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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 /c 2 ) bosons Discovered in 1983 at CERN ( UA1 ) 1984 Nobel Prize to . Stochastic cooling.

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Introduction to particle physics Part V

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

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

  3. The Wand Z propagators • Does not reduce to photon case for M0 • Polarization vector has threeindep. comp. The metric Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

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

  5. p2 p4 p3 p1 • 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

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

  7. 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

  8. Muon Decay andFermi Theoryof 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

  9. 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

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

  11. Island Physics… • 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

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