Estimate of neutrino masses from Koide's relation

We apply Koide's mass relation of charged leptons to neutrinos and quarks, with both the normal and inverted mass schemes of neutrinos discussed. We introduce the parameters kν, ku and kd to describe the deviations of neutrinos and quarks from Koide's relation, and suggest a quark-lepton complementarity of masses such as kl+kd≈kν+ku≈2. The masses of neutrinos are determined from the improved relation, and they are strongly hierarchical (with the different orders of magnitude of 10−5 eV, 10−3 eV, and 10−2 eV).