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

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

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 1 GeV to $2\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\mathrm{GeV}$. By using the parameters ${k}_{u}$, ${k}_{d}$, and ${k}_{\ensuremath{\nu}}$ to describe the deviations of quarks …