from $Zb\bar b$ results [@Haber:1999zh], the combined upper bound for the lightest Higgs boson is lower than 269 GeV, depending on what the lighest is. Therefore, the model can be well testable at current and future collider experiments.

In Sec. 2, a brief review of the GM model is given. The transition matrix for two-body elastic scatterings is calculated in the high-energy limit, and its eigenmatrix is obtained in Sec. 3. In Sec. 4, the condition of S-wave unitarity is imposed for the eigenmatrix of the transition matrix, and bounds on the Higgs boson masses are evaluated. Conclusions are presented in Sec. 5.

Georgi-Machacek Model
=====================

The GM model contains a complex $SU(2)_L$ doublet field $\phi$ ($Y$=1), a real $SU(2)_L$ triplet field $\xi$ ($Y$=0) and a complex $SU(2)_L$ triplet field $\chi$ ($Y$=2) [@Georgi:1985nv], and respects the global $SU(2)_R$ symmetry in the Higgs potential [@Chanowitz:1985ug] . They can be described by the form of $SU(2)_L\otimes SU(2)_R$ multiplets $\Phi$ and $\Delta$ in the potential; =(

[cc]{} \^[0]{}&\^[+]{}\
\^- & \^0

),   =(

[ccc]{} \^[0]{}&\^+&\^[++]{}\
\^- & \^0 &\^+\
\^[–]{} &\^- &\^0

)  , where $\phi=(\phi^+, \phi^0)^T$, $\xi=(\xi^+, \xi^0, \xi^-)^T$ and $\chi=(\chi^{++}, \chi^+, \chi^0)^T$, and $\phi^-=-(\phi^+)^\ast$, $\xi^-=-(\xi^+)^\ast$ and $\chi^-=-(\chi^+)^\ast$ [@Gunion:1989ci]. The most general 