Light sterile neutrino from extra dimensions and four-neutrino solutions to neutrino anomalies

We propose a four-neutrino model that can reconcile the existing data coming from underground experiments in terms of neutrino oscillations, together with the hint from the Liquid Scintillation Neutrino Detector (LSND) experiment and a possible neutrino contribution to the hot dark matter of the Universe. It applies the idea that extra compact dimensions, probed only by gravity and possibly gauge-singlet fields, can lower the fundamental scales such as the Planck, string, or unification scales. Our fourth light neutrino νₛ (s for sterile) is identified with the zero mode of the Kaluza-Klein states. To a first approximation νₛ combines with the ν_μ in order to form a Dirac neutrino with mass in the eV range leaving the other two neutrinos massless. The smallness of this mass scale (suitable for LSND and hot dark matter) arises without appealing either to a seesaw mechanism or to a radiative mechanism, but from the volume factor associated with the canonical normalization of the wave function of the bulk field in the compactified dimensions. On the other hand the splitting between ν_μ and νₛ (atmospheric scale) as well as the mass of the two other neutrinos (solar mass scale) arise from the violation of the fermion number on distant branes. We also discuss alternative scenarios involving flavor-changing interactions. In one of them νₑ can be in the electron-volt range and therefore, be probed in beta decay studies.