Unitarity bounds in the Higgs model including triplet fields with custodial symmetry

We study bounds on Higgs-boson masses from perturbative unitarity in the Georgi-Machacek model, whose Higgs sector is composed of a scalar isospin doublet and a real and a complex isospin triplet field. This model can be compatible with the electroweak precision data without fine-tuning because of the imposed global $SU(2{)}_R$ symmetry in the Higgs potential, by which the electroweak rho parameter is unity at the tree level. All possible two-body elastic-scattering channels are taken into account to evaluate the $S$-wave amplitude matrix, and then the condition of perturbative unitarity is imposed on the eigenvalues to obtain constraint on the Higgs parameters. Masses of all scalar bosons turn out to be bounded from above, some of which receive more strict upper bounds as compared to that in the standard model (712 GeV). In particular, the upper bound of the lightest scalar boson, whatever it would be, is about 270 GeV.