# Fundamentals of Electroweak Theory

### Distributed for Karolinum Press, Charles University

This monograph of Prof. Horejší is based on a series of his lectures which took place at Faculty of Mathematics and Physics of Charles University during 1990s. The author gives a thorough and easy-to-read account of the basic principles of the standard model of electroweak interactions, describes various theories of electromagnetic and weak interactions, and explains the gauge theory of electroweak interactions. Five appendices expound on some special techniques of the Standard Model, used in the main body of the text. Thanks to the author's pedagogical skills and professional erudition, the book can be read just with a preliminary knowledge of quantum field theory.

Preface

Conventions and notation

1 Beta decay

1.1 Kinematics

1.2 Fermi theory

1.3 Generalization of Fermi theory and parity violation

1.4 The electron energy spectrum

1.5 The e - v angular correlation

1.6 Longitudinal polarization of electrons

1.7 Neutrino helicity

1.8 The V and A coupling constants

1.9 Mean lifetime of the neutron

Problems

2 Universal V - A theory 52

2.1 Two-component neutrino

2.2 Left-handed chiral leptons

2.3 Muon decay

2.4 Universal interaction of V - A currents

2.5 Cabibbo angle and selection rules for strangeness

2.6 Pion decays into leptons

2.7 Beta decay of charged pion

2.8 Nucleon matrix elements of the weak current

2.9 C,P and CP

Problems

3 Intermediate vector boson W

3.1 Difficulties of Fermi-type theory

3.2 The case for intermediate vector boson

3.3 Difficulties of the simple IVB model

3.4 Electromagnetic interactions of W bosons

3.5 The case for electroweak unification

Problems

4 Gauge invariance and Yang-Mills field

4.1 Abelian gauge invariance

4.2 Non-Abelian gauge invariance

Problems

5 Electroweak unification and gauge symmetry

5.1 SU(2) x C7(l) gauge theory for leptons

5.2 Charged current weak interaction

5.3 Electromagnetic interaction

5.4 Unification condition and W boson mass

5.5 Weak neutral currents

5.6 Low energy neutrino-electron scattering

5.7 Interactions of vector bosons

5.8 Cancellation of leading divergences

Problems

6 Higgs mechanism for masses

6.1 Residual divergences: need for scalar bosons

6.2 Goldstone model

6.3 Abelian Higgs model

6.4 Higgs mechanism for SU(2) x [7(1) gauge theory

6.5 Higgs boson interactions

6.6 Yukawa couplings and lepton masses

6.7 Higgs-Yukawa mechanism and parity violation

6.8 Custodial symmetry

6.9 Non-standard Higgs multiplets

Problems

7 Standard model of electroweak interactions

7.1 Leptonic world - brief recapitulation

7.2 Difficulties with three quarks

7.3 Fourth quark and GIM construction

7.4 GIM construction

7.5 Kobayashi-Maskawa matrix

7.6 R-gauges

7.7 Gauge independence of scattering amplitudes

7.8 Equivalence theorem for longitudinal vector bosons

7.9 Effects of ABJ anomaly

7.10 Synopsis of the GWS standard model

Problems

A Dirac equation and its solutions

B Scattering amplitudes, cross sections and decay rates

C Beta decay of polarized neutron

D Massive vector bosons

E Basics of the ABJ anomaly

References

Bibliography

Index

**Physical Sciences: **
Physics and Astronomy

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