Effects of heavy Majorana neutrinos at lepton-proton colliders

We discuss the prospects of detecting the processes $e^+p\to\bar\nu_e\ell^+\ell'^+X$ and $\nu_ep\to e\ell^+\ell'^+X$ ($\ell,\ell'=e,\mu,\tau$) under the conditions of the present $ep$ collider HERA and of future colliders. These high-energy processes are assumed to be mediated by the exchange of heavy Majorana neutrinos (HMN). We consider two simple scenarios for the HMN mass spectrum: the effective singlet ($m_1\ll m_2<m_3...$) and the effective doublet ($m_1<m_2\ll m_3...$). For the latter case, the cross section includes information about CP-violating phases.