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...

 

[sir-pinski]

, thank you for your question. Beta decay of a charged lepton, such as a muon or an electron, when its mass is close to the mass of the W boson (m_W), is an interesting case that has been studied extensively in the field of particle physics. However, the calculation of this decay in the generic case, where the mass is neither much smaller nor much greater than m_W, is not a straightforward task and there is no single definitive solution.

One approach to calculating lepton beta decay in this case is to use the Standard Model (SM) of particle physics, which describes the interactions between fundamental particles and the forces that govern them. In the SM, beta decay is described by the weak interaction, which is mediated by the W boson. The mass of the W boson is an important parameter in this calculation, and its value has been measured experimentally to be around 80 GeV.

The traditional formulas for muon decay and top quark decay, which you mentioned, are derived from the SM and take into account the masses of the particles involved. However, when the mass of the lepton is close to m_W, these formulas do not provide an accurate description of the decay process. Instead, one needs to consider the full SM framework and use more sophisticated techniques to calculate the decay rate.

There have been several studies and calculations of lepton beta decay when the mass is close to m_W, but there is no single, definitive result. Different approaches and approximations have been used, and the results may vary depending on the specific assumptions made. Some of these calculations can be found in textbooks and articles, but there is no consensus on a single solution.

In terms of solving this as an exercise, it is definitely a challenging and interesting problem that could be proposed to students studying particle physics. However, it would require a strong understanding of the SM and its mathematical formalism, and it may be more suitable for advanced students or researchers in the field.

In summary, while there have been several studies and calculations of lepton beta decay when the mass is close to m_W, there is no single definitive result. It remains an open and active area of research in particle physics, and further studies and calculations may provide more insights into this interesting case. Thank you for your question and I hope this response has been helpful.