Lepton beta decay when m near m_W?

[arivero@unizar.es]

lepton beta decay when m near m_W?

Has anybody seen somewhere, article or textbook or website, the
calculation of beta decay of a charged lepton in the generic case,
when mass is neither a lot smaller nor a lot greater than the mass of
the W?

It should be some result interpolating between the traditional
formulas of muon decay and top quark decay. One could expect it to be
solved as exercise somewhere, or at least proposed to be solved.

Hints?

Alejandro

 

[blechman]

At tree leve, all you need to do is replace Fermi's constant with the W-boson propogator:

$$G_F\rightarrow\frac{ig^2}{t-m_W^2}$$

up to factors of 2 which are easily found. Other than that change, it's pretty much exactly the same as muon decay.

Strictly out of curiosity: why do you care? No leptons are anywhere near the W-mass...