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 $H_{5}^{++}\rightarrow W^{+}W^{+}$, Drell-Yan production of a neutral Higgs boson $pp\rightarrow H_{5}^{0}(\gamma\gamma)H_{5}^{+}$, and for the light scalars at LEP $e^{-}e^{+}\rightarrow Z\eta$, and at ATLAS and CMS in different final states such as $pp\rightarrow\eta\rightarrow2\gamma$ and $pp\rightarrow h\rightarrow\eta\eta\rightarrow4\gamma,2\mu2\tau,2\mu2b,2\tau2b$. 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.