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I attempted to calculate the leptonic lifetimes based upon Electroweak Theory, and I am inquiring as to what I have done wrong in my calculations?

Electron lifetime:

[tex]\tau_{e} = \frac{192 \pi^3 \hbar}{10^{9} e G_F^2 m_{e}^5}[/tex]

[tex]\tau_{e} = 8.266 \cdot 10^5 \; \text{s}[/tex]

[tex]\tau_{e} = \text{stable}[/tex] - Wikipedia

Mass correction x-axis:

[tex]x = \frac{m_{e}^2}{m_{\mu}^2}[/tex]

Mass correction function:

[tex]f(x) = 1 - 8x - 12x^2 \ln \left( \frac{1}{x} \right) + 8x^3 - x^4[/tex]

Muon lifetime:

[tex]\tau_{\mu} = \frac{192 \pi^3 \hbar}{10^{9} e G_F^2 m_{\mu}^5 f\left( \frac{m_{e}^2}{m_{\mu}^2} \right)}[/tex]

[tex]\tau_{\mu} = 2.18779092 \cdot 10^{-6} \; \text{s}[/tex]

[tex]\tau_{\mu} = 2.19703421 \cdot 10^{-6} \; \text{s}[/tex] - Wikipedia

Mass correction x-axis:

[tex]x = \frac{m_{e}^2}{m_{\tau}^2}[/tex]

Tau lifetime:

[tex]\tau_{\tau} = \frac{192 \pi^3 \hbar}{10^{9} e G_F^2 m_{\tau}^5 f\left( \frac{m_{e}^2}{m_{\tau}^2} \right)}[/tex]

[tex]\tau_{\tau} = 1.626 \cdot 10^{-12} \; \text{s}[/tex]

[tex]\tau_{\tau} = 2.937 \cdot 10^{-13} \; \text{s}[/tex] - Wikipedia

Reference:

http://en.wikipedia.org/wiki/Electron" [Broken]

http://en.wikipedia.org/wiki/Muon" [Broken]

http://en.wikipedia.org/wiki/Tau_lepton" [Broken]

http://physics.nist.gov/cgi-bin/cuu/Value?gf|search_for=fermi"

http://en.wikipedia.org/wiki/Fermi_coupling_constant" [Broken]

http://en.wikipedia.org/wiki/Physical_constant" [Broken]

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