Left-right-symmetric electroweak models with triplet Higgs field

We examine the predictions of the conventional SU(2${)}_{\mathit{L}}$⊗SU(2${)}_{\mathit{R}}$⊗U(1${)}_{\mathit{B}\mathrm{-}\mathit{L}}$ left-right-symmetric model in the case where the minimal Higgs sector (containing one bidoublet, one L-triplet, and one R-triplet Higgs field) and the standard lepton representations (incorporating right-handed partners for the observed neutrinos) are adopted. We show that a complete analysis of spontaneous symmetry breaking for the Higgs sector leads to a highly restrictive range of possibilities for global minima that are simultaneously consistent with all experimental observations (such as lepton masses, ${\mathit{K}}_{\mathit{L}}$-${\mathit{K}}_{\mathit{S}}$ mixing, etc.). As a result, the possible phenomenologies for the gauge and Higgs bosons of the model are very limited. For instance, we demonstrate that in the absence of explicit CP violation in the Higgs potential, spontaneous CP violation does not arise and the fermion couplings exhibit ‘‘manifest’’ left-right symmetry. Further, we find no entirely natural solutions other than ones in which all of the extra (non-standard-model) gauge and Higgs bosons associated with the left-right-symmetric extension are extremely heavy (typically, more massive than ${10}^7$ GeV). Only by ‘‘fine-tuning’’ certain parameters of the Higgs potential is it possible to bring these extra particles down to an observable mass scale. Alternatively, symmetries can be introduced to eliminate the terms in the Higgs potential associated with these parameters, but only at the sacrifice of introducing undesirable consequences for fermion masses. Many of the pitfalls and problems are illustrated using a simplified model. Overall, we emphasize the necessity of performing a complete minimization of the Higgs sector before extracting phenomenology.