Low-scale seesaw and the CP violation in neutrino oscillations

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 ${\nu }_{1R}$ and ${\nu }_{2R}$ having a Majorana mass term with mass M, which conserves the lepton charge L. The RH neutrino ${\nu }_{2R}$ 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 ${\nu }_{1R}$, $l=e,\mu ,\tau$. In this approach the smallness of neutrino masses is related to the smallness of the Yukawa coupling of ${\nu }_{1R}$ 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 $\left|g_{\ell 2}\right|$ can be much larger than $\left|g_{\ell 1}\right|$, of the order $\left|g_{\ell 2}\right|\sim {10}^{-4}\text{–}{10}^{-2}$, 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 δ is predicted to have approximately one of the values $\delta \simeq \pi /4,3\pi /4$, or $5\pi /4,7\pi /4$, 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.