The pattern of neutrino masses and how to determine it

Abstract

Our knowledge of the neutrino sector of the Standard Model has recently undergone a revolution. Deficits of the atmospheric muon neutrino flux and the solar electron neutrino flux compared to their predicted values can be understood in terms of neutrino oscillations and we can therefore infer that neutrinos have non-degenerate masses. Additional but somewhat less secure evidence for \bar\nu_\mu \to \bar\nu_e and \nu_\mu\to\nu_e oscillations has been found in the LSND accelerator experiment. Because these experiments have widely different L/E_\nu ranges (\approx 10 to 10^4 km/GeV for atmospheric, \approx 10^{11} for solar, and \approx 1 for LSND), the mass-squared differences required to explain the phenomena must be distinct. Given the observations, an important next step is to deduce the pattern of neutrino masses and mixings. Such studies depend on the number of neutrinos. The invisible width of the Z-boson measured in LEP experiments gives N_\nu = 2.993\pm 0.011, consistent with the usual \nu_e, \nu_\mu and \nu_\tau "active" neutrinos. But there may also be right-handed "sterile" neutrinos with no weak interactions. Only the observation of oscillations of the active neutrinos to sterile neutrinos can test for their existence. In the following, we first discuss the atmospheric and solar neutrino data in a 3-neutrino framework and then later generalize our considerations to include the LSND data with oscillations of four neutrinos.