A particle of mass M and 4-momentum P decays into two particles of masses m₁ and m₂.

(a) Use the conservation of energy and momentum in the form, p₂ = P ? ?₁, and the invariance of scalar products of 4-vectors to show that the total energy of the first particle in the rest frame of the decaying particle is

and that E₂ is obtained by interchanging m₁ and m₂.

(b) Show that the kinetic energy T_i of the ith particle in the same frame is

T_i = ?M(1 ? m_i/M ???M/2M)

where ?M = M ? m₁ ? m₂ is the mass excess or Q value of the process.

(c) The charged pi-meson (M = 139.6 MeV) decays into a mu-meson (m1 = 105.7 MeV) and a neutrino (m₂ = 0). Calculate the kinetic energies of the mu-meson and the neutrino in the pi-meson's rest frame. The unique kinetic energy of the muon is the signature of a two-body decay. It entered importantly in the discovery of the pi-meson in photographic emulsions by Powell and ??workers in 1947.

Transcribed Image Text:

м? + m? т?