Related papers: Excellent approximate solution to the mysterious m…
We present a short historical and bibliographical review of the lepton mass formula of Yoshio Koide, as well as some speculations on its extensions to quark and neutrino masses, and its possible relations to more recent theoretical…
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 recent experimental estimate for tau lepton mass comes significantly near to a theoretical value proposed by us in 1992. We recall our argumentation supporting this proposal.
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…
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 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…
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…
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 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…
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 U(3) \times SU(2) family gauge symmetry,…
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…
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…
For some time the measured value of tau-lepton mass continues to approach closer and closer a particular figure 1776.80 MeV predicted by an intrinsically composite model of three generations of leptons and quarks, introduced almost two…
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…
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.
Recently we have proposed mechanisms to explain origins of the charged lepton spectrum as well as Koide's mass formula, on the basis of U(3)\times O(3) family gauge symmetry. In this note, we review the basic ideas of these mechanisms.…
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…
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…
We propose a phenomenological form of the charged lepton mass matrix, which extends the idea of ``lopsided'' mass matrix in the literature. The features of the form are that both the 2-3 and 1-3 elements of the charged lepton mass matrix…
In the framework of the recently proposed electroweak theory on a Planck lattice, we are able to solve approximately the lattice Dyson equation for the fermion self-energy functions and show that the large difference of charged lepton and…