Why are the legs needed in a penguin diagram?

[guimauve]

In the penguin diagrams you have a loop that allows the quark to change into another quark of the same charge such as b->s or s->d. I understand why the loop with the quark and W are needed to get you from b->s or s->d but why (in the example of the attached picture) do you need the gluon vertex to make the additional particle/anti-particle pair? Why can't the diagram just be a "b" coming in, an intermediate loop with a W and a u,c,t quark, and then an "s" going out? Why does there need to be an additional vertex in the loop where a gluon, photon or Z branches off?

 

[JustinLevy]

If you only had b->s, or s->d, where would the extra energy go?
For momentum and energy conservation you need another particle to be involved.

 

[epenguin]

I have never formalised it, for me it's just intuitive.

 

[Vanadium 50]

If you have a b->s transition with no additional particles coming out, that means you have the wrong basis and can re-diagonalize so this doesn't occur.

 

[blechman]

rephrasing JustinLevy's response in more brute-force terms: if you go ahead and write down that loop integral without the additional photon or gluon, it vanishes - go ahead and try it.