Muon Distance and Mandelstam Variables
See attached file for full problem description.
3.18 (a) A pion at rest decays into a muon and a neutrino (pi^- –> mu^- + V_mu). On the average, how far will the muon travel (in vacuum) before disintegrating?
(b) The length of the muon track in Figure 1.7 is about 0.6 mm (the photograph has been enlarged). How do you explain this?
3.23 For elastic scattering of identical particles, A + A –> A + A, show that the Mandelstam variables (Problem 3.22) become
s = 4(p^2 + m^2c^2)/c^2
t = -2p^2(1 – cos theta)/c^2
u = -2p^2(1 + cos theta)/c^2
where p is the CM momentum of the incident particle, and theta is the scattering angle.