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I have been learning how to draw Feynman diagrams for various decays. I just came across an interesting video where they draw the following diagram for $K^+ \to 2\pi^++\pi^-$:

enter image description here

My question is as follows: How does one know what quark should emit the gluon? Why can any of the other quarks not emit the gluon?

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    $\begingroup$ Note also that diagrams like the one you have in your question are more 'cartoons' than formal Feynman diagrams, because the in and out states (Kaons, pions, ...) are complicated nonperturbative objects. $\endgroup$ Commented Oct 2, 2022 at 15:02

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The answer is that this is just one diagram. You need to draw diagrams that cover all posibilities, so there will be diagrams where each quark emits the gluon. There will also be diagrams where multiple quarks emit gluons that interact with the other quarks. Now, maybe they showed this diagram because it produces the largest contribution to the final result? I don't know if that's the case here, but I think that could be predicted by checking to see how far off mass-shell the intermediate states have to be when they conserve momentum (possible when there are no loops).

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