Koide formula
Encyclopedia
The Koide formula is an unexplained relation discovered by Yoshio Koide in 1981. It relates the masses of the three charged leptons so well that it predicted the mass of the tau.
It is clear that . The superior bound follows if we assume that the square roots can not be negative. R. Foot remarked that can be interpreted as the squared cosine of the angle between the vector
and the vector
The mystery is in the physical value. The masses of the electron
, muon
, and tau are measured respectively as me = , mμ = , and mτ = , where the digits in parentheses are the uncertainties
in the last figures. This gives Q = . Not only is this result odd in that three apparently random numbers should give a simple fraction, but also that Q is exactly halfway between the two extremes of and 1.
While the original formula appeared in the context of preon models, other ways have been found to produce it, but in the whole this, it has never been explained nor understood.
Similar matches have been found for quarks depending on running masses, and for triplets of quarks not of the same flavour
Formula
The Koide formula is:It is clear that . The superior bound follows if we assume that the square roots can not be negative. R. Foot remarked that can be interpreted as the squared cosine of the angle between the vector
and the vector
The mystery is in the physical value. The masses of the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
, and tau are measured respectively as me = , mμ = , and mτ = , where the digits in parentheses are the uncertainties
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...
in the last figures. This gives Q = . Not only is this result odd in that three apparently random numbers should give a simple fraction, but also that Q is exactly halfway between the two extremes of and 1.
While the original formula appeared in the context of preon models, other ways have been found to produce it, but in the whole this, it has never been explained nor understood.
Similar matches have been found for quarks depending on running masses, and for triplets of quarks not of the same flavour