  We consider the possibility to detect right-handed neutrinos, which are
mostly singlets of the Standard Model gauge group, at future accelerators.
Substantial mixing of these neutrinos with the active neutrinos requires a
cancellation of different contributions to the light neutrino mass matrix at
the level of 10^{-8}. We discuss possible symmetries behind this cancellation
and argue that they always lead to conservation of total lepton number. Light
neutrino masses can be generated by small perturbations violating these
symmetries. In the most general case, LHC physics and the mechanism of neutrino
mass generation are essentially decoupled; with additional assumptions,
correlations can appear between collider observables and features of the
neutrino mass matrix.
