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Seesaw mechanism constrains from below mixing between active and sterileneutrinos for fixed sterile neutrino masses. Signal events associated withsterile neutrino decays inside a detector at fixed target experiment aresuppressed by the mixing angle to the power of four. Therefore sensitivity ofexperiments such as SHiP and DUNE should take into account minimal possiblevalues of the mixing angles. We extend the previous study of this subjectarXiv:1312.2887 to a more general case of non-zero CP-violating phases in theneutrino sector. Namely, we provide numerical estimate of minimal value ofmixing angles between active neutrinos and two sterile neutrinos with the thirdsterile neutrino playing no noticeable role in the mixing. Thus we obtain asensitivity needed to fully explore the seesaw type I mechanism for sterileneutrinos with masses below 2 GeV, and one undetectable sterile neutrino thatis relevant for the fixed-target experiments. Remarkably, we observe a strongdependence of this result on the lightest active neutrino mass and the neutrinomass hierarchy, not only on the values of CP-violating phases themselves. Allthese effects sum up to push the limit of experimental confirmation ofsterile-active neutrino mixing by several orders of magnitude below the resultsof arXiv:1312.2887 from $10^{-10}$ - $10^{-11}$ down to $10^{-12}$ and even to$10^{-20}$ in parts of parameter space; nonzero CP-violating phases areresponsible for that.

Numerical estimate of minimal active-sterile neutrino mixing for sterile neutrinos at GeV scale