Constraining the scalar septet model through vector boson scattering

The scalar septet model extends the Standard Model Higgs sector by an isospin septet with hypercharge chosen to preserve $\rho \equiv M_W^2/M_Z^2 \cos^2\theta_W = 1$. In this paper we constrain the model at high septet masses using perturbative unitarity of longitudinal vector boson scattering amplitudes. We also apply the constraints from LHC searches for doubly-charged Higgs bosons produced in vector boson fusion, which constrain the model at lower septet masses. We point out some important differences between the septet model and extended Higgs models that preserve custodial symmetry in the scalar spectrum.