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

Abstract

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<Qν(MZ)<0.6), up-type quarks (QU(MZ)∼0.89) and down-type quarks (QD(MZ)∼0.74) are also examined from MZ up to the typical seesaw scale MR∼1014 GeV, and they are found to be nearly stable against radiative corrections. The approximate stability of QU(μ) and QD(μ) is mainly attributed to the strong mass hierarchy of quarks, while that of Ql(μ) and Qν(μ) is essentially for the reason that the lepton mass ratios are rather insensitive to radiative corrections.