Local Decay for Weak Interactions with Massless Particles

TL;DR

This paper models the weak decay of the Z^0 boson into neutrinos, proving the existence of a unique ground state and establishing decay and relaxation properties using Mourre's theory.

Contribution

It introduces a rigorous mathematical framework for weak decay processes involving massless particles, with new proofs of spectral and decay properties.

Findings

Existence of a unique ground state for the Hamiltonian.

Establishment of a limiting absorption principle.

Demonstration of local decay and relaxation to the ground state.

Abstract

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.