Constraints on large scalar multiplets from perturbative unitarity

Abstract

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 $T\ensuremath{\le}7/2$ (i.e., $n\ensuremath{\le}8$) for a complex scalar multiplet and $T\ensuremath{\le}4$ (i.e., $n\ensuremath{\le}9$) for a real scalar multiplet, where $n=2T+1$ is the number of isospin states in the multiplet.