GIM mechanism and Z0 suppression?

[arivero]

In what sense does the GIM mechanism implies the existence of a c quark? It seems that all that is required for Z0 suppression is to postulate that the mixed strange must be orthogonal to the mixed down quark.

 

[Hawkwind]

In what sense does the GIM mechanism implies the existence of a c quark? It seems that all that is required for Z0 suppression is to postulate that the mixed strange must be orthogonal to the mixed down quark.

In the standard model, flavor changing neutral currents are mediated in higher orders perurbation theory by the so-called box diagrams exchanging virtual W bosons and quarks. Glashow, Iliopoulos and Maiani had realized that the contribution from the s-quark exchange interferes destructively with the contribution by the postulated c exchange. This is what the suppresses the flavor changing neutral current. See for instance
http://www.scholarpedia.org/article/Glashow-Iliopoulos-Maiani_mechanism

 

[arivero]

In the standard model, flavor changing neutral currents are mediated in higher orders perurbation theory by the so-called box diagrams exchanging virtual W bosons and quarks. Glashow, Iliopoulos and Maiani had realized that the contribution from the s-quark exchange interferes destructively with the contribution by the postulated c exchange. This is what the suppresses the flavor changing neutral current. See for instance
http://www.scholarpedia.org/article/Glashow-Iliopoulos-Maiani_mechanism

Thanks. If you look at such link, you will see that there is not such a thing as a destructive interference of the c exchange. Probably, some divulgator confused c=Cabibbo and c=charm in the formulae.

 

[Vanadium 50]

The author of the article is the I of GIM, so he probably understands it. And he claims there is a destructive interference: "Here comes the second ingredient of the mechanism. GIM observed that, with a fourth quark, there is a second diagram, with c replacing u, Figure 2. In the limit of exact flavour symmetry the two diagrams cancel. "

 

[Hawkwind]

Thanks. If you look at such link, you will see that there is not such a thing as a destructive interference of the c exchange. Probably, some divulgator confused c=Cabibbo and c=charm in the formulae.

I am referring to the statement:

Here comes the second ingredient of the mechanism. GIM observed that, with a fourth quark, there is a second diagram, with c replacing u, Figure 2.

In the limit of exact flavour symmetry the two diagrams cancel.

This is what I meant with "destructive interference".

Another important thing is that consideration of all diagrams is required to obtain a finite result. During calculation, you have to regularize each diagram dimensionally or by a cut-off. When summing them up, the divergent parts of the various diagrams cancel and the cut-off will drop out.
So, you need all quark families filled up completely in order to be able to make a quantitative prediction:
(d,u) and (s,c) in the 4-quark model
or
(d,u), (s,c) and (b,t) in the 6 quark model.
This is what is called GIM mechanism (or Kobayashi-Maskawa in the 6 quark model).

 

[arivero]

I am referring to the statement:

...

This is what I meant with "destructive interference".

Ah, ok, I thought you were answering also the second part of my question, which was about Z0 suppression. But yes, when you consider the cancellation of W contributions, then you have these square boxes and they need a complete flavour symmetry to cancel them. Fine. GIM mechanism is more than "generalisation of the Cabibbo universality", and I have failed to notice it.

I didn't fail to note that the curator (not the author) of the entry was I. (and btw, thanks for the link!). But really your phrase was "the contribution from the s-quark exchange interferes destructively with the contribution by the postulated c exchange". It is true that in the mechanism there is a s-quark, there is a c-quark, and there are situations of destructive interference. But if you look at it honestly, your phrase does not fit with any of the processes described there. And still I have read your exact statement in other places, where only the first process (generalized Cabibbo universality) was needed, but the second ingredient (exact flavour symmetry) was invoked.

 

[Vanadium 50]

The Z0 is a different case. You can couple quarks to the Z in any basis you like, but when you diagonalize it, you regain the flavor basis. Therefore the Z does not introduce any FCNC's.

 

[arivero]

The Z0 is a different case. You can couple quarks to the Z in any basis you like, but when you diagonalize it, you regain the flavor basis. Therefore the Z does not introduce any FCNC's.

Yep, probably what hapenner is that G I and M included this fact in their paper, and then most of the descriptions of GIM mechanism keep including also this argument about the FCNC. Or "strangeness-changing neutral currents", as Aitchison-Hey call them in their section about the GIM mechanism.

From your comments and Hawkwind's comment, it seems that modernly we should call "GIM mechanism" not to the whole paper, but only to the one for the charged currents. In this sense I agree that it implies a c quark.

 

[Hawkwind]

From your comments and Hawkwind's comment, it seems that modernly we should call "GIM mechanism" not to the whole paper, but only to the one for the charged currents. In this sense I agree that it implies a c quark.

Yes, that's in fact, what GIM is referring to: "flavor changing neutral currents".
Its implication is that the quarks have to come in doubletts: for each quark of the down type, there must be a corresponding partner quark of the up type and vice versa.

 

[arivero]

ha, it is true, that the box of the Ws is also a "neutral" current, a sum of charged positive and charged negative.

 

[Hawkwind]

ha, it is true, that the box of the Ws is also a "neutral" current, a sum of charged positive and charged negative.

Agreed: the sum of these box graphs (and still higher orders) should be regarded as an effective fcnc vertex.
BTW, I was wondering about your last statement referring to the "modern" interpretation of the GIM-paper. In fact, I had learned this stuff 30 years ago and I am not aware of any change in interpretation of GIM.