We point out that hints of deviations from unitarity in the first row of the CKM matrix may be explained by the presence of a single vector-like top. We study how the stringent experimental constraints arising from CP Violation in the kaon sector and
from meson mixing such as $D^0$-$overline{D}^0$, $K^0$-$overline{K}^0$ and $B^0_{d,s}$-$overline{B}^0_{d,s}$ can be satisfied in the proposed framework. In order for the deviations from unitarity to be of the required size while keeping the theory perturbative, the new top quark should have a mass $m_T lesssim 7$ TeV which could be probed in upcoming experiments at the energy frontier.
We consider seesaw type-I models including at least one (mostly-)sterile neutrino with mass at the eV scale. Three distinct situations are found, where the presence of light extra neutrinos is naturally justified by an approximately conserved lepton
number symmetry. To analyse these scenarios consistently, it is crucial to employ an exact parametrisation of the full mixing matrix. We provide additional exact results, including generalise
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 wi
th 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.
