93%(14)13 out of 14 people found this document helpful
This preview shows page 1 - 2 out of 2 pages.
253a/SchwartzDue October 12, 2010Problem Set 51. Radioactive decay. The muon decays to an electron and two neutrinos through an intermediatemassive particle called theW−boson. The muon, electron andW−all have charge-1.a) Write down a Lagrangian that would allow forμ−→e−νeνμ. Assume theWand otherparticles are all scalars, and thee−, νeandνμare massless. Call the couplingg.b) Calculate|M|2for this decay in the limit that theWmass,mW, is large.c) The decay rate (=1lifetime) is proportional to|M|2. The couplinggshould be dimension-less (like the couplingefor the photon), but appears dimensionful because we ignorespin. If theWspin were included, you would get extra factors ofpμ, which would turninto a factor ofs√=mμin|M|2. Use dimensional analysis to figure out what power ofmμshould be there. Also, throw in a1(2π)3for the 3-body phase space.d) Look up the muon mass and lifetime on pdglive.lbl.gov. Pick some reasonable perturba-tive value forgand use the muon mass and lifetime to esimate theWmass.e) The tauon,τ