# Dark matter in Inert Doublet Model with one scalar singlet and $U(1)_X$ gauge symmetry

## TL;DR

This paper explores a dark matter model extending the Standard Model with an extra $U(1)_X$ gauge symmetry, analyzing its parameter space, experimental constraints, and potential detection prospects at future colliders.

## Contribution

It introduces a novel inert doublet model with a scalar singlet and $U(1)_X$ symmetry, providing detailed phenomenological analysis and experimental viability of the dark matter candidate.

## Key findings

- Allowed parameter regions consistent with current experimental limits.
- Dark matter mass range from light to heavy, depending on model parameters.
- Future collider detection possible for dark matter masses between 10-60 GeV.

## Abstract

We study Dark Matter (DM) abundance in the framework of the extension of the Standard Model (SM) with an additional $U(1)_X$ gauge symmetry. One complex singlet is included to break the $U(1)_X$ gauge symmetry, meanwhile one of the doublets is considered inert to introduce a DM candidate. The stability of the DM candidate is analyzed with a continuous $U(1)_X$ gauge symmetry as well as discrete $Z_2$ symmetry. We find allowed regions for the free model parameters which are in agreement with the most up-to-date experimental results reported by CMS and ATLAS collaborations, the upper limit on WIMP-nucleon cross section imposed by XENON1T collaboration and the upper limit on the production cross-section of a $Z^{\prime}$ gauge boson times the branching ratio of the $Z^{\prime}$ boson decaying into $\ell^-\ell^+$. We also obtain allowed regions for the DM candidate mass from the relic density reported by the PLANCK collaboration including light, intermediate and heavy masses; depending mainly on two parameters of the scalar potential, $\lambda_{2x}$ and $\lambda_{345}=\lambda_3+\lambda_4+2\lambda_5$. We find that trough $pp\rightarrow \chi\chi \gamma$ production, it may only be possible for a future hadron-hadron Circular Collider (FCC-hh) to be able to detect a DM candidate within the range of masses 10-60 GeV.