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Unformatted text preview: 253a/Schwartz Due October 12, 2010 Problem Set 5 1. Radioactive decay. The muon decays to an electron and two neutrinos through an intermediate massive particle called the W boson. The muon, electron and W all have charge- 1 . a) Write down a Lagrangian that would allow for e e . Assume the W and other particles are all scalars, and the e , e and are massless. Call the coupling g . b) Calculate |M| 2 for this decay in the limit that the W mass, m W , is large. c) The decay rate ( = 1 lifetime ) is proportional to |M| 2 . The coupling g should be dimension- less (like the coupling e for the photon), but appears dimensionful because we ignore spin. If the W spin were included, you would get extra factors of p , which would turn into a factor of s = m in |M| 2 . Use dimensional analysis to figure out what power of m should be there. Also, throw in a 1 (2 ) 3 for the 3-body phase space. d) Look up the muon mass and lifetime on pdglive.lbl.gov. Pick some reasonable perturba- tive value for g and use the muon mass and lifetime to esimate the...
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