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253a/SchwartzDue November 9, 2010Problem Set 91. Consider the following diagram fore+e-→μ+μ-in QEDa) What other diagrams contribute at the same order in perturbation theory?b) Show explicitly that the sum of this diagram and the diagram with the photonscrossed is gauge invariant (independent ofξ).2. Parity Violation.We calculated thate+e-→μ+μ-has a1 +cos2θangular dependence. This agreeswith experiment, as the simulated data in Figure 1 shows. However, the angular distribu-tion for scattering into muon neutrinose+e-→νμν¯μis very different, as shown in thesimulated data in Figure 2. (This simulation is somewhat idealized – interference hasbeen dropped, but the physics is correct and has been observed.)Minus1.0Minus0.50.00.51.00100200300400500600cosΘeventsFigure 1.e+e-→μ+μ-Minus1.0Minus0.50.00.51.00100200300400500600cosΘeventsFigure 2.e+e-→νμν¯μa) Atlowenergy, the total cross sectionσtotfore+e-→νμν¯μscattering grows withenergy, in contrast to the totale+e-→μ+μ-cross section. Show that this is con-