On the Viability of Minimal Neutrinophilic Two-Higgs-Doublet Models

We study the constraints that electroweak precision data can impose, after the discovery of the Higgs boson by the LHC, on neutrinophilic two-Higgs-doublet models which comprise one extra $SU(2)\times U(1)$ doublet and a new symmetry, namely a spontaneously broken $\mathbb{Z}_2$ or a softly broken global $U(1)$. In these models the extra Higgs doublet, via its very small vacuum expectation value, is the sole responsible for neutrino masses. We find that the model with a $\mathbb{Z}_2$ symmetry is basically ruled out by electroweak precision data, even if the model is slightly extended to include extra right-handed neutrinos, due to the presence of a very light scalar. While the other model is still perfectly viable, the parameter space is considerably constrained by current data, specially by the $T$ parameter. In particular, the new charged and neutral scalars must have very similar masses.