Constraints on the septet-doublet mixing models from oblique parameters

The limitations of the doublet-septet mixing models by the deviations of electroweak oblique parameters $\Delta S$ and $\Delta T$ are studied. In the minimal model, the mixture of the septet $\eta$ and the scalar doublet in the standard model (SM) is driven by a non-Hermitian dimension-7 operator. For a smaller bare mass of the septet, $\Delta S$ gives a stringent constraint on the mixing angle $\sin\beta$ between the CP-odd neutral parts of the SM Higgs doublet and $\eta$. In general, increasing the mass of the scalar septet $M_\eta$ will enhance the deviation of $T$ from the SM, whereas it decreases the magnitude of $\Delta S$ for a larger bare mass within the range $M_\eta\lesssim 400\,{\rm GeV}$. We also examine two extended models from the ordinary doublet-septet mixture pattern. One of them is based on a inert doublet-septet mixing pattern, in which there is no vacuum expectation value for the neutral component of $\eta$, and a stable dark matter could naturally exist. For a benchmark point with this inner doublet mass of $M_\chi=250{\rm}$ and $M_\eta=400\,{\rm GeV}$ in this model, the mixing coefficient is found to be less than $1.8$. The other extension is constructed by imposing a doubly charged scalar mixed with the doubly charged component of the septet. Apart from the contribution by the septet-doublet admixture, $\Delta S$ is suppressed by a factor of $s_W^2$ and $\Delta T$ has a significant constraint due to the vanishing vacuum polarization of $Z$ at the momentum transfer $p^2=0$.