Related papers: What Physics Does The Charged Lepton 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…
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.
Koide has pointed out that the mass relation $m_e + m_{\mu} + m_{\tau} = {2 \over 3}(\sqrt{m_e} + \sqrt{m_{\mu}} + \sqrt{m_{\tau}})^2 $ is consistent with the most recent measurements of the tau lepton mass. We point out that this relation…
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…
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…
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}…
Based on the experimental data and estimations of the charged leptons and quarks masses, a close power law with exponent 3/4 has been found, connecting charged leptons masses and up quarks masses. A similar mass relation has been suggested…
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…
There are two formulas for charged lepton mass relation: One is a formula (formula A) which was proposed based on a U(3) family model on 1982. The formula A will be satisfied only masses switched off all interactions except for U(3) family…
In the framework of a mass formula proposed previously (transforming in a specific way three free parameters into three masses), a simple empirical sum rule for three charged-lepton masses is found, predicting m_\tau = 1776.9926 MeV, when…
On the basis of the so-called supersymmetric yukawaon model, it is investigated what form of the superpotential W can lead to the observed charged lepton mass spectrum. A simple form of W can speculate reasonable values of K(\mu)=(m_e…
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…
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…
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…
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…
The mass relations among respective quark family members are predicted and similar mass relation for the lepton family member are obtained. The volume of the volume element is also calculated which is (3/2)^(1/2).
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 $2\times10^{16} {GeV}$. By using the parameters…
We derive empirical relationships among elementary fermion masses based on relatively simple exponential formulae involving quantum numbers for the electromagnetic and strong interactions, with a weak correction factor motivated by a simple…
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…