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Higgs bosons pair production is well known for its sensitivity to probing thesign and size of Higgs boson self coupling, providing a way to determinewhether there is an extended Higgs sector. The Georgi-Machacek (GM) modelextends the Standard Model (SM) with an $SU(2)_L$ triplet scalar field that hasone real and one complex components. The Higgs self coupling now has a widerrange than that in the SM, with even the possibility of a sign flip. The newheavy singlet Higgs boson $H^{0}_{1}$ can contribute to s-channel production ofthe $hh$ pairs. In this work, we study non-resonant/resonant Higgs boson pairproductions $p p \rightarrow hh$ and $p p \rightarrow H^{0}_{1} \rightarrowhh$, focusing exclusively on the contribution of $H^0_1$. We show thesensitivity for Higgs boson pair production searches at the 13-TeV LHC with theluminosities of $3.2,\ 30$ and $100$~fb$^{-1}$.

Higgs boson pair productions in the Georgi-Machacek model at the LHC