Higgs production at future $e^+e^-$ colliders in the Georgi-Machacek model

We study how the dominant single and double SM-like Higgs ($h$) production at future $e^+e^-$ colliders is modified in the Georgi-Machacek (GM) model. On imposing theoretical, indirect and direct constraints, significant deviations of $h$-couplings from their SM values are still possible; for instance, the Higgs-gauge coupling coupling can be corrected by a factor $\kappa_{hVV}\in[0.93,1.15]$ in the allowed parameter space. For the Higgs-strahlung $e^+e^-\to hZ$ and vector boson fusion processes $e^+e^-\to h\nu\bar{\nu},~he^+e^-$, the cross section could increase by $32\%$ or decrease by $13\%$. In the case of associated production with a top quark pair $e^+e^-\to ht\bar{t}$, the cross section can be enhanced up to several times when the custodial triplet scalar $H_3^0$ is resonantly produced. In the meanwhile, the double Higgs production $e^+e^-\to hhZ~(hh\nu\bar{\nu})$ can be maximally enhanced by one order of magnitude at the resonant $H_{1,3}^0$ production. We also include exclusion limits expected from future LHC runs at higher energy and luminosity and discuss their further constraints on the relevant model parameters. We find that the GM model can result in likely measurable deviations of Higgs production from the SM at future $e^+e^-$ colliders.