Local decay for weak interactions with massless particles

Jean-Marie Barbaroux (1, 2) , Jérémy Faupin (3) , Jean-Claude Guillot (4)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E8 Dynamique quantique et analyse spectrale
3 IECL - Institut Élie Cartan de Lorraine
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: Spectral Theory; Standard Model; Weak Interactions; Local Decay; Mourre Theory

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Jean-Marie Barbaroux, Jérémy Faupin, Jean-Claude Guillot. Local decay for weak interactions with massless particles. Journal of Spectral Theory, 2019, 9 (2), pp.453-512. ⟨10.4171/JST/253⟩. ⟨hal-01465309⟩