Neutrino masses with a "zero sum" condition:: mν1+mν2+mν3=0 -: art. no. 037302

It is well known that the neutrino mass matrix contains more parameters than experimentalists can hope to measure in the foreseeable future even if we impose CP invariance. Thus, various authors have proposed Ansatze to restrict the form of the neutrino mass matrix further. Here we propose that m(nu 1)+m(nu 2)+m(nu 3)=0. With this condition, the absolute neutrino mass can be obtained in terms of the mass-squared differences. When combined with the accumulated experimental data, this condition predicts two types of mass hierarchies, with one of them characterized by m(nu 3)approximate to-2m(nu 1)approximate to-2m(nu 2)approximate to0.063 eV, and the other by m(nu 1)approximate to-m(nu 2)approximate to0.054 eV and m(nu 3)approximate to0.0064 eV. The range predicted for \m(nu 1)\+\m(nu 2)\+\m(nu 3)\ is below the cosmological upper bound of 0.69 eV from recent Wilkinson Microwave Anisotropy Probe data and can be probed in the near future. We also point out some implications for direct laboratory measurement of neutrino masses and the neutrino mass matrix.