to make a fine-tuning on the size of vacuum expectation values of the triplet fields; i.e., to set tiny values on them. Another possibility is to impose the custodial symmetry to the Higgs sector, so that the rho parameter is predicted to be unity at the tree level. In 1985 Georgi and Machacek proposed such a model with one real triplet ($Y$=0) and one complex triplet ($Y$=2) in addition to the Higgs doublet [@Georgi:1985nv]. Chanowitz and Golden have explicitly constructed the Higgs potential of this model [@Chanowitz:1985ug]; i.e., imposing the custodial $SU(2)_{\rm V}$ symmetry to the potential, VEVs of all the isospin triplets become common, and then the tree-level value of the rho parameter is unity. They also have shown that the quantum correction from the scalar sector is stabilized by such a global symmetry, so that the rho parameter is corrected at the loop level only due to explicit $SU(2)_{\rm V}$ violation in the other sectors such as hypercharge interaction and Yukawa interaction, just like in the SM. Several phenomenological studies have been done on this model in Refs. [@Gunion:1989ci; @Vega:1989tt; @Gunion:1990dt; @Godbole:1994np; @Cheung:1994rp; @Akeroyd:1998zr; @Haber:1999zh; @Cheung:2002gd].

Generally in extended Higgs models, there are many free parameters in the 