  We consider a mathematical model for the weak decay of the intermediate boson
$Z^0$ into neutrinos and antineutrinos. We prove that the total Hamiltonian has
a unique ground state in Fock space and we establish a limiting absorption
principle, local decay and a property of relaxation to the ground state for
initial states and observables suitably localized in energy and position. Our
proofs rest, in particular, on Mourre's theory and a low-energy decomposition.
