Revisiting the decoupling limit of the Georgi-Machacek model with a scalar singlet

We study the connection between collider and dark matter phenomenology in the singlet extension of the Georgi-Machacek model. In this framework, the singlet scalar serves as a suitable thermal dark matter (DM) candidate. Our focus lies on the region v_χ < 1 GeV, where v_χ is the common vacuum expectation value of the neutral components of the scalar triplets of the model. Setting bounds on the model parameters from theoretical, electroweak precision and LHC experimental constraints, we find that the BSM Higgs sector is highly constrained. Allowed values for the masses of the custodial fiveplets, triplets and singlet are restricted to the range 140 GeV < $M_{H_5^0}$ \( {M}_{H_5^0} \) < 350 GeV, 150 GeV < $M_{H_3^0}$ \( {M}_{H_3^0} \) < 270 GeV and 145 GeV < M_H < 300 GeV. The extended scalar sector provides new channels for DM annihilation into BSM scalars that allow to satisfy the observed relic density constraint while being consistent with direct DM detection limits. The allowed region of the parameter space of the model can be explored in the upcoming DM detection experiments, both direct and indirect. In particular, the possible high values of BR( $H_5^0$ \( {H}_5^0 \) → γγ) can lead to an indirect DM signal within the reach of CTA. The same feature also provides the possibility of exploring the model at the High-Luminosity run of the LHC. In a simple cut-based analysis, we find that a signal of about 4σ significance can be achieved in final states with at least two photons for one of our benchmark points.