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 Q l = 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) 6= 2/3), but the discrepancy between Ql(μ) and Q pole l 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 ofQU(μ) andQD(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. E-mail: [email protected] E-mail: [email protected] 1 1 Thanks to the precise measurements of three charged lepton masses [1], me = (0.510998918± 0.000000044) MeV , mμ = (105.6583692± 0.0000094) MeV , mτ = (