Introduction to particle physics Part IV

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