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1 Introduction to Particle Physics1

1.1 The natural System of Units1

1.2 The Planck Natural system of units4

1.3 Invariants in kinematics5

1.4 Cross sections and Luminosities7

1.4.1 Luminosity for fixed target experiments7

1.4.2 Luminosity for colliding beam experiments8

1.5 Kinematics of particle decay10

1.6 Invariants in the scattering of two particles11

1.7 Transformation properties of non invariant quantities14

2 Elements of Group Theory17

2.1 Definitions17

2.2 Matrix groups18

2.2.1 The exponential of a matrix20

2.2.2 Determination of the independent parameters23

2.3 The structure constants26

2.4 Representations27

2.4.1 The fundamental representation27

2.4.2 The adjoined representation30

2.5 Homomorphism-isomorphism32

2.6 Some further examples33

2.7 The proper orthogonal groups O(3)and O(4)35

2.8 Symmetries and conservation laws-Noether's theorem39

3 The Dirac Theory45

3.1 Preliminaries-The Klein Gordon equation45

3.2 The Dirac equation47

3.2.1 The spinors u and v49

3.2.2 Projection operators52

3.2.3 Various representations of the Dirac Matrices52

3.3 Interpretation of negative energy solutions53

3.4 The notion of helicity54

3.5 Charge conjugation for 4-spinors57

3.6 Types of currents58

4 The standard Model-Symmetry and particle content61

4.1 The essential ingredients61

4.2 The notion of a local symmetry61

4.3 Non Abelian gauge transformation63

4.3.1 Transformations associated with a non Abelian group64

4.3.2 Some Examples65

4.4 Gauge invariant Lagrangians67

4.4.1 Only gauge fields67

4.4.2 Lagrangian in the presence of scalar fields69

4.4.3 Lagrangian in the presence of fermion fields70

4.5 The particle content of the SM70

4.6 The electroweak Lagrangian71

5 The Higgs Mechanism73

5.1 The Higgs Mechanism in global gauge transformations73

5.2 The Higgs Mechanism in gauge theories79

5.3 Fundamental theorem of Higgs Mechanism87

6 The Group SU(3)-Quantum Chromodynamics89

6.1 Quantum chromodynamics QCD89

6.2 The one gluon exchange potential92

6.2.1 Proeess involving only baryons92

6.2.2 processes involving the creation of a q？ pair93

6.2.3 processes involving interaction of mesons93

6.3 Low energy formalism94

6.3.1 The orbital part at the quark level95

6.3.2 The kinetic energy part95

6.3.3 The confining potential95

6.3.4 Fitting the strength of the confining potential96

6.4 Matrix elements involving two quarks97

6.4.1 The confining potential97

6.4.2 The one gluon exchange potential97

7 Fermion Masses and Currents99

7.1 Fermion masses99

7.2 The currents103

7.2.1 The EM current105

7.2.2 The charged currents105

7.2.3 The neutral currents106

7.3 The contact interaction108

7.4 Determination of the Standard Model Parameters109

7.5 Summary110

8 Rates and Cross Sections in Electroweak Theory111

8.1 Brief review and formulae111

8.2 Decay widths and cross section112

8.2.1 The decay of a vector boson113

8.3 Muon-antimuon production in electron-positron colliders117

8.4 neutrino electron scattering120

9 Supersymmetry for Pedestrians125

9.1 Introduction125

9.2 The particle content of MSSM126

9.2.1 gauge particles126

9.2.2 Fermions and s-fermions127

9.2.3 The Higgs content127

9.3 The Higgs mechanism127

9.4 The Fermion masses130

9.5 Supersymmetry breaking132

9.6 Some remarks about the particle spectrum132

10 SU(5)An Example of Grand Unification137

10.1 Mathematical Introduction137

10.2 The structure of the GUT SU(5)137

10.3 The particle content139

10.3.1 The Fermions139

10.3.2 The gauge bosons140

10.3.3 The Higgs content141

10.4 The Higgs Mechanism141

10.5 The gauge boson masses144

10.6 Gauge couplings144

10.7 Baryon Asymmetry146

11 A Brief Introduction to Cosmology151

11.1 Cosmological Principles151

11.2 The expanding Universe-The big bang scenario151

11.2.1 The receding of galaxies152

11.2.2 The background microwave radiation155

11.2.3 The abundance of primordial 4He and other light elements in the Universe156

11.3 Evolution of the Universe157

11.4 The Cosmological Constant-Dark Energy161

11.5 The standard cosmological model164

11.6 The proper length and the horizon165

11.6.1 The proper length entering the prototype candles166

11.6.2 The horizon167

11.7 temperature168

11.7.1 The relic neutrinos170

11.8 The role of dark matter174

11.8.1 The rotational velocities174

11.8.2 Gravitational lensing178

11.8.3 The observation of bullet cluster178

11.9 Dark energy181

11.9.1 Observations with standard candles182

11.9.2 The microwave background radiation-The earliest picture of the Universe184

11.10 The WMAP and PLANCK Observations188

12 Neutrino oscillations193

12.1 Introduction193

12.2 The formalism194

12.3 Neutrino oscillation experiments196

12.4 The absolute scale of the neutrino mass203

12.5 Neutrinos as probes209

13 C,P,T and all that211

13.1 Space inversion P211

13.1.1 Parity conservation-parity violation214

13.2 The helicity of the neutrinos217

13.2.1 The determination ofthe helicity of neutrinos219

13.2.2 Weak interaction and handedness221

13.3 Charge Conjugation221

13.3.1 Charge conjugation for 4-spinors223

13.3.2 Transformation of currents224

13.3.3 Symmetry relation of the Dirac nass term224

13.3.4 Symmetry relation of the Majorana mass term225

13.3.5 The charge conjugation of composite systems225

13.3.6 How good a symmetry is the charge conjugation?226

13.4 Time reversal227

13.4.1 Time reversal in classical mechanics227

13.4.2 Time reversal in quantum mechanics229

13.4.3 Premature evidence for T violation231

13.5 CP the combined action of P and C symmetries231

13.5.1 The neutral Kaon system233

13.5.2 Strangeness oscillations236

13.5.3 Kaon regeneration236

13.5.4 CP Violation239

13.5.5 Evidence for T-violation243

13.6 The combined symmetry CPT244