Eur. Phys. J. C (2016) 76: 140
https://doi.org/10.1140/epjc/s10052-016-3990-3

Regular Article - Theoretical Physics

Explorations of two empirical formulas for fermion masses

Department of Physics, College of Sciences, Northeastern University, Shenyang, 110819, China

^* e-mail: linan@mail.neu.edu.cn

Received: 21 December 2015
Accepted: 25 February 2016
Published online: 14 March 2016

Abstract

Two empirical formulas for the lepton and quark masses (i.e. Kartavtsev’s extended Koide formulas), and , are explored in this paper. For the lepton sector, we show that , only if the uncertainty of the tauon mass is relaxed to about 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 is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to GeV. We find that is always slightly larger than 2/3, but the discrepancy is merely about 5 %.