Estimate of neutrino masses from Koide's relation

Abstract

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 $k_{\nu }$, $k_u$ and $k_d$ to describe the deviations of neutrinos and quarks from Koide's relation, and suggest a quark-lepton complementarity of masses such as $k_l+k_d\approx k_{\nu }+k_u\approx 2$. 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 $10^{-2}eV$).

arXiv comment12 latex pages, 4 figures, version in publication

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• Energy scale independence of Koide's relation for quark and lepton masses
• The strange formula of Dr. Koide
• A New Look at an Old Mass Relation
• Neutrino masses from lepton and quark mass relations and neutrino oscillations
• Determining quark and lepton mass matrices by a geometrical interpretation
• Some New Symmetric Relations and the Prediction of Left and Right Handed Neutrino Masses using Koide's Relation
• A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model
• Origin of fermion generations from extended noncommutative geometry