Constraints on large scalar multiplets from perturbative unitarity

We determine the constraints on the isospin and hypercharge of a scalar electroweak multiplet from partial wave unitarity of tree-level scattering diagrams. The constraint from SU(2)L interactions yields T≤7/2 (i.e., n≤8) for a complex scalar multiplet and T≤4 (i.e., n≤9) for a real scalar multiplet, where $n=2T+1$ is the number of isospin states in the multiplet.