Reflexos e Reflexões: Koide

quarta-feira, 20 de maio de 2009

Koide - Fórmula

The Koide formula is an unexplained relation discovered in 1981. It relates the masses of the three charged leptons so well that it predicted the mass of the tauon.

The Koide formula is:

$Q = \frac{m_e + m_{\mu} + m_{\tau}}{(\sqrt{m_e}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2}$

The superior bound follows if we assume that the square roots can not be negative. R. Foot remarked that ¹⁄_3Q can be interpreted as the squared cosine of the angle between the vector

$(\sqrt{m_e},\sqrt{m_{\mu}},\sqrt{m_{\tau}})$

and the vector

(1,1,1).

The mystery is in the physical value. The masses of the electron, muon, and tauon are measured respectively as m_e = 0.511 MeV/c², m_μ = 105.7 MeV/c², and m_τ = 1,777 MeV/c². This gives Q = ²⁄₃ ± 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.