Remarks on models with singlet neutrino in large extra dimensions

Small Dirac masses for neutrinos are natural in models with singlet fermions in large extra dimensions with quantum gravity scale M_{\ast} \sim 1- 100 TeV. We study two modifications of the minimal model in order to obtain the mass scale relevant for atmospheric neutrino oscillations with at most O(1) higher-dimensional Yukawa couplings and with M_{\ast} \sim a few TeV. 1) In models with singlet fermions in smaller number of extra dimensions than gravity, we find that the effects on BR (\mu \to e \gamma) and on charged-current universality in \pi^- \to e \bar{\nu}, \mu \bar{\nu} decays are suppressed as compared to that in the minimal model with neutrino and gravity in the same space. 2) If small Dirac masses for the singlets are added along with lepton number violating couplings, then the mass scales and mixing angles for neutrino oscillations can be different from those relevant for \mu \to e \gamma and \pi^- \to e \bar{\nu}, \mu \bar{\nu}. Thus, in both modified models the constraints on M_{\ast} from BR (\mu \to e \gamma) and \pi^- \to e \bar{\nu}, \mu \bar{\nu} decays can be significantly relaxed. Furthermore, constraints from supernova 1987a strongly disfavor oscillations of active neutrinos to sterile neutrinos in both the minimal and the modified models.