On the Koide-like relations for the running masses of charged leptons, neutrinos and quarks

Current experimental data indicate that the Koide relation for the pole masses of charged leptons, which can be parametrized as Qlpole=2/3, is valid up to the accuracy of O(10−5). We show that the running masses of charged leptons fail in satisfying the Koide relation (i.e., Ql(μ)≠2/3), but the discrepancy between Ql(μ) and Qlpole is only about 0.2% at μ=MZ. The Koide-like relations for the running masses of neutrinos (1/3