PS5 - 253a\/Schwartz Due Problem Set 5 1 Radioactive decay The muon decays to an electron and two neutrinos through an intermediate massive particle

PS5 - 253a/Schwartz Due Problem Set 5 1 Radioactive decay...

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253a/Schwartz Due October 12, 2010 Problem Set 5 1. Radioactive decay. The muon decays to an electron and two neutrinos through an intermediatemassive particle called theWboson. The muon, electron andWall have charge-1.a) Write down a Lagrangian that would allow forμeνeνμ. 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
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