We study the constraints on the new parameters in the gauge sector of gauged two Higgs doublet model using the electroweak precision test data collected from the Large Electron Positron Collider (LEP) at and off the -pole as well as the current Drell-Yan and high-mass dilepton resonance data from the Large Hadron Collider (LHC). Impacts on the new parameters by the projected sensitivities of various electroweak observables at the Circular Electron Positron Collider (CEPC) proposed to be built in China are also discussed. We also clarify why the Stüeckelberg mass for the hypercharge (1) is set to be zero in the model by showing that it would otherwise lead to the violation of the standard charge assignments for the elementary quarks and leptons when they couple to the massless photon.

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With theoretical constraints such as perturbative unitarity and vacuum stability conditions and updated experimental data of Higgs measurements and direct searches for exotic scalars at the LHC, we perform an updated scan of the allowed parameter space of the Georgi-Machacek (GM) model. With the refined global fit, we examine the allowed parameter space for inducing strong first-order electroweak phase transitions (EWPTs) and find only the one-step phase transition is phenomenologically viable. Based upon the result, we study the associated gravitational wave (GW) signals and find most of which can be detected by several proposed experiments. We also make predictions on processes that may serve as promising probes to the GM model in the near future at the LHC, including the di-Higgs productions and several exotic scalar production channels.