Constraints on the septet-doublet mixing models from oblique parameters

TL;DR

This paper investigates how mixing between scalar septets and doublets affects electroweak precision parameters, constraining model parameters and exploring extensions with dark matter candidates and doubly charged scalars.

Contribution

It provides new constraints on septet-doublet mixing models from oblique parameters and explores extended models with dark matter and doubly charged scalars.

Findings

Stringent constraints on mixing angle from $ riangle S$

Increasing septet mass affects $ riangle T$ and $ riangle S$

Extended models can include dark matter and doubly charged scalars

Abstract

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 $p^2=0$.