• DOI:10.1140/EPJC/S10052-016-3990-3
• Corpus ID: 118867494

Explorations of two empirical formulas for fermion masses

@article{Gao2015ExplorationsOT,
  title={Explorations of two empirical formulas for fermion masses},
  author={Guangping Gao and Nan Li},
  journal={The European Physical Journal C},
  year={2015},
  volume={76},
  pages={1-7}
}

• G. Gao, Nan Li
• Published 20 December 2015
• Physics
• The European Physical Journal C

Two empirical formulas for the lepton and quark masses (i.e. Kartavtsev’s extended Koide formulas), $$K_l=(\sum _l m_l)/(\sum _l\sqrt{m_l})^2=2/3$$Kl=(∑lml)/(∑lml)2=2/3 and $$K_q=(\sum _q m_q)/(\sum _q\sqrt{m_q})^2=2/3$$Kq=(∑qmq)/(∑qmq)2=2/3, are explored in this paper. For the lepton sector, we show that $$K_l=2/3$$Kl=2/3, only if the uncertainty of the tauon mass is relaxed to about $$2\sigma $$2σ confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and $$K_q$$Kq is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to $$10^{12}$$1012 GeV. We find that $$K_q$$Kq is always slightly larger than 2/3, but the discrepancy is merely about 5 %.