Intermediate mass Higgs bosons at TeV $e\gamma$ colliders in the $\mathcal{M}\mathcal{S}\mathcal{S}\mathcal{M}$

We study the cross sections for the production of intermediate mass Higgs bosons via the reactions $e^{-}\gamma \to {\nu }_e{W}^{-}{\mathrm{\Phi }}^0$, $e^{-}\gamma \to {\nu }_e{H}^{-}{\mathrm{\Phi }}^0$, $e^{-}\gamma \to e^{-}{Z}^0{\mathrm{\Phi }}^0$ and $e^{-}\gamma \to e^{-}{H}^{+}{H}^{-}$ in the Minimal Supersymmetric Standard Model (with ${\mathrm{\Phi }}^0=H^0,h^0$ and, where possible, $A^0$) at TeV energies, taking into account $b$–tagging capabilities. We find that the rates for $e^{-}\gamma \to {\nu }_e{W}^{-}{\mathrm{\Phi }}^0$ are large enough to permit the discovery of at least one between $h^0$ and $H^0$ over the whole intermediate mass range of $M_{A^0}$, at all $\tan \beta$, using the $(jj)(b\bar{b})$ final state. The $\mathcal{C}\mathcal{P}$-odd neutral $A^0$ and the charged $H^{\pm }$’s can be detected via the processes $e^{-}\gamma \to {\nu }_e{H}^{-}{A}^0$, with $A^0\rightarrow b\bar b$,and$e^-\gamma\rightarrow e^-H^+H^-$,resortingtotheleptonicdecay$H^\pm\rightarrow \nu_\tau\tau^+(\bar\nu_\tau\tau^-)$,butonlyfor$M_{A^0}\approx60$ GeV. Finally, we present explicit formulae for the helicity amplitudes of these processes.