On the Koide-like Relations for the Running Masses of Charged Leptons, Neutrinos and Quarks

الأصل · EN

Current experimental data indicate that the Koide relation for the pole masses of charged leptons, which can be parametrized as Qpoleₗ = 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 Qpoleₗ 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.