English

A universal shape of empirical mass formula for all leptons and quarks

High Energy Physics - Phenomenology 2007-05-23 v1

Abstract

A specific universal shape of empirical mass formula is proposed for all leptons ν1,ν2,ν3\nu_1, \nu_2, \nu_3 and e,μ,τe^-, \mu^-, \tau^- as well as all quarks u,c,tu, c, t and d,s,bd, s, b of three generations, parametrized by three free constants μ,ϵ,ξ \mu, \epsilon, \xi assuming four different triplets of values. Four such triplets of parameter values are determined or estimated from the present data. Mass spectra in the four cases are related to each other by shifting the triplet of parameters μ,ϵ,ξ \mu, \epsilon, \xi. For charged leptons ξ0\xi \simeq 0 (but probably ξ0\xi \neq 0). If for them ξ\xi is put to be exactly 0, then mτ=1776.80m_\tau = 1776.80 MeV is predicted after the input of experimental mem_e and mμm_\mu (the central value of experimental mτ=1776.990.26+0.29m_\tau = 1776.99^{+0.29}_{-0.26} MeV corresponds to ξ=1.8×1030 \xi =1.8\times 10^{-3}\neq 0). For neutrinos 1/ξ01/\xi \simeq 0 (but 1/ξ01/\xi \neq 0 in the case of normal hierarchy mν12mν22mν32m^2_{\nu_1} \ll m^2_{\nu_2} \ll m^2_{\nu_3}). If for neutrinos 1/ξ1/\xi is conjectured to be exactly 0, then (mν1,mν2,mν3)(1.5,1.2,5.1)×102(m_{\nu_1}, m_{\nu_2}, m_{\nu_3}) \sim (1.5, 1.2, 5.1)\times 10^{-2} eV are predicted after the input of experimental estimates mν22mν128.0×105eV2|m^2_{\nu_2} - m^2_{\nu_1}| \sim 8.0\times 10^{-5} {\rm eV}^2 and mν32mν222.4×103eV2|m^2_{\nu_3} - m^2_{\nu_2}| \sim 2.4\times 10^{-3} {\rm eV}^2. Thus, the mass ordering of neutrino states 1 and 2 is then inverted, while the position of state 3 is normal.

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Cite

@article{arxiv.hep-ph/0602018,
  title  = {A universal shape of empirical mass formula for all leptons and quarks},
  author = {Wojciech Krolikowski},
  journal= {arXiv preprint arXiv:hep-ph/0602018},
  year   = {2007}
}

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16 pages