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

The Weak Interactions Responsible for -decay Mediated by heavy (80-90 GeV/c2) bosons Discovered in 1983 at CERN (UA1) 1984 Nobel Prize to Simon van der Meer Carlo Rubia Stochastic cooling Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Accelerator Detector

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

The week coupling is LARGE Weak interactions are weak because gauge bosons are heavy ` Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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; http://budker.berkeley.edu/Physics129_2010/Phys129.html