We consider a version of the low-scale type I seesaw mechanism for generating small neutrino masses, as an alternative to the standard seesaw scenario. It involves two right-handed (RH) neutrinos $ u_{1R}$ and $ u_{2R}$ having a Majorana mass term with mass $M$, which conserves the lepton charge $L$. The RH neutrino $ u_{2R}$ has lepton-charge conserving Yukawa couplings $g_{ell 2}$ to the lepton and Higgs doublet fields, while small lepton-charge breaking effects are assumed to induce tiny lepton-charge violating Yukawa couplings $g_{ell 1}$ for $ u_{1R}$, $l=e,mu,tau$. In this approach the smallness of neutrino masses is related to the smallness of the Yukawa coupling of $ u_{1R}$ and not to the large value of $M$: the RH neutrinos can have masses in the few GeV to a few TeV range. The Yukawa couplings $|g_{ell 2}|$ can be much larger than $|g_{ell 1}|$, of the order $|g_{ell 2}| sim 10^{-4} - 10^{-2}$, leading to interesting low-energy phenomenology. We consider a specific realisation of this scenario within the Froggatt-Nielsen approach to fermion masses. In this model the Dirac CP violation phase $delta$ is predicted to have approximately one of the values $delta simeq pi/4,, 3pi/4$, or $5pi/4,, 7pi/4$, or to lie in a narrow interval around one of these values. The low-energy phenomenology of the considered low-scale seesaw scenario of neutrino mass generation is also briefly discussed.
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