Energy scale independence of Koide's relation for quark and lepton masses

Abstract

Koide's mass relation of charged leptons has been extended to quarks and neutrinos, and we prove here that this relation is independent of energy scale in a huge energy range from $1GeV$ to $2\times 10^{16}GeV$. By using the parameters $k_u$, $k_d$ and $k_{\nu }$ to describe the deviations of quarks and neutrinos from the exact Koide's relation, we also check the quark-lepton complementarity of masses such as $k_l+k_d\approx k_{\nu }+k_u\approx 2$, and show that it is also independent (or insensitive) of energy scale.

arXiv comment16 Latex pages, 2 figures, final version to appear in PRD

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• Extended Empirical Fermion Mass Relation
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• Remark on Koide's Z3-symmetric parametrization of quark masses
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• Determining quark and lepton mass matrices by a geometrical interpretation
• Asymptotic Helicity Conservation in SUSY
• 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