Constraining the Georgi-Machacek Model with a Light Higgs

In this work, we investigate the viability of a light Higgs ($\eta$) scenario in the Georgi-Machacek (GM) model, where we consider all theoretical and experimental constraints such as the perturbativity, vacuum stability, unitarity, electroweak precision tests, the Higgs di-photon and undetermined decays and the Higgs total decay width. In addition, we consider more recent experimental bounds from the searches for doubly-charged Higgs bosons in the VBF channel $H_5^{++}\to W^{+}{W}^{+}$, Drell-Yan production of a neutral Higgs boson $pp\to H_5^0(\gamma \gamma )H_5^{+}$, and for the light scalars at LEP $e^{-}{e}^{+}\to Z\eta$, and at ATLAS and CMS in different final states such as $pp\to \eta \to 2\gamma$ and $pp\to h\to \eta \eta \to 4\gamma ,2\mu 2\tau ,2\mu 2b,2\tau 2b$. By combining these bounds together, we found a parameter space region that is significant as the case of the SM-like Higgs to be the light CP-even eigenstate, and this part of the parameter space would be tightened by the coming analyses.