On the Addition of a Large Scalar Multiplet to the Standard Model

We consider the addition of a single SU(2) multiplet of complex scalarfields to the Standard Model (SM). We explicitly consider the various possiblevalues of the weak isospin J of that multiplet, up to and including J =7/2. We allow the multiplet to have arbitrary weak hypercharge. The scalarfields of the multiplet are assumed to have no vacuum expectation value; themass differences among the components of the multiplet originate in itscoupling, present in the scalar potential (SP), to the Higgs doublet of the SM.We derive exact bounded-from-below and unitarity conditions on the SP, therebyconstraining those mass differences. We compare those constraints to the onesthat may be derived from the oblique parameters.