Status of negative coupling modifiers for extended Higgs sectors

In this work, we study the status of negative coupling modifiers in extended Higgs sectors, focusing on the ratio of coupling modifiers that probes custodial symmetry violation $\lambda_{WZ} = \kappa_{W}/\kappa_{Z}$. Higgs sectors with multiplets larger than doublets are the only weakly coupled models that give tree-level modifications to $\lambda_{WZ}$, and we explore all such models allowed by the constraint from the $\rho$ parameter and perturbative unitarity. This class of models has a custodial symmetry violating potential, while the vacuum configuration preserves the symmetry. We apply precision measurements from ATLAS and CMS and show that each data set can exclude a vast set of models with $\lambda_{WZ} < 0$ at greater than 95\% confidence level. We give evidence that $\lambda_{WZ}<0$ is excluded in all weakly coupled models. [Erratum for this work on page 19 changing our claims of complete exclusion of negative $\lambda_{WZ}$ to a softer version where only the minimal models are excluded.]