Weak coupling strength constant

[neelakash]

When it is said that the relative strength of weak interaction is $$\ 10^{-5}$$,what does this mean?

On calculation I am getting $$\alpha_w=\10^{-3}$$ with $$\ G_F=\ 1.16\times\ 10^{-5} \ GeV^{-2}$$

I had an impression that $$\alpha_w$$ should be $$\ 10^{-5}$$.Which one is correct?

 

[hamster143]

"relative strength" is not a very well-defined concept. The ratio of weak to electromagnetic interaction strengths depends a lot on the energy scale.

 

[sir-pinski]

The relative strength of weak interaction being \ 10^{-5} means that it is 10,000 times weaker than the strong interaction, which has a relative strength of about 1. This value is represented by the weak coupling constant, denoted by \alpha_w, which is a dimensionless quantity that describes the strength of the weak interaction.

In your calculation, you have correctly determined the value of \alpha_w to be approximately 10^{-3}, which is consistent with the experimental value. The confusion may arise from the fact that the value of the Fermi constant, denoted by G_F, is also often used to describe the strength of the weak interaction. However, G_F has units of energy squared, which is why it is expressed in terms of GeV^{-2}.

So, to clarify, both \alpha_w and G_F describe the strength of the weak interaction, but they are two different quantities with different units. The value of \alpha_w being 10^{-3} is correct, while the value of G_F being 1.16\times\ 10^{-5} \ GeV^{-2} is also correct. I hope this clears up any confusion.