Naturalness problems for ρ=1 and other large one-loop effects for a standard-model Higgs sector containing triplet fields

Extensions of the Higgs sector of the standard model (SM) that employ only doublet and singlet Higgs-field representations are not the only ones that guarantee {ρ}=1 at the tree level. Higgs sectors containing triplet (and higher) representations can be constructed in such a way that there is a tree-level custodial SU(2) symmetry yielding {ρ}=1. However, this custodial SU(2) is inevitably violated at the one-loop level. We explore the implications of this violation in the context of a Higgs sector containing triplet fields. In particular, we show that it leads to one-loop corrections to {ρ} and to certain mixings among the Higgs bosons and gauge bosons of the model that are quadratically divergent, thereby creating a new naturalness problem for {ρ} and for certain Higgs-boson couplings. This new class of naturalness problems first arises for a Higgs sector with triplet representations, making such a sector an interesting case study. A priori, deviations from {ρ}=1 induced at one loop are of arbitrary magnitude and sign. We demonstrate that the fine-tuning required to keep one-loop corrections to {ρ} and the Higgs-boson couplings small is similar in nature to that required in the SM to keep the SM Higgs-boson mass in the perturbative regime.