Related papers: A note on Koide's lepton mass relation
The charged lepton mass relation $K \equiv (m_e +m_\mu+m_\tau)/(\sqrt{m_e} %+\sqrt{m_\mu} +\sqrt{m_\tau})^2= 2/3 $ is excellently satisfied by observed masses (pole masses). However, the formula $K=2/3$ should be never satisfied with the…
The recent devolopment on the charged lepton mass forumula m_e+m_{\mu}+m_{\tau}={2/3}(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_{\tau}})^2 is reviewed. An S_3 or A_4 model will be promising for the mass relation.
A charged lepton mass formula $(m_e +m_\mu + m_\tau)/(\sqrt{m_e}+\sqrt{m_\mu} + \sqrt{m_\tau})^2 =2/3$ is well-known. Since we can, in general, have two relations for three quantities, we may also expect another relation for the charged…
A finite group generated by four Z_3 transformations is applied to lepton families in a supersymmetric model, resulting in the charged-lepton masses m_i being proportional to v_i^2, where v_i are three vacuum expectation values. This may be…
On the basis of a supersymmetric yukawaon model, Sumino's relation for charged lepton masses is re-derived. A relation between values of $K(\mu) \equiv (m_e +m_\mu + m_\tau)/(\sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_\tau})^2$ and $\kappa(\mu)…
Why the charged lepton mass formula m_e +m_\mu +m_\tau = {2/3} (\sqrt{m_e}+\sqrt{m_\mu} +\sqrt{m_\tau})^2 is mysterious is reviewed, and guiding principles to solve the mystery are presented. According to the principles, an example of such…
Brannen has recently pointed out that the observed charged lepton masses satisfy the relation m_e +m_\mu +m_\tau = {2/3} (\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_\tau})^2, while the observed neutrino masses satisfy the relation m_{\nu 1} +m_{\nu 2}…
Treating the Koide equation and another efficient charged-lepton mass formula (having the form of a mass sum rule) as a system of two mathematically independent algebraic equations for three charged-lepton masses, we predict the tauon mass…
We apply Koide's mass relation of charged leptons to neutrinos and quarks, with both the normal and inverted mass schemes of neutrinos discussed. We introduce the parameters $k_{\nu}$, $k_u$ and $k_d$ to describe the deviations of neutrinos…
Koide's mass formula is an empirical relation among the charged lepton masses which holds with a striking precision. We propose a mechanism for cancelling the QED correction to Koide's formula. This is discussed in an effective theory with…
Current experimental data indicate that the Koide relation for the pole masses of charged leptons, which can be parametrized as $Q^{pole}_l = 2/3$, is valid up to the accuracy of $O(10^{-5})$. We show that the running masses of charged…
The charged lepton masses obey to high precision the so-called Koide relation. We propose a generalization of this relation to quarks. It includes up and down quarks of the three generations and is numerically reasonably close to the Koide…
In 1981, Yoshio Koide noticed that the square root values of the charged lepton masses satisfy the relation \[ Q=\frac{m_e+m_{\mu}+m_{\tau}}{(\sqrt{m_e}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2} \approx \frac{2}{3} \] Inspired by this relation, we…
According to our microscopic cosmological model, masses of charged leptons are induced by curvatures of hyper-spherical surfaces embedded in a 3D time-like subspace, leading to a solution of the lepton mass hierarchy problem and to a…
The QED processes e^+ e^- -> e^+ e^- \mu^+ \mu^- and e^+ e^- -> e^+ e^- \tau^+ \tau^- are studied with the L3 detector at LEP using an untagged data sample collected at centre-of-mass energies 161 GeV < sqrt{s} < 209 GeV. The tau-pairs are…
The reconstruction of tau-pair production, $e^{+}e^{-} \to \tau^{+}\tau^{-}$, from the subsequent 3-prong ($\tau^{+} \rightarrow \pi^{+} \pi^{-} \pi^{+} \bar{\nu}_{\tau}$) and 1-prong ($\tau^{-} \to \ell^{-} \bar{\nu}_{\ell} \nu_{\tau}$,…
The lepton mass ratios are calculated using a geometric unified theory, taking the leptons as the only three possible families of topological excitations of the electron or the neutrino. The theoretical results give 107.5916 Mev for the…
An energy scan near the $\tau$ pair production threshold has been performed using the BESIII detector. About $24$ pb$^{-1}$ of data, distributed over four scan points, was collected. This analysis is based on $\tau$ pair decays to $ee$,…
The observed charged lepton masses satisfy the relations $K \equiv (m_e +m_\mu+m_\tau)/(\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^2 =2/3$ and $\kappa \equiv \sqrt{m_e m_\mu m_\tau}/(\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^3 =1/486$ with…
The various mass relations among members of quark and lepton families are given. Three mass relations for the charm, beauty, and top quark family members are given and three mass relations for the electron, muon, and tau lepton family…