Electron-muon colliders at high energies to discover heavy sterile neutrinos

We study high-energy charged-lepton-flavor-violating (cLFV) channels in $e^- \mu^+$ scattering to probe heavy sterile neutrinos, which arise naturally in minimal extensions of the Standard Model. For $\sqrt{s} \le 2M_W$, we consider the process $e^- \mu^+ \to e^+ \mu^-$, which is dominated by one-loop box diagrams. We numerically evaluate these diagrams, involving a high-energy extension of the Inami-Lim functions, and find that the amplitudes are strongly suppressed because of their quartic dependence on light-heavy mixing. Using current bounds on active-sterile neutrino mixing, we determine the maximal rates allowed by existing constraints. For $\sqrt{s} > 2M_W$, we analyze the process $e^- \mu^+ \to W^+ W^-$ and compute the corresponding cross sections in both single-sterile and minimal type-I seesaw scenarios. We find this latter process to be significantly more promising for revealing the presence of heavy sterile neutrinos at $e-\mu$ colliders.