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I am struggling to understand the construction of the Feynman diagrams for the following decays:

Question about drawing diagrams for phi meson decay

The answer is given as follows:

Diagrams for phi meson decay

I do not understand how the quark anti-quark pair in each diagram is produced. In the two weak interactions, the W boson changes the quark flavour but what is producing the other quarks? In the other interaction there is no mediating particle at all. Is it possible the answer is wrong and a gluon is missing? Is anyone able to explain these diagrams?

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The quark anti-quark pair can come from a gluon radiated from one of the other quarks or photon radiated from any of the intermediate or final state particles. These "pair production" parts of Feynman diagrams are sometimes omitted because there are several options for this with the same number of lattices.

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