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In this paper, we study the mass distribution of elementary fermions and find a set of empirical relations to describe the mass distribution of elementary fermions. This inspires us to investigate in depth the origin of elementary fermion mass hierarchies and generations. We present a theoretical model to explain why the elementary fermions have three generations and discuss the origin of the fundamental fermion mass hierarchies and spin.
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Keywords:
- mass hierarchies /
- elementary fermion /
- generation /
- spin
[1] Abe S, Ebihara T, Enomoto S, et al. 2008 Phys. Rev. Lett. 100 221803
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[2] Allison W, Alner G J, Ayres D S, et al. 2005 Phys. Rev. D 72 052005
Google Scholar
[3] 曹俊 2014 中国科学: 物理学 力学 天文学 44 1025
Cao J 2014 Scientia Sinica Physica, Mechanica & Astronomica 44 1025
[4] Bednyakov A, Pikelner A 2020 Phys. Rev. D 101 091501(R
Google Scholar
[5] Mohr P J, Newel D B, Taylor B N 2016 Rev. Mod. Phys. 88 035009
Google Scholar
[6] Particle Data Group 2016 Chin. Phys. C 40 100001
Google Scholar
[7] Zyla P A, Barnett R M, Beringer J, et al. 2020 Prog. Theor. Exp. Phys. 2020 083C01
Google Scholar
[8] Aghanim N, Akrami Y, Ashdowne Y, et al. 2020 Astronomy & Astrophysics 641 A6
[9] 舒菁 2018 科学通报 63
Shu J 2018 Chin. Sci. Bull. 63
[10] Bogdan A D, Patrick J F 2008 J. High Energy Phys. 2008 100
[11] Steven W 2020 Phys. Rev. D 101 035020
Google Scholar
[12] Steven W 1964 Phys. Rev. 135 B1049
Google Scholar
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图 1 观测值和经验值的相关性 (a)
$N_{\rm{o}}(n)$ 与$N_{\rm{e}}(n)$ 的比较; (b)$L_{\rm{o}}(l)$ 与$L_{\rm{e}}(l)$ 的比较Figure 1. Correlation between theoretical and observed values: (a) the correlation between
$N_{\rm{o}}(n)$ and$N_{\rm{e}}(n)$ for$n = 1, 2, 3$ ; (b) the correlation between$L_{\rm{o}}(l)$ and$L_{\rm{e}}(l)$ for$l = 1, 2, 3$ .表 1 基本费米子的质量分布
Table 1. Mass distribution of elementary fermions.
代 $l=1$ $l=2$ $l=3$ $n=1$ ${\rm d}\,[4.64_{-0.17}^{+0.48}]$ ${\rm c}\,[1270\pm20]$ ${\rm t}\,[172760\pm300]$ $n=2$ ${\rm e}\,[0.5109989461\pm0.0000000031]$ $\text{µ}\,[105.6583745\pm0.0000024]$ $\text{τ[}\,[1776.82\pm0.12]$ $n=3$ ${\rm u}\,[2.16_{-0.26}^{+0.49}]$ ${\rm s}\,[93_{-5}^{+11}]$ ${\rm b}\,[4180_{-20}^{+30}]$ $n=4$ $\text{ν}_ {\rm e}$ $\text{ν}_\text{µ}$ $\text{ν}_\text{τ}$ 
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[1] Abe S, Ebihara T, Enomoto S, et al. 2008 Phys. Rev. Lett. 100 221803
Google Scholar
[2] Allison W, Alner G J, Ayres D S, et al. 2005 Phys. Rev. D 72 052005
Google Scholar
[3] 曹俊 2014 中国科学: 物理学 力学 天文学 44 1025
Cao J 2014 Scientia Sinica Physica, Mechanica & Astronomica 44 1025
[4] Bednyakov A, Pikelner A 2020 Phys. Rev. D 101 091501(R
Google Scholar
[5] Mohr P J, Newel D B, Taylor B N 2016 Rev. Mod. Phys. 88 035009
Google Scholar
[6] Particle Data Group 2016 Chin. Phys. C 40 100001
Google Scholar
[7] Zyla P A, Barnett R M, Beringer J, et al. 2020 Prog. Theor. Exp. Phys. 2020 083C01
Google Scholar
[8] Aghanim N, Akrami Y, Ashdowne Y, et al. 2020 Astronomy & Astrophysics 641 A6
[9] 舒菁 2018 科学通报 63
Shu J 2018 Chin. Sci. Bull. 63
[10] Bogdan A D, Patrick J F 2008 J. High Energy Phys. 2008 100
[11] Steven W 2020 Phys. Rev. D 101 035020
Google Scholar
[12] Steven W 1964 Phys. Rev. 135 B1049
Google Scholar
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