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I am reading about the charged current weak interaction. The notes I am using state that, with the charged current weak interaction, transitions across quark generations are possible, but suppressed. They then state that the Feynman diagrams (modulo crossing symmetry)

$d \to W^- + u$,

$s \to W^- + u$,

and $b \to W^- + u$

are all possible. There are a couple of things about this which I am unclear about.

Firstly, I'm not too sure about in which sense these are "suppressed". Can anyone shed any light on this?

Secondly, I am not sure how to interpret the wording above. Are these three simply examples of vertices which are allowed, or is this a list of absolutely all of the vertices which are allowed?

Thanks!

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There is something called the CKM matrix that is related to the suppression of generation changing decays. Quarks are paired by generation in the standard model, an up' quark is paired with a down' quark (I'll explain why I added a prime in a moment), and tree level diagrams don't allow cross-generation decays.

But the problem is that the generations as far as weak interactions are concerned are not quite the same thing as generations for mass eigenstates. So the down' quark is a state that is mostly composed of the usual down quark, but has some components of strange and bottom quarks too.

$$d' = V_{ud} d + V_{us} s + V_{ub} b$$

where the coefficient $|V_{ud}|^2$ is much bigger than the other two. The CKM matrix is just the collection of these coefficients.

So even though only the $d'$ quark can go to the $u'$ quark, since $d'$ has a $s$ component this means that an $s$ quark can go to a $u$ quark (and similarly for the transition $s'$ to $c'$, $c'$ has a $u$ component), but it will be suppressed by factors of the CKM matrix coefficients

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