Doubly Charged Higgs Bosons and Spontaneous Symmetry Breaking at eV and TeV Scales

In this paper, beyond standard models are considered with additional scalar triplets without modification of the gauge group (Higgs Triplet Model—HTM) and with an extended gauge group $SU{\left(2\right)}_R\otimes SU{\left(2\right)}_L\otimes U\left(1\right)$ (Left–Right Symmetric Model—LRSM). These models differ drastically in possible triplet vacuum expectation values (VEV). Within the HTM, we needed to keep the triplet VEV at most within the range of GeV to keep the electroweak $\rho$ parameter strictly close to 1, down to electronvolts due to the low energy constraints on lepton flavor-violating processes and neutrino oscillation parameters. For LRSM, the scale connected with the $SU{\left(2\right)}_R$ triplet is relevant, and to provide proper masses of non-standard gauge bosons, VEV should at least be at the TeV level. Both models predict the existence of doubly charged scalar particles. In this paper, their production in the $e^{+}{e}^{-}$ collider is examined for making a distinction in the s- and t- channels between the two models in scenarios when masses of doubly charged scalars are the same.