Renormalization and radiative corrections to masses in a general Yukawa model

Abstract

We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields [Formula: see text], general Yukawa couplings and a [Formula: see text] symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the [Formula: see text] symmetry by vacuum expectation values (VEVs) of the [Formula: see text]. Introducing the shifted fields [Formula: see text] whose VEVs vanish, [Formula: see text] renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the [Formula: see text]. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.