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

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

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;

4. Cross Sections Effective area Inclusive vs. exclusive
Elastic vs. inelastic (different reactions are called channels)
Resonances
Physics 129, Fall 2010, Prof. D. Budker;

5. Cross Sections Effective area Differential cross section
Physics 129, Fall 2010, Prof. D. Budker;

6. Cross Sections
Physics 129, Fall 2010, Prof. D. Budker;

7. Cross Sections
Some cross-sections diverge (e.g., for Rutherford scattering)
Effective cut-off
Physics 129, Fall 2010, Prof. D. Budker;

8. Cross Sections
Physics 129, Fall 2010, Prof. D. Budker;

9. Mandelstam Variables Universally used!
Physics 129, Fall 2010, Prof. D. Budker;

10. Units of cross section
Origin: Uranium nucleus cm as "big as a barn"
Unit
Symbol m2
cm2
megabarn Mb
10−22
10−18
barn b
10−28
10−24
millibarn mb
10−31
10−27
microbarn (or "outhouse"[3]) μb
10−34
10−30
nanobarn nb
10−37
10−33
picobarn pb
10−40
10−36
femtobarn fb
10−43
10−39
attobarn ab
10−46
10−42
shed[4][5] (10−24 barn)
[none]
10−52
10−48
Physics 129, Fall 2010, Prof. D. Budker;

11. Cross Sections Luminosity:
number of particles in a beam per unit area per unit time
Physics 129, Fall 2010, Prof. D. Budker;

12. Luminosity What about colliding beams?
Luminosity = collision frequency  n1  n2 / beam area
Physics 129, Fall 2010, Prof. D. Budker;

13. Luminosity
Physics 129, Fall 2010, Prof. D. Budker;

14. LHC luminosity: reality check
Physics 129, Fall 2010, Prof. D. Budker;

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;

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;

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;

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;

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;

20. The Feynman-Diagram Rules
For each diagram:
Label external momenta pi , label internal momenta qi, 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;

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;

22. Example/interlude: Diagrams in
Physics 129, Fall 2010, Prof. D. Budker;

23. Example/interlude: Diagrams in
Vanishes for
Vanishes in the high-frequency limit
Physics 129, Fall 2010, Prof. D. Budker;

24. Relativistic Equations
Nonrelativistic
Relativistic; spin zero
Physics 129, Fall 2010, Prof. D. Budker;

25. The Dirac Equation (relativistic, spin ½)
Introduce 44 Dirac Matrices:
Relativistic; spin 1/2
Physics 129, Fall 2010, Prof. D. Budker;

26. Solving the Dirac Equation
Assume wavefunction independent of position:
Physics 129, Fall 2010, Prof. D. Budker;

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;

28. Dirac Spinor Algebra Some useful facts about spinors:
How do Dirac spinors transform under P?
Physics 129, Fall 2010, Prof. D. Budker;

29. Dirac Spinor Algebra Introduce another matrix: What about 4 ?
Physics 129, Fall 2010, Prof. D. Budker;

30. Bilinear Covariants
Physics 129, Fall 2010, Prof. D. Budker;

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