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

Zhi-zhong Xing; He Zhang

doi:10.1016/j.physletb.2006.02.051

paper

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

arXiv:hep-ph/0602134 · doi:10.1016/j.physletb.2006.02.051

Abstract

Current experimental data indicate that the Koide relation for the pole masses of charged leptons, which can be parametrized as $Q_{l}^{p o l e} = 2/3$ , is valid up to the accuracy of $O (1 0^{- 5})$ . We show that the running masses of charged leptons fail in satisfying the Koide relation (i.e., $Q_{l} (μ) \neq = 2/3$ ), but the discrepancy between $Q_{l} (μ)$ and $Q_{l}^{p o l e}$ is only about 0.2% at $μ = M_{Z}$ . The Koide-like relations for the running masses of neutrinos ( $1/3 < Q_{ν} (M_{Z}) < 0.6$ ), up-type quarks ( $Q_{U} (M_{Z}) \sim 0.89$ ) and down-type quarks ( $Q_{D} (M_{Z}) \sim 0.74$ ) are also examined from $M_{Z}$ up to the typical seesaw scale $M_{R} \sim 1 0^{14}$ GeV, and they are found to be nearly stable against radiative corrections. The approximate stability of $Q_{U} (μ)$ and $Q_{D} (μ)$ is mainly attributed to the strong mass hierarchy of quarks, while that of $Q_{l} (μ)$ and $Q_{ν} (μ)$ is essentially for the reason that the lepton mass ratios are rather insensitive to radiative corrections.

arXiv comment11 pages, 3 figures

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

Abstract

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