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Particle Physics Leif J¨Onsson

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Particle Physics Leif J¨Onsson Lectures in Particle physics Autumn 2010, updated 2012 Leif Jonsson¨ [email protected] Acknowledgements: I am indebted to Hannes Jung for many contributions during the preparatory phase of these lecture notes. In the continous process of upgrading and improv- ing the content I have profited very much from discussions and suggestions by Cecilia Jarlskog, Magnus Hansson, Albert Knutsson and Sakar Osman. All mistakes are entirely my responsibil- ity. Contents 1 Introduction 5 1.1 Units in High Energy Physics . ....................... 8 1.2 Resolving Fundamental Particles . ....................... 9 1.3 Relativity ..................................... 9 1.3.1 Lorentz Transformation . ....................... 10 1.3.2 Velocity Addition . ....................... 11 1.3.3 Momentum and Mass . ....................... 12 1.3.4 Energy . .............................. 14 1.3.5 More Relations .............................. 15 1.3.6 Example of Time Dilation: The Muon Decay . ............ 16 1.3.7 Four Vectors . .............................. 16 1.3.8 Invariant mass .............................. 17 1.3.9 Reference systems . ....................... 18 2 Quantum Mechanics 20 2.1 The Photoelectric Effect . ....................... 20 2.2 The Schr¨odinger Equation . ....................... 20 2.3 The Double Slit Experiment (Interference Effects) ................ 22 2.4 The Uncertainty Principle . ....................... 23 2.5 Spin . ..................................... 25 2.6 Conservation Laws . .............................. 26 2.6.1 Leptons and Lepton Number ....................... 26 2.6.2 Parity . .............................. 31 2.6.3 Helicity . .............................. 33 2.7 The Klein-Gordon Equation . ....................... 33 2.7.1 The Continuity Equation . ....................... 35 2.8 Antiparticles: The Hole Theory and Feynmans Interpretation . ..... 36 2.9 The Dirac Equation . .............................. 37 2.10 Strangeness . .............................. 38 2.11 Isospin (Isotopic spin) ............................... 43 2 3 The Forces of Nature 47 3.1 Vacuum and Virtual Particles . ....................... 49 3.2 Electromagnetic Interaction and QED . ................ 49 3.2.1 Feynamn Diagrams . ....................... 50 3.2.2 Electromagnetic Scattering Processes . ................ 50 3.2.3 Calculation of scattering amplitudes . ................ 52 3.2.4 Differential Cross Section . ....................... 54 3.2.5 Higher Order Contributions to ee Scattering . ............ 57 3.2.6 Regularization and Renormalization................... 57 3.2.7 Summary of Amplitude Calculations . ................ 60 3.2.8 Pair Production and Annihilation . ................ 60 3.2.9 Compton Scattering . ....................... 63 3.3 Weak Interaction . .............................. 64 3.3.1 Some Other Examples of Weak Decays . ................ 66 3.3.2 Properties of the Weak Force Mediators . ................ 67 3.3.3 The Electroweak Theory of Weinberg and Salam ............ 69 3.3.4 The Higgs Mechanism . ....................... 71 3.3.5 Electroweak Interaction With Quarks . ................ 76 3.3.6 Quark Mixing . .............................. 78 3.3.7 The Prediction of the Charm Quark . ................ 81 3.4 Experimental Discoveries of Particles . ................ 84 3.4.1 Resonance Particles . ....................... 84 3.4.2 Significance . .............................. 84 3.4.3 The Experimental Discovery of Charm . ................ 85 3.4.4 Charmed Particles . ....................... 87 3.4.5 The Discovery of the tau-lepton . ................ 87 3.4.6 The Discovery of the b-quark ....................... 88 3.4.7 The Discovery of the t-quark ....................... 89 3.4.8 The discovery of Higgs? . ....................... 93 3.5 Are There More Families? . ....................... 97 3.6 Strong Interactions . .............................. 98 3.6.1 More Feynman Diagrams . ....................... 102 3.6.2 Asymptotic Freedom and Confinement . ................ 103 3.6.3 Unification of the Forces . ....................... 105 3.6.4 Hadronization . .............................. 105 3.6.5 Jets . .............................. 108 3.6.6 Testing QCD . .............................. 109 4 Deep Inelastic Scattering 114 4.1 Kinematics . .............................. 114 4.2 The Behaviour of the Structure Function . ................ 116 4.3 Scaling . ..................................... 118 4.4 Scaling Violation . .............................. 119 4.5 Charged Current Processes . ....................... 122 4.6 Comparison of Neutral and Charged Current Processes . ............ 123 5 Extensions of the Standard Model 125 5.1 Grand Unified Theories .............................. 125 5.2 Supersymmetry (SUSY) . ....................... 127 5.3 String Theories . .............................. 131 6 Experimental Methods 135 6.1 Accelerators . .............................. 135 6.1.1 Linear Accelerators . ....................... 136 6.1.2 Circular Accelerators . ....................... 137 6.2 Colliders . ..................................... 138 6.2.1 Circular Colliders . ....................... 138 6.2.2 Linear Colliders . ....................... 140 6.3 Collision Rate and Luminosity . ....................... 141 6.4 Secondary Beams................................. 142 6.5 Detectors ..................................... 144 6.5.1 Scintillation Counters . ....................... 144 6.5.2 Tracking Chambers . ....................... 145 6.5.3 Calorimeters . .............................. 153 6.6 Particle Identification . .............................. 156 6.6.1 Time of Flight .............................. 157 6.6.2 Ionization Measurement . ....................... 157 6.6.3 Cherenkov Radiation . ....................... 158 7 Cosmology 160 7.1 Formation of Galaxies .............................. 162 7.2 The Creation of a Star . .............................. 163 7.3 The Death of a Star . .............................. 163 8 Appendix A 165 4 Chapter 1 Introduction The aim of particle physics is to find the basic building blocks of matter and to understand how they are bound together by the forces of nature. This would help us to understand how the Universe was created. The definition of the basic building blocks, or elementary particles, is that they have no inner structure; they are pointlike particles. At the end of the 19th century it was generally believed that matter was built out of a few fundamental types of atoms. However, in the beginning of 1900 over 90 different varieties of atoms were known, which was an uncomfortably large number for considering the atom to be fundamental. Already in the late 1890’s J.J. Thompson found that by applying an electric field between two electrodes, contained in a cathod ray tube, electrons were emitted when the cathod was heated. This was the first indication that the atoms are not indivisable and led Thompson to propose what was called the ’plum pudding’ model, in which the electrons are evenly dis- tributed in a soup of positive charge. Around the same time W. R¨ontgen found that a new form of penetrating radiation was emitted if a beam of electrons was brought to hit a piece of matter. The radiation, which was called X-rays, was proven to be electromagnetic radiation but with a wavelength much shorter than visible light. In France H. Becquerel together with P. and M. Curie observed that a radiation with properties similar to X-rays were emitted spontaneously from a piece of Uranium. In the beginning of the 20th century the cloud chamber, or expansion chamber, was developed. It causes condensation of a supersaturated vapour into drops along the path of an ionizing particle passing through the gas volume of the detector. This happens as a result of an adiabatic expansion by which the temperature of the vapour decreases and droplets are grown by condensation along the particle track. The cloud chamber enabled more accurate studies of this radition and revealed that there were three different types of radiation; α-particles, β-radiation and γ-radiation. The α-particles turned out to be identical to He4 nu- clei, the γ- radiation is electromagnetic radiation with even shorter wavelenths than X-rays and β-radiation is simlply electrons. The discovery of radioactivity opened up the possibility to per- form more systematic studies of matter. Thus, in 1911 E. Rutherford set up an experiment were α-particles from a radioactive source were allowed to hit a thin gold foil and the deflection of the α-particles was observed. From the unexpectedly large deflection of some of the α-particles he concluded that the positive charge of the atom had to be concentrated to a small volume (10−15 meter) in the centre of the atom and that the electrons were orbiting around this nucleus, defining the size of the atom to 10−10 meter. This can be regarded as the start of modern parti- cle physics. The discovery of Rutherford led to the atomic model of Niels Bohr who realized 5 that the nucleus of the atom must contain positively charged particles, protons. In 1932 James Chadwick discovered a new particle with no charge and with a mass close to the proton mass, the neutron. The neutron provided the explanation to why, for example, helium is four times as heavy as hydrogen and not just twice as heavy, as could be assumed if the nucleus contained only protons. Up to the point where the particle accelerators were developed the research was performed using cosmic rays and radioactive elements as particle sources. A historical review of the
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