Naturally light sterile neutrinos

A simple model to accomodate light sterile neutrinos naturally with large mixing with the usual neutrinos has been proposed. The standard model gauge group is extended to include an SU(2)S gauge symmetry. Heavy triplet higgs scalars give small masses to the lefthanded neutrinos, while a heavy doublet higgs scalar give mixing with the sterile neutrinos of the same order of magnitude. The neutrino mass matrix thus obtained can explain the solar neutrino deficit, the atmospheric neutrino deficit, the LSND data and hot dark matter. Lepton number is violated here through decays of the heavy triplet higgs, which generates the lepton asymmetry of the universe, which in turn generates a baryon asymmetry of the universe. E-mail: [email protected] permanent address Recently the Super Kamiokande [1] announced a positive evidence of neutrino oscillations. They attribute the νμ deficit in the atmospheric neutrino to a νμ oscillating into a νatm, where νatm could be a ντ or a sterile neutrinos (which is a singlet under the standard model) with ∆matmos = m2νμ − matm ∼ (0.5 − 6) × 10−3eV. There are also indications of neutrino oscillations in the neutrinos coming from the sun. The solar neutrino deficit can be explained if one considers νe → νsol oscillations (where νsol could be νμ or ντ or a sterile neutrino) with the mass squared difference [2] ∆msolar = m 2 νsol −mνe ∼ (0.3− 1.2)× 10−5eV, This mass squared difference is for resonant oscillation [3]. If one assumes vacuum oscillation solution of the solar neutrino deficit, then this number will be several orders of magnitude smaller. If we assume a three generation scenario, νatm is then identified with ντ and νsol could be a νμ or a ντ . Consider, νsol ≡ ντ , which implies, m2νμ − m2νe = [m2νμ − m2ντ ] + [m2ντ − m2νe] = ∆matmos + ∆msolar ∼ 10−2eV. Then we cannot explain the LSND result [4], which announced a positive evidence of νμ → νe oscillations with the mass squared difference (alternate explanation is not possible [5]) ∆mLSND = m 2 νμ −mνe ∼ (0.2− 2)eV . This conclusion is true even if we consider νsol ≡ νμ. As a solution to this problem one can say that either LSND result is wrong or there has to be some other explanation for the solar neutrino deficit. But a more popular solution is to extend the standard model to incorporate a sterile neutrino and explain all these experiments [6]. Since LEP data [7] ruled out any possibility of a fourth SU(2)L doublet left-handed neutrino, this fourth neutrino has to be a sterile neutrino, which does not interact through any of the standard model gauge bosons. Incorporating such light sterile neutrino with large mixing with the other light neutrinos in extensions of the standard model is non-trivial [6]. Recently there is one attempt to extend the radiative neutrino mass generation model by Zee [8] to incorporate a sterile neutrino [9]. However, that model cannot explain the baryon asymmetry of the universe.