Energy scale independence of Koide's relation for quark and lepton masses

  title={Energy scale independence of Koide's relation for quark and lepton masses},
  author={Nan Li and Bo Qiang Ma},
  journal={Physical Review D},
  • Nan Li, B. Ma
  • Published 5 January 2006
  • Physics
  • Physical Review D
Koide's mass relation of charged leptons has been extended to quarks and neutrinos, and we prove here that this relation is independent of energy scale in a huge energy range from 1 GeV to 2x10{sup 16} GeV. By using the parameters k{sub u}, k{sub d}, and k{sub {nu}} to describe the deviations of quarks and neutrinos from the exact Koide's relation, we also check the quark-lepton complementarity of masses such as k{sub l}+k{sub d}{approx_equal}k{sub {nu}}+k{sub u}{approx_equal}2, and show that… 

Tables from this paper

Family gauge symmetry as an origin of Koide's mass formula and charged lepton spectrum
Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We present a model of charged lepton sector within an effective field theory with
Explorations of two empirical formulas for fermion masses
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
Asymptotic helicity conservation in SUSY
We summarize the extensive work started in [1], according to which total helicity is conserved for any two‐to‐two process, at sqrt s >> MSUSY and fixed angles, in any SUSY extension of SM.
A4 symmetry and lepton masses and mixing
AbstractStimulated by Ma’s idea, which explains the tribimaximal neutrino mixing by assuming an A4 flavor symmetry, a lepton mass matrix model is investigated. A Frogatt–Nielsen-type model is
Fermion flavour observables : renormalisation invariants and model building using discrete symmetries
We very briefly review the current status of flavour physics with much of the emphasis on the experimental and the theoretical aspects of neutrino oscillations. Later we move on to study flavour
New framework for determining physical properties-II: properties of photons
The mathematical forms which describe the structures of all the basic electromagnetic particles, leptons and photons alike, are discussed in this article. Specifically, an equation is presented which


  • Lett. B 609, 309
  • 2005
  • Rev. D 57, 3986
  • 1998
  • Nuovo Cimento 34, 201 (1982); Y. Koide, Phys. Lett. B 120, 161
  • 1983
Tarasov , Dubna Report No
  • Phys . Lett . B
  • 2005
C 45
  • 39 (1989); Y. Koide, Mod. Phys. Lett. A 5, 2319 (1990); Y. Koide, H. Fusaoka, Z. Phys. C 71, 459 (1996); Y. Koide, M. Tamimoto, Z. Phys. C 72, 333 (1996); Y. Koide, Phys. Rev. D 60, 077301
  • 1999
in Proceedings of the Workshop on Unified Theory and the Baryon Number of the Universe
  • edited by O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979); M. Gell-Mann, P. Ramond, R. Slansky, in Supergravity, edited by F. van Nieuwenhuizen and D. Freedman (North Holland, Armsterdam, 1979); R.N. Mohapatra, G. Senjanovic, Phys. Rev. Lett. 44, 912
  • 1980
  • Rev. D 28, 252
  • 1983
C 72
  • 333
  • 1996
  • Phys. Lett. A 10, 3077
  • 1995
  • Rev. D 66, 093006
  • 2002