Charged scalar production at the compact linear collider for the $$S_3 \otimes \mathbb {Z}_2$$S3⊗Z2 model

We present a model with $$S_3 \otimes \mathbb {Z}_2$$ model plus a sterile neutrino and its phenomenological expectations for the production of charged scalars at the compact linear collider. At tree level, our model predicts a total cross section in between 0.1 and $$10^{-5}$$ pb for the $$e^- e^+ \rightarrow H^+ H^-$$ process, considering all possible mass values for the charged scalar in the CLIC experiment. We also show that this prediction holds regardless of the masses of the other exotic particles and their couplings. We also show that an indirect detection from its effects in the $$e \overline{e} \rightarrow e \overline{e}$$ + missing energy process is possible under specific conditions, or a direct detection under other circumstances. However, one cannot use this process to study the sterile neutrinos present in this model, given that they have a small influence in the total cross-section for the direct detection of the exotic scalar to be possible.