# Feynman diagrams of phi-meson decay

I am learning how to make Feynman diagrams, and I have a couple of questions about two possible decays of the phi-meson.

The first question relates to the reaction $$\phi \rightarrow\text{K}^+ + \text{K}^-$$ as seen in the picture below. Each gluon decays into an $$u\bar{u}$$ pair - I think. I don't know how to interpret the central horizontal line of this diagram. Does it symbolize the annihilation of the last $$u\bar{u}$$ pair, and if so, why isn't the resultant gluons included in the diagram?

My second question relates to the decay $$\phi \rightarrow \rho ^{+} + \pi^-$$ (the left reaction below). According to the author, this decay proceeds through an intermediary state with at least 3 gluons. Why isn't 2 gluons enough? That is, why can't the $$s\bar{s}$$ annihilate into 2 gluons that in turn split into a $$u\bar{u}$$ and a $$d\bar{d}$$ pair, respectively, which then combine into the two resultant mesons?

The picture is taken from "Particles and Nuclei" by Bogdan Povh, etc., 7th edition

• I do not understand what you mean by horizontal linesee en.wikipedia.org/wiki/OZI_rule . I see an up incoming(antiup by the arrow direction) exchanging a gluon with the s incoming ( antis), andan s and up going out. The correct lower diagram is in the wiki link. – anna v May 17 at 11:25
• I refer to the only horizontal line in the diagram. – Simon G. May 17 at 11:34
• well, there is no problem with it – anna v May 17 at 11:57
• You do understand that the symbolic value of the diagram would not be affected if you raised a little the upper right gluon vertex dot, for instance. Then you could poetically visualize (that's all this visualization is: an intuitive metaphor!) the left vertex as creating a u quark pair, and the right vertex as a gluon absorbed by the quark recently created. As long as you appreciate this is all intuition-building "soft" visualization, not math. – Cosmas Zachos May 17 at 18:30
• Thanks, that helps. I still don't understand, however, why we need two gluons in this interaction. The strange quark could emit one gluon that in turn could split into an up anti-up pair; this would give the same products. – Simon G. May 18 at 15:02