# Scalar Electroweak Multiplet Dark Matter

## TL;DR

This paper analyzes scalar electroweak multiplet dark matter, deriving a general potential, clarifying Higgs portal interactions, and exploring relic density and detection constraints for specific multiplets.

## Contribution

It introduces a comprehensive scalar potential with three Higgs portal couplings and studies the phenomenology of $Y=0$ multiplets, especially septuplet and quintuplet cases.

## Key findings

- Relic density and direct detection depend on a single effective coupling.
- Current limits suggest such dark matter would be a subdominant component.
- The Higgs portal interactions are more complex than previously thought.

## Abstract

We revisit the theory and phenomenology of scalar electroweak multiplet thermal dark matter. We derive the most general, renormalizable scalar potential, assuming the presence of the Standard Model Higgs doublet, $H$, and an electroweak multiplet $\Phi$ of arbitrary SU(2$)_L$ rank and hypercharge, $Y$. We show that, in general, the $\Phi$-$H$ Higgs portal interactions depend on three, rather than two independent couplings as has been previously considered in the literature. For the phenomenologically viable case of $Y=0$ multiplets, we focus on the septuplet and quintuplet cases, and consider the interplay of relic density and spin-independent direct detection cross section. We show that both the relic density and direct detection cross sections depend on a single linear combination of Higgs portal couplings, $\lambda_{\rm eff}$. For $\lambda_{\rm eff}\sim \mathcal{O}(1)$, present direct detection exclusion limits imply that the neutral component of a scalar electroweak multiplet would comprise a subdominant fraction of the observed DM relic density.