2. Let's consider the combination of QED and scalar QED, meaning we have a Dirac fermion (mass m) and a charged scalar mass M that both interact with the photon:
F = F + i - m + D - M
a. Let's call our fermion e- so we can connect with material in class. Consider the process e+e- -> Find the tree diagrams and calculate the amplitude M.
b. Square the amplitude, summing and averaging over the electron's spin. For simplicity, neglect the electron's mass m, but don't neglect the scalar mass M.
c. Compare the angular dependence of the scalar pair production's differential cross-section with that of the e+e- -> pair production's we have studied in class (in the limit where the electron mass is zero while the muon mass is nonzero). Also, calculate the total cross-section e+e- -> o and compare its energy dependence to o(e+e- -> u+-).
d. Using crossing symmetry, find the matrix element squared for e-* -> e-*