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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 $ΔS$ and $ΔT$ are studied. In the minimal model, the mixture of the septet $η$ 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, $ΔS$ gives a stringent constraint on the mixing angle $\sinβ$ between the CP-odd neutral parts of the SM Higgs doublet and $η$. In general, increasing the mass of the scalar septet $M_η$ will enhance the deviation of $T$ from the SM, whereas it decreases the magnitude of $ΔS$ for a larger bare mass within the range $M_η\lesssim 400\,{\rm GeV}$. 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 $η$, and a stable dark matter could naturally exist. For a benchmark point with this inner doublet mass of $M_χ=250{\rm}$ and $M_η=400\,{\rm GeV}$ 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, $ΔS$ is suppressed by a factor of $s_W^2$ and $ΔT$ has a significant constraint due to the vanishing vacuum polarization of $Z$ at the momentum transfer $p^2=0$.