PHYS402 01

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Published on October 16, 2007

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PHYS402: Particle Physics II:  PHYS402: Particle Physics II The Particle Physics Frontier Peter Ratoff Lancaster University Outline of the Course:  Outline of the Course Review of the Standard Model [1] Experimental Techniques [2-3] Symmetry Principles [4] Building the Standard Model [5-10] Gauge Theories and the Higgs Boson[11] Weak Mixing and CP Violation [12-13] Beyond the Standard Model [14] Outlook and Future Accelerators [15] Recommended books and sources:  Recommended books and sources Particle Physics (2nd ed) - Martin and Shaw (Wiley) we will cover most of this book during the course it is at the correct level and is an excellent reference Introduction to High Energy Physics (3rd ed) - D.H.Perkins (Addison Wesley) very good for some topics but not quite as up to date The Fundamental Particles and their Interactions - W.Rollnick (Addison Wesley) another useful source at about the right level World Wide Web - limitless source of info! CERN public pages at public.web.cern.ch/Public Fermilab public pages atwww.fnal.gov/pub/hep_descript.html Stanford Virtual Visitor Center at www2.slac.stanford.edu/vvc/home.html PHYS402: Particle Physics II:  PHYS402: Particle Physics II Lecture 1 Review of the Standard Model The Standard Model:  The Standard Model The main components of the Model are: The particles and fields Matter particles Force particles The Higgs Boson A theoretical framework Re-normalizable Yang-Mills Gauge Theory The Standard Model Lagrangian Calculational tools - Feynman Diagrams The Standard Model: Matter and Force Particles:  The Standard Model: Matter and Force Particles The Standard Model: The Higgs Boson:  The Standard Model: The Higgs Boson A direct consequence of the Higgs mechanism - the means by which the SM particles acquire mass - is the existence of a neutral scalar, the Higgs boson, with a mass M < 200 GeV This particle has not been observed and the current experimental constraint is M > 114 GeV (95% CL) Finding the Higgs boson is the primary goal of particle physics this decade! The Higgs mechanism 1:  The Higgs mechanism 1 The Physical Vacuum: The Higgs field pervades space ... The Higgs mechanism 2:  The Higgs mechanism 2 A particle moving through space ... The Higgs mechanism 3:  The Higgs mechanism 3 … acquires mass and inertia The Higgs mechanism 4:  The Higgs mechanism 4 Spontaneous symmetry breaking ... The Higgs mechanism 5:  The Higgs mechanism 5 … results in the production of Higgs bosons Yang-Mills Gauge Theory:  Yang-Mills Gauge Theory Success of QED theory in 1940’s (R.Feynman et al Nobel Prize 1965) prompted theorists to analyse mathematical properties of the theory and seek generalisation to apply to other forces  Discovery of the Gauge Principle - QED is locally gauge invariant - and renormalization (cancellation of infinities from higher-orders) Yang and Mills (1954) generalised the idea of local gauge invariance but a theory of weak interactions based on this principle was only renormalizable with massless force particles, inconsistent with the short range nature of weak interactions Electroweak unification:  Electroweak unification P.Higgs (1964) introduced the idea of spontaneous symmetry breaking permitting the construction of a theory of weak interactions with massive force particles (W bosons) In the 1960’s Weinberg, Salam and Glashow (Nobel Prize 1979) used the Higgs mechanism to construct a unified theory of weak and electromagnetic interactions, predicting the existence of Z bosons The electroweak theory was proven to be completely renormalizable in 1974 (G. t’Hooft and M.Veltman Nobel Prize 1999) The Standard Model Lagrangian:  The Standard Model Lagrangian Success of electroweak unification immediately prompted a gauge theory of the strong interaction, Quantum Chromodynamics (QCD), based on the exchange of massless coloured gluons between quarks The Standard Model is the sum of QCD and the electroweak theory which together account for the interactions of the 3 families of quarks and leptons All the interactions between the particles of the SM are specified by the Lagrangian - including the coupling strengths and dynamical properties The full SM Lagrangian contains many terms, even in the most compact notation, and covers several pages when written out in full ! Feynman Diagrams:  Feynman Diagrams The SM Lagrangian specifies the allowed interactions Calculational methods have to be developed to derive reaction cross-sections and decay rates, including higher order processes The Feynman diagrams and rules provide a simple and elegant technique for performing these calculations Examples of Feynman Diagrams:  Examples of Feynman Diagrams Electrons, Positrons and Photons lowest order higher order Feynman rules:  Feynman rules Each line and vertex has a precise mathematical meaning External legs represent amplitudes of initial and final state particles Internal lines - propagators - represent the amplitude of the exchanged force particle in momentum space (Fourier transform) Vertices represent coupling strength of interacting particles Write down all possible diagrams for a given initial/final state and sum the set of amplitudes  transition probability

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