamma]ff-diagrams 244

5.9.2 Zff-diagrams 247

5.9.3 Wff-diagrams 249

5.9.4 Hff-diagrams 253

5.10 Limiting cases: Q[superscript 2] [right arrow] 0 255

5.10.1 Taylor expansions for Q[superscript 2] [right arrow] 0 255

5.10.2 [gamma]ff diagrams 256

5.10.3 Zff-diagrams 257

5.10.4 Wff-diagrams 257

5.11 Appendix: the Standard Model vertices: V,S [right arrow] f[subscript 1]f[subscript 2] 258

5.11.1 (Z, A) vertices 258

5.11.2 W vertices 259

5.11.3 H vertices 260

5.12 Box diagrams for f[subscript 1]f[subscript 2] [right arrow] f[subscript 3]f[subscript 4] 261

5.12.1 General definitions 261

5.12.2 Calculation of a box diagram in the [xi] = 1 gauge 263

5.12.3 A library of boxes for NC-processes 267

5.12.4 A library of boxes for CC processes 272

5.13 Appendix: Box diagrams for e[superscript +]e[superscript -] [right arrow] ff 276

6 One-loop renormalization in the Standard Model 277

6.2 Prelude 279

6.3 The OMS schemes 279

6.4 The GMS scheme 285

6.5 Vector boson wave-function renormalization 286

6.6 Fermion wave-function renormalization 290

6.6.1 Equivalence to the OMS scheme 292

6.7 Renormalization with unstable particles 293

6.7.1 Fermion-loop approximation: massless fermions 294

6.7.2 Fermion-loop approximation: finite top mass 295

6.7.3 Running couplings 295

6.7.4 Transition to the line-shape framework 300

6.8 One-loop renormalization of the electric charge 302

6.8.1 Electric charge renormalization: the [xi] = 1 gauge 302

6.8.2 Electric charge renormalization: the R[subscript xi] gauge 306

6.8.3 The OMS scheme in the unitary gauge 308

6.9 Muon decay 309

6.9.1 Muon decay: the [xi] = 1 gauge 310

6.9.2 Muon decay: the R[subscript xi] gauge 314

6.10 Towards a choice of the input parameter set 315

6.11 One-loop in the GMS framework 317

6.11.1 Renormalization equations and their solution 319

6.11.2 The Z-propagator 321

6.11.3 Large effects in radiative corrections 322

6.11.4 Dyson re-summed propagators 325

6.11.5 Re-summation of large corrections: basics 328

6.11.6 Re-summation: improvements 331

6.12 The W mass 339

6.12.1 What to use for M[subscript w] in loops 341

6.12.2 M[subscript w] and the LEP2 IPS 344

6.12.3 Vector boson propagators in the t-channel 345

6.13 The observable [Delta]r 347

6.13.1 The observable [Delta]r in the unitary gauge 349

6.13.2 The gauge invariance of [Delta]r and its calculation in the [xi] = 1 gauge 353

6.13.3 Re-summation of large corrections 353

6.13.4 [Delta]r in the standard MS scheme 355

6.14 One-loop renormalization and CKM mixing 358

6.15 Gauge parameter dependence: the building blocks 361

6.16 Tadpoles, M[subscript H], renormalization and all that 367

6.16.1 [Delta]r and screening

theorem 370

7 One-loop neutral current amplitudes 372

7.1 The partial widths of the Z boson 372

7.1.1 The partial widths of Z in the GMS approach 373

7.1.2 The partial widths of Z in the OMS approach 380

7.2 The process e[superscript +]e[superscript -] [right arrow] ff 389

7.2.1 The Born amplitude and diagrams 390

7.2.2 The amplitude in the GMS approach 391

7.2.3 The amplitude in the OMS approach 397

8 Higher-order electroweak and QCD corrections 408

8.1 Higher-order corrections 408

8.2 Two-loop, heavy-top corrections 408

8.2.1 Two-loop leading correction for Zbb vertex 410

8.3 Mixed two-loop, QCD-weak corrections 410

8.3.1 Two-loop self-energies 411

8.3.2 Mixed QCD corrections in the OMS scheme 413

8.3.3 Mixed two-loop effects in the Z [right arrow] bb vertex 414

8.3.4 More on QCD corrections to [Delta rho] 415

8.4 Light quark production and QCD radiation 416

8.5 Sub-leading two-loop heavy-top corrections 417

8.5.1 Implementation of two-loop EW corrections within GMS approach 420

8.5.2 Implementation of two-loop EW corrections within the OMS approach 422

8.6 Assessment of the theoretical precision 425

8.6.1 Parametric uncertainties 425

8.6.2 Theoretical uncertainties 426

8.7 Appendix: The two-loop, sub-leading ingredients 430

8.8 Appendix: Auxiliary functions for sub-leading corrections 433

9 Applications for LEP1/SLC phenomenology 435

9.1 The pseudo-observables 435

9.1.1 Pseudo-observables and experimental data 440

9.1.2 Fitting the experimental data 441

9.2 Realistic observables 444

9.3 The final state radiation of pairs in e[superscript +]e[superscript -] annihilation 448

9.3.1 Hadron radiation 451

9.3.2 A summary of corrections to Z decay into l[superscript +]l[superscript -] 454

9.4 The initial state radiation of pairs 455

10 One-loop corrected partial widths of the W boson 459

10.1 The partial widths of W in the GMS approach 459

10.1.1 QED corrections: the massless approach 460

10.1.2 QCD corrections 468

10.2 The partial widths of W in the OMS approach 469

10.2.1 One-loop corrections to the W decay amplitude in the unitary gauge 469

10.2.2 The gauge invariance of the W decay amplitude 471

10.2.3 The OMS W width in one-loop approximation 472

11 One-loop corrected H partial widths 474

11.2 The H fermionic partial widths in the GMS approach 475

11.2.1 QED corrections 475

11.2.2 Full electroweak corrections in the GMS scheme 478

11.3 The H fermionic partial widths in the OMS approach 481

11.3.1 One-loop corrections to the H decay amplitude 481

11.3.2 The OMS H width in the one-loop approximation 483

11.3.3 The decay H [right arrow] tt 484

11.4 QCD corrections 485

11.5 The H partial width into ZZ 489

11.6 The H partial widths into [gamma gamma](gg) 493

11.6.1 A summary of results for the MSM Higgs boson 495

12 QCD corrections for two-fermion production 496

12.1 QCD and the Z decay 496

12.2 QCD radiator functions 500

12.3 Dimensional regularization and [gamma subscript 5] 501

12.4 An inventory of QCD radiator functions 503

12.5 The cross-section e[superscript +]e[superscript -] [right arrow] ff and QCD 505

12.6 QCD corrections for the forward-backward asymmetry 506

13 Production of on-shell vector (scalar) bosons 509

13.2 Born processes, e[superscript +]e[superscript -] [right arrow] W[superscript +]W[superscript -], ZZ, [gamma]Z, [gamma gamma], HZ 511

13.2.1 Lowest order Ward identities 513

13.2.2 Lowest order helicity amplitudes 513

13.3 Narrow width approximation 516

14 One-loop corrections for e[superscript +]e[superscript -] [right arrow] VV 518

14.2 Triple gauge boson couplings 518

14.2.1 Ward identities for trilinear couplings 520

14.2.2 Properties of the operators 522

14.2.3 The trilinear couplings made explicit 524

14.3 Renormalization: all the ingredients 527

14.3.1 The wave-function of a vector boson 527

14.3.2 Treatment of internal fermion propagators 528

14.4 Complete and over-complete bases 530

14.5 Renormalization of the annihilation diagrams 534

14.5.1 Renormalization at [characters not reproducible] ([alpha]) 535

14.5.2 The Complete Loop framework 536

14.5.3 Renormalization: back to the GMS scheme 540

14.6 Renormalization of the conversion diagrams 545

14.6.1 Off-shell [gamma](Z) e[superscript +]e[superscript -] and Wev vertices 545

14.7 A digression: e[superscript +]e[superscript -] [right arrow] H[gamma] 553

14.7.1 The off-shell e[superscript +]e[superscript -] H vertex 556

14.8 Renormalization: e[superscript +]e[superscript -] [right arrow] HZ 557

14.9 High-energy limit of vertex corrections 559

14.10 Box diagrams for e[superscript +]e[superscript -] [right arrow] W[superscript +]W[superscript -] 562

14.11 Soft bremsstrahlung for e[superscript +]e[superscript -] [right arrow] WW 564

14.12 Infrared limit of virtual corrections in e[superscript +]e[superscript -] [right arrow] WW 569

14.12.1 The infrared limit of vertex diagrams 570

14.12.2 The infrared limit of the box diagrams 572

14.13 Appendix: complete collection of bosonic vertices 576

14.14 Appendix: Infrared limit of box diagrams 583

15 The annihilation e[superscript +]e[superscript -] [right arrow] ff away from the Z-resonance 587

15.2 Pair production away from the Z-resonance 588

15.3 Realistic distributions away from the Z-resonance 591

16 Four-fermion production in e[superscript +]e[superscript -] annihilation 597

16.2 A classification of four-fermion processes 597

16.3 Observables in four-fermion production 601

16.3.1 The fully extrapolated setup 601

16.3.2 The deterministic approach 608

16.4 Gauge invariance and the width of a vector boson 617

16.4.1 More Ward identities 623

16.5 The Fermion-Loop scheme and its applications 627

17 A determination of the W boson mass 633

17.2 Semi-leptonic channel lv [right arrow] qq 635

17.3 Fully-hadronic channel qq [right arrow] qq 638

17.3.1 The CKM matrix 643

18 Phenomenology of the MSM Higgs boson 644

18.2 The strategy of the calculation 647

18.3 Theoretical uncertainties 648

18.4 The Higgs signal and its background 650

18.5 Numerical results and comments 652.

Notes:

Includes bibliographical references (pages [669]-677) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

019850280X

OCLC:

41266148