A beam of \(\pi^{-}\)mesons is directed at a proton target and produces a variety of final states. For each of the particle states listed below propose a reaction that leads to a final state containing at least this particle. Draw a simple labeled diagram showing quark, lepton and boson lines as done, Choose a reaction that you expect to be one of the most important ways for this final state containing the particle to be produced, keeping in mind the relative strengths of the strong, electromagnetic and weak interactions. Assume that the \(\pi^{-}\) beam has sufficient energy for each reaction to be kinematically allowed:

(a) \(\Delta^{++}\)resonance;

(b) \(Z^{0}\) boson;

(c) electron neutrino, \(u_{e}\);

(d) \(K^{-}\)meson; and

(e) anti-neutrino and a charmed baryon.