FUNDAMENTALS OF ELECTROWEAK THEORY SECOND EDITION

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FUNDAMENTALS
OF ELECTROWEAK THEORY
SECOND EDITION
Jiˇr´ı Hoˇrejˇs´ı
jiri.horejsi@mff.cuni.cz
Institute of Particle and Nuclear Physics
Faculty of Mathematics and Physics
Charles University
Prague
2022
arXiv:2210.04526v1 [hep-ph] 10 Oct 2022
Abstract
The present text is an updated version of an earlier author’s book on the electroweak
theory (published originally in 2002, ISBN 80-246-0639-9). It reflects the ultimate
completion of the standard model by the long-awaited discovery of the Higgs boson
(ten years after the first edition) and incorporates also some minor corrections of the
previous text, removing typos, etc. As regards an immediate motivation to come up
with such an update of the original rather old book, the 10th anniversary of the Higgs
boson discovery seems to be an opportune moment for doing it now. The publication
of the current upgraded text within the e-print arXiv is aimed at its best possible
availability for any interested reader.
CONTENTS
Preface to second edition 6
Preface to first edition 7
Conventions and notation 10
1 Beta decay 11
1.1 Kinematics ................................. 11
1.2 Fermitheory................................. 13
1.3 Generalization of Fermi theory and parity violation . . . . . . . . . . . 17
1.4 The electron energy spectrum . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 The e−¯νangularcorrelation ....................... 26
1.6 Longitudinal polarization of electrons . . . . . . . . . . . . . . . . . . . 29
1.7 Neutrinohelicity .............................. 34
1.8 The Vand Acouplingconstants...................... 36
1.9 Mean lifetime of the neutron . . . . . . . . . . . . . . . . . . . . . . . . 40
Problems ..................................... 42
2 Universal V−Atheory 44
2.1 Two-component neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2 Left-handed chiral leptons . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3 Muondecay................................. 48
2.4 Universal interaction of V−Acurrents.................. 53
2.5 Cabibbo angle and selection rules for strangeness . . . . . . . . . . . . 55
2.6 Pion decays into leptons . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.7 Beta decay of charged pion . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.8 Nucleon matrix elements of the weak current . . . . . . . . . . . . . . . 72
2.9 C,Pand CP ................................. 76
Problems ..................................... 79
3 Intermediate vector boson W82
3.1 Difficulties of Fermi-type theory . . . . . . . . . . . . . . . . . . . . . . 82
3.2 The case for intermediate vector boson . . . . . . . . . . . . . . . . . . 87
3
CONTENTS 4
3.3 Difficulties of the simple IVB model . . . . . . . . . . . . . . . . . . . . 93
3.4 Electromagnetic interactions of Wbosons ................ 96
3.5 The case for electroweak unification . . . . . . . . . . . . . . . . . . . . 100
Problems ..................................... 104
4 Gauge invariance and Yang–Mills field 105
4.1 Abelian gauge invariance . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 Non-Abelian gauge invariance . . . . . . . . . . . . . . . . . . . . . . . 108
Problems ..................................... 114
5 Electroweak unification and gauge symmetry 115
5.1 SU(2) ×U(1) gauge theory for leptons . . . . . . . . . . . . . . . . . . 115
5.2 Charged current weak interaction . . . . . . . . . . . . . . . . . . . . . 119
5.3 Electromagnetic interaction . . . . . . . . . . . . . . . . . . . . . . . . 120
5.4 Unification condition and Wbosonmass ................. 123
5.5 Weakneutralcurrents ........................... 125
5.6 Low energy neutrino-electron scattering . . . . . . . . . . . . . . . . . . 126
5.7 Interactions of vector bosons . . . . . . . . . . . . . . . . . . . . . . . . 131
5.8 Cancellation of leading divergences . . . . . . . . . . . . . . . . . . . . 133
Problems ..................................... 137
6 Higgs mechanism for masses 140
6.1 Residual divergences: need for scalar bosons . . . . . . . . . . . . . . . 140
6.2 Goldstonemodel .............................. 143
6.3 AbelianHiggsmodel ............................ 148
6.4 Higgs mechanism for SU(2) ×U(1) gauge theory . . . . . . . . . . . . 154
6.5 Higgs boson interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.6 Yukawa couplings and lepton masses . . . . . . . . . . . . . . . . . . . 163
6.7 Higgs–Yukawa mechanism and parity violation . . . . . . . . . . . . . . 167
6.8 Custodialsymmetry ............................ 169
6.9 Non-standard Higgs multiplets . . . . . . . . . . . . . . . . . . . . . . . 174
Problems ..................................... 177
7 Standard model of electroweak interactions 179
7.1 Leptonic world – brief recapitulation . . . . . . . . . . . . . . . . . . . 179
7.2 Difficulties with three quarks . . . . . . . . . . . . . . . . . . . . . . . . 181
7.3 Fourth quark and GIM construction . . . . . . . . . . . . . . . . . . . . 184
7.4 GIMconstruction.............................. 187
7.5 Kobayashi–Maskawa matrix . . . . . . . . . . . . . . . . . . . . . . . . 194
7.6 R-gauges................................... 201
7.7 Gauge independence of scattering amplitudes . . . . . . . . . . . . . . . 209
7.8 Equivalence theorem for longitudinal vector bosons . . . . . . . . . . . 214
7.9 EffectsofABJanomaly .......................... 220
7.10 Synopsis of the GWS standard model . . . . . . . . . . . . . . . . . . . 228
Problems ..................................... 239
CONTENTS 5
Epilogue 243
A Dirac equation and its solutions 244
B Scattering amplitudes, cross sections and decay rates 257
C Beta decay of polarized neutron 267
D Massive vector bosons 270
E Basics of the ABJ anomaly 280
References 287
Bibliography 292
Index 296
摘要：

FUNDAMENTALSOFELECTROWEAKTHEORYSECONDEDITIONJirHorejsjiri.horejsi@m .cuni.czInstituteofParticleandNuclearPhysicsFacultyofMathematicsandPhysicsCharlesUniversityPrague2022AbstractThepresenttextisanupdatedversionofanearlierauthor'sbookontheelectroweaktheory(publishedoriginallyin2002,ISBN80-246-0...

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