Koide formula
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This unexplained relation was discovered by Yoshio Koide in 1981, and relates the masses of the three leptons so well that it predicted the mass of the tau lepton.
Let
It is clear that 1 / 3 < Q < 1 from the definition.The superior bound follows if you assume that the square roots can not be negative; R. Foot remarked that 1 / 3Q can be interpreted as the cosine squared of the angle between the vector 
and (1,1,1).
The mystery is in the physical value. The masses are measured as 
, which gives
Not only is this result odd in the three apparently random numbers should give a simple fraction, but also that Q is exactly halfway between the two extremes of 1/3 and 1.
This result has never been explained or understood.
[edit] References
Phys. Rev. D 28, 252–254 (1983)
Physics Letters B, Volume 120, Issues 1-3 , 6 January 1983, Pages 161-165
[edit] Further reading
The Strange Formula of Dr Koide - A review of the history of the Koide Formula
The Koide Formula - Summary article.
