# Supression factor for triangle diagrams

1. May 9, 2012

### frizzie

I'm pretty shaky with my understanding of much beyond simple tree-level calculations. When people talk about triangle diagrams, they sometimes say one will get a 'supression factor' of xxx. For example, in the consider the triangle diagram for H$\rightarrow\gamma\gamma$ with Ws running around the loop (attached). I want to know, without doing the full calculation, whether that would be more or less suppressed than second-order H$\rightarrow b \bar{b}$ (the same triangle diagram, except with bottom quark external legs instead of photons and a quark where the vertical W is.)

My thought was that you can use the cutting rules, so the relevant difference between the two is that H$\rightarrow\gamma\gamma$ has two WW$\gamma$ vertices and a W propagator, and H$\rightarrow b \bar{b}$ has two Wbb vertices and a fermion propagator. But plugging everything in, I get that H$\rightarrow\gamma\gamma$ should be more suppressed than second-order H$\rightarrow b \bar{b}$, which isn't correct. Does my approach make any sense?

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2. May 11, 2012

### kurros

Hmm, well there is no such vertex as Wbb. W's change up type quarks to down types and vice versa, so the quark in the loop must be some up type quark. So you have a CKM suppression factor in each of those vertices also. Although it will probably just be a top quark in the loop and I think the CKM factor V_tb is practically 1 so this is not too much of a bother. I suppose also that the top propagator is a bigger suppression than the bottom one so there is that too.