Charged Higgs scalar production in the single-top-quark mode (and others) at futureepcolliders in the minimal supersymmetric standard model

We study charged Higgs boson production at future electron-proton colliders in the frame-work of the minimal supersymmetric standard model. We focus our attention to the case of single-top-quark production and decay through the channel $\overrightarrow{t}{\mathrm{bH}}^{\pm }$ and of vector-scalar fusion via $W^{\pm *}{\Phi }^{*}\to H^{\pm }$ (where $\Phi =H,$ $h,$ and $A$). We consider the signature $H^{\pm }\to \tau {\nu }_{\tau }$ and compare it to the irreducible background from standard model interactions. For $M_{H^{\pm }}\lesssim m_t,$ the $H^{\pm }$ signal is accessible through lepton universality breaking if $M_A\lesssim 100–120\mathrm{GeV}$ at both low and large values of tan β. Furthermore, although the bulk of the production cross section comes from single-top-quark events, a sizable contribution due to vector-scalar-scalar interactions should be observable at large tan β, this possibly offering some insight into the structure of the scalar sector of the theory. The possibility of the CERN collider running in the $\mathrm{LEP}\oplus \mathrm{LHC}$ mode is considered in detail.