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

2. The Weak Interactions Responsible for -decay
Mediated by heavy (80-90 GeV/c2) bosons
Discovered in at CERN (UA1)
1984 Nobel Prize to
Simon van der Meer Carlo Rubia
Stochastic cooling
Physics 129, Fall 2010, Prof. D. Budker;
Accelerator
Detector

3. The W and Z propagators
Does not reduce to photon case for M0
Polarization vector has three indep. comp.
The metric
Physics 129, Fall 2010, Prof. D. Budker;

4. The W vertex Weak Coupling Constant:
Numerical factors are conventional
 --- vector coupling (as in QED)
 5 --- axial-vector coupling
“V-A” interaction `
Physics 129, Fall 2010, Prof. D. Budker;

5. Amplitude according to the rules:
What are the units here?
Remember normalization:
Proper averaging over polarizations gives (neglecting lepton masses): `
Physics 129, Fall 2010, Prof. D. Budker;

6. Cross-section The cross-section formula reads:
No dependence on angles!
 Isotropic cross-section!
Cross-section goes E2 (typical for weak processes) `
Physics 129, Fall 2010, Prof. D. Budker;

7. Not quite how Griffiths would draw this
Muon Decay p1 p3 p2
Amplitude according to the Rules:
Calculation of the muon lifetime (see Griffiths) yields:
Note scaling with muon mass: = -1 (m)5
Not quite how Griffiths would draw this p4 `
Physics 129, Fall 2010, Prof. D. Budker;

8. Muon Decay and Fermi Theory of weak interactions
Note that coupling comes together with W mass
Historically, the Fermi coupling constant was used:
The largest coefficient “of order unity”
With =c=1, F `
Physics 129, Fall 2010, Prof. D. Budker;

9. The week coupling is LARGE
Weak interactions are weak because gauge bosons are heavy `
Physics 129, Fall 2010, Prof. D. Budker;

10. Island Physics… Why are numerical coefficients (usually) ~1?
(The 1923 exception “proves” the rule…)
The answer is unexpected: this is due to…
3 dimensions of space
Unit sphere (R=1) in N dimensions:
Physics 129, Fall 2010, Prof. D. Budker;

11. Island Physics… With =c=1, []=Energy=Mass
How to calculate muon lifetime…
with no Griffiths and no internet
Remember that this is an allowed weak decay
Rate  goes as |M|2  (GF)2
What else can enter ?  m
That’s it! (Neglecting light-lepton masses)
With =c=1, []=Energy=Mass
Physics 129, Fall 2010, Prof. D. Budker;