A postscript on penguin diagrams


In my previous post I drew the following one-loop contribution to the b to s flavour-changing amplitude:

Diagrams such as the one above are a little sketchy because of the mass difference involved between the in- and out-states. For large mass differences, this brushes up against 4-momentum conservation. (Try boosting in to the b rest frame and consider energy conservation, for example.) [1] If you wanted a process with kinematic enhancement, consider the Penguin diagram where pair production from the loop can be used to carry off the energy difference:

The green wiggly line is, say, a photon. (You could have stuck it on the W line had you preferred.) For large-enough energies, the photon will want to pair-produce into a particle/anti-particle pair. The point is that the photon carries away the 4-momentum difference between the incoming b and outgoing s states, increasing the phase space for the process to occur.

This, by the way, is what penguin diagrams are good for. Lots of general-level articles explain their etymological history, but few actually go to the trouble of explaining why they’re of any importance relative to diagrams without the penguin’s `feet.’


[1] If the in- and out- states of the first diagram above are taken to be physical (on-shell), then the process has no viable phase space in which to occur. However, this isn’t a problem is the diagram is a sub-diagram of a larger process, so that one or both of the ends of can be taken to be off-shell. With the penguin diagram, the two `feet’ allow us to access a larger phase space.

One Response to “A postscript on penguin diagrams”

  1. 1 andy.s

    What are you using to draw those Feynman diagrams? It looks kind of like Jaxodraw, but I didn’t think it did colors.

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