Full one-loop radiative corrections to $e^+ e^-\to H^+H^-$ in the inert doublet model

We compute the full one-loop radiative corrections for charged scalar pair production $e^{+}e^{-}\to H^{+}H^{-}$ in the inert doublet model. The on-shell renormalization scheme has been used. We take into account both the weak contributions as well as the soft and hard QED corrections. We compute both the real emission and the one-loop virtual corrections using the Feynman diagrammatic method. The resummed cross section is introduced to cure the Coulomb singularity which occurs in the QED corrections. We have analyzed the parameter space of the inert doublet model in three scenarios after taking into account theoretical constraints, the collider experimental bounds, and dark matter search bounds as well. It is found that the weak interaction dominates the radiative corrections, and its size is determined by the triple Higgs coupling $\lambda_{h^0 H^+ H^-}$, which is further connected to the mass of the charged scalar. In the scenario where all the constraints are taken into account, we find that for $\sqrt{s}=250$ GeV and $\sqrt{s}=500$ GeV, the weak corrections are around $-6\% \sim-5\%$ and $-10\% \sim -3\%$, respectively. While for $\sqrt{s}=1000$ GeV, the weak corrections can reach $-15\% \sim +25\%$. The new feature is that the weak corrections can be positive near the threshold when the charged scalar is heavier than 470 GeV. Six benchmark points for future collider searches have been proposed.