Three little known equalities:(adsbygoogle = window.adsbygoogle || []).push({});

From Smirnov:

[tex] \theta_{\mbox{sun}} + \theta_{\mbox{cabibbo}} = {\pi \over 4} [/tex]

From De Vries:

[tex] \ln {m_\tau \over m_\mu} = \pi - {1 \over \pi} [/tex]

From Smirnov again:

[tex] \sqrt {m_\mu \over m_\tau} \sim \sin \theta_{\mbox{Cab.} } [/tex]

Can anyone predict them?

de Vries has a secondary formula for the electron-muon relationship, namely

ln(mu/me) / (2pi-3/pi) = 1.000627.

In principle one could recast them in terms of hyperbolic cosines and sines, for instance 1pi-1/pi= 2 sinh(ln(pi)) but it does not clarify the situation.

See also:

https://www.physicsforums.com/showthread.php?t=36624

http://arxiv.org/abs/hep-ph/0405088

http://www.chip-architect.com/news/2004_07_27_The_Electron.html [Broken]

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