Energy scale independence of Koide's relation for quark and lepton masses
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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 $2\times10^{16} {GeV}$. 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.
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Cited by 2 Pith papers
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A minimization theorem for the Koide ratio and its Standard Model calibration
A theorem establishes that the one-particle extension of any Koide-ratio mass set reaches a unique minimum Qmin = Q0/(1+Q0) at m* = [(sum mi)/(sum sqrt(mi))]^2, with the lepton-plus-charm case landing 6 ppm above the ...
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A minimization theorem for the Koide ratio and its Standard Model calibration
Extending any positive-mass set by one particle minimizes the Koide ratio to Q0/(1+Q0) at m* = [(sum mi)/(sum sqrt(mi))]^2; adding the charm mass to leptons yields a value only 6 ppm above the ideal 2/5.
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