Dark matter in inert doublet model with one scalar singlet and U(1)X gauge symmetry

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 ′ gauge boson times the branching ratio of the Z ′ boson decaying into ℓ - ℓ + . 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, λ 2 x and λ 345 = λ 3 + λ 4 + 2 λ 5 . We find that trough p p → χ χ γ 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.