Renormalisation d’un doublet de bosons en interaction avec un doublet de fermions

Abstract

A study is made of the remormalization of the system in which two bosons of the same tensorial type interact with two different pairs of unlike fermions. The renormalization constants of the vertices are first explicitly defined. Then to renormalize the two boson fields and boson masses, 3 + 3 renormalization constants are required. These are determined explicity as a function of the unrenormalized vacuum polarization operators. A prescription for the renormalization of these operators is given. The high-energy limits of the boson propagators are related to the field renormalization constants. The resulting formulae generalize, in matrix form, the usual formulae for the single boson theory. Some care must be taken for the generalization to the case of unstable bosons. The case of two bosons interacting with a single pair of fermions is also briefly discussed.