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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?

Decay of phi-meson into a positive and a negative kaon

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?

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

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  • $\begingroup$ 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. $\endgroup$ – anna v May 17 at 11:25
  • $\begingroup$ I refer to the only horizontal line in the diagram. $\endgroup$ – Simon G. May 17 at 11:34
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    $\begingroup$ well, there is no problem with it $\endgroup$ – anna v May 17 at 11:57
  • $\begingroup$ 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. $\endgroup$ – Cosmas Zachos May 17 at 18:30
  • $\begingroup$ 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. $\endgroup$ – Simon G. May 18 at 15:02

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