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Food fot TheorDev

  1. Aug 6, 2004 #1

    arivero

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    Gold Member

    Three little known equalities:

    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
     
  2. jcsd
  3. Aug 6, 2004 #2

    arivero

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    Gold Member

    For instance, taking logarithms we have

    [tex]\ln (\sin \theta_C) \sim - \sinh (\ln \pi)[/tex]
     
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