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Introduction to Particle Physics: Key Concepts and Discoveries in the Field

This course, led by Professor D. Budker, explores essential topics in particle physics, including the discovery of weak neutral currents via the Gargamelle bubble chamber at CERN in 1973, particle decay, cross-sections, and the Fermi Golden Rule. It provides insights into decay probabilities, luminosity, Mandelstam variables, and constructing Feynman diagrams. With an emphasis on understanding particle interactions and fundamental principles, this presentation is an excellent resource for students and enthusiasts wanting to deepen their grasp of particle physics concepts.

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Introduction to Particle Physics: Key Concepts and Discoveries in the Field

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  1. Physics 129, Fall 2010; Prof. D. Budker Introduction to particle physicsPart IV

  2. Bubble chamber The Gargamelle at CERN: discovered weak neutral currents in 1973 Great topics for oral presenantion! Professor Donald A. Glaser Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  3. How particles decay • Decay probability goes as dt: • Particles do not age! • Board work: Mean Lifetime = 1/ • Branching Ratios • Partial decay rates add Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  4. Cross Sections • Effective area • Inclusive vs. exclusive • Elastic vs. inelastic (different reactions are called channels) • Resonances Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  5. Cross Sections • Effective area • Differential cross section Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  6. Cross Sections Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  7. Cross Sections • Some cross-sections diverge (e.g., for Rutherford scattering) • Effective cut-off Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  8. Cross Sections Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  9. Mandelstam Variables Universally used! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  10. Units of cross section Origin: Uranium nucleus 10-24 cm2---as "big as a barn" Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  11. Cross Sections • Luminosity: • number of particles in a beam per unit area per unit time Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  12. Luminosity • What about colliding beams? • Luminosity = collision frequency  n1  n2 / beam area Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  13. Luminosity Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  14. LHC luminosity: reality check Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  15. The Fermi Golden Rule • mi– mass of ith particle • pi– 4-momentum of ith particle • S– statistical factor accounting for identical particles • M– amplitude (p1, …. , pn) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  16. The Fermi Golden Rule • Kinematic constraints: • All outgoing particles are on the mass shell • All outgoing particles have positive energy • Energy & momentum conservation Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  17. The Fermi Golden Rule • 2π rules: • Every δ gets a 2π • Every d gets a 1/(2π) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  18. The Fermi Golden Rule • With the kinematic constraints, the G.R. simplifies to: • For two-body decay: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  19. The Feynman-Diagram Rules • Goal: figure out amplitude M • Draw all possible diagrams for the process • The amplitudes from different diagrams add Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  20. The Feynman-Diagram Rules • For each diagram: • Label external momentapi,label internal momentaqi,draw arrows (arbitrary for internal lines) • For each vertex, write coupling constant • Each internal line  propagator: • For each vertex: energy/momentum conservation: (minus for outgoing lines) • Add for each internal line; integrate • Erase the resulting ; multiply by • The result is M ; examples in Ch. 6 of Griffiths Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  21. Higher-order diagrams • Problem: loop integrals (logarithmically) diverge at large q • This is not because the diagrams are bad! • Regularization: introduce a heavy particle  cut-off (p. 219) • Renormalization; running coupling constants…. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  22. Example/interlude: Diagrams in Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  23. Example/interlude: Diagrams in • Vanishes for • Vanishesin the high-frequency limit Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  24. Relativistic Equations Nonrelativistic Relativistic; spin zero Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  25. The Dirac Equation (relativistic, spin ½) • Introduce 44 Dirac Matrices: Relativistic; spin 1/2 Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  26. Solving the Dirac Equation • Assume wavefunctionindependent of position: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  27. Solving the Dirac Equation • Four independent solutions: • The Dirac Sea • Plane wave solutions (Sec. 7.2) Electron  Electron  Positron  Positron  Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  28. Dirac Spinor Algebra • Some useful facts about spinors: • How do Dirac spinors transform under P? Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  29. Dirac Spinor Algebra • Introduce another matrix: What about 4 ? Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  30. Bilinear Covariants Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  31. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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