Spectral theory near thresholds for weak interactions with massive particles

Abstract

We consider a Hamiltonian describing the weak decay of the massive vector boson $Z^0$ into electrons and positrons. We show that the spectrum of the Hamiltonian is composed of a unique isolated ground state and a semi-axis of essential spectrum. Using an infrared regularization and a suitable extension of Mourre’s theory, we prove that the essential spectrum below the boson mass is purely absolutely continuous.