  In a recently proposed neutrinophilic two-Higgs doublet model, the low-energy
(sub-MeV) effective theory consists of a real scalar with a vev of O(0.1) eV
and three Dirac neutrinos. Other models could lead to the same low energy
theory. In this Brief Report, we study constraints on the parameter space of
the model, including vacuum stability, unitarity, perturbativity and the
effects on the invisible Z width. Interestingly, we find that all neutrinos
become massless at temperatures above approximately 1000 K, but can find no
phenomenological effects of this finding. The most direct test of the model is
that it predicts that in a galactic supernova, the energy distributions of the
electron, muon and tau neutrinos will be Fermi-Dirac with identical
temperatures, unlike the conventional distributions.
