Koide formula

This unexplained relation was discovered by Yoshio Koide in 1981, and relates the masses of the three charged leptons so well that it predicted the mass of the tau lepton.

Let

$Q\; =\; frac\{m\_e\; +\; m\_\{mu\}\; +\; m\_\{\; au\{(sqrt\{m\_e\}+sqrt\{m\_\{mu+sqrt\{m\_\{\; au)^2\}$

It is clear that

The mystery is in the physical value. The masses of the electron, muon, and tau lepton are measured respectively as $m\_e\; =\; 0.511\; m\{MeV\}/c^2,\; m\_\{mu\}=105.7\; m\{MeV\}/c^2,\; m\_\{\; au\}\; =\; 1777\; m\{MeV\}/c^2$, which gives

$Q\; =\; frac\{2\}\{3\}\; pm\; 0.01\; \%$

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 1/3 and 1.

This result has never been explained nor understood.

References

[http://prola.aps.org/abstract/PRD/v28/i1/p252_1 Phys. Rev. D 28, 252–254 (1983)]

Physics Letters B, Volume 120, Issues 1-3 , 6 January 1983, Pages 161-165

Further reading

[http://www.arxiv.org/abs/hep-ph/0505220 The Strange Formula of Dr Koide] - A review of the history of the Koide Formula