Constraints on large scalar multiplets from perturbative unitarity

TL;DR

This paper derives bounds on the size of scalar electroweak multiplets based on unitarity constraints, limiting their isospin and hypercharge values to ensure theoretical consistency.

Contribution

It provides the first explicit unitarity bounds on the isospin and hypercharge of scalar multiplets in the electroweak sector.

Findings

Complex scalar multiplet must have isospin T <= 7/2.

Real scalar multiplet must have isospin T <= 4.

Constraints restrict the possible sizes of scalar multiplets in models.

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 <= 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.