D0-> K+ K- Decay Suppression - A Puzzling Question

[milch]

Hey community!

Since a couple of hours I've been dealing with the question why the decay $$D^0 \rightarrow K^+ K^-$$ is suppressed.
If I draw the Feynman diagram for the first order decay, everything seems pretty alright as the charm quark can couple with a strange quark. The resulting W+ can then produce an up and anti-strange quark which gives above K mesons.
What piece am I missing?

 

[mfb]

up and anti-strange are two different generations, there you get the Cabibbo suppression (compared to $D^0 \rightarrow K^- \pi^+$).

It is not a rare decay. It's just not as frequent as the decay to $K^- \pi^+$.

 

[milch]

Aaah, somehow I thought the Cabibbo suppression just applies in case of a quark-quark decay. But it holds whenever any kind of quark coupling is involved (independent of the "direction" I go in the diagram), right? (Sorry in advance for these basic questions..)

 

[Orodruin]

Correct, whenever you have a coupling of a W with quarks belonging to different generations, you get a suppression (an even larger suppression if the generations are 1,3 or 2,3).