ИСТИНА

For physically interesting scenarios in the seesaw type I models it is needed to combine very small active (standard) neutrino masses $\sim F^2 v^2/M_{M}$ with moderately heavy $M_{HNL}$ within the LHC and next colliders energy reach, and not too small mixing $\sim \sqrt{{m_\nu}/M_{HNL}}$ providing observable signals at the luminosity frontier. This is achieved either by fine-tuning of the mixing matrices in a specific scenarios with additional symmetries, or in the framework of Casas-Ibarra diagonalisation where the mixing can be enhanced. First sort of models gives quasi-Dirac neutrinos processed by the standard calculation technique, which are not fully consistent with the second sort of models not using the "Dirac limit"{$,$} evaluating with Majorana Feynman rules. Collider studies are performed using socalled "model independent approach" or "phenomenological seesaw type I model" with one generation of HNL and mixing independent of HNL mass. It is interesting to consider explicit forms of mixing for three HNL generations beyond theDirac limit" in view of the available data.