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Literature states neutral pion decay by QED cannot occur directly because the pion is uncharged. pion decay from http://www.physnet.org/modules/pdf_modules/m279.pdf

However, I cannot see why Photons are not allowed to interact with the Quarks directly. direct interaction

Please elaborate which statement is false and why.

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    $\begingroup$ You do not give a link for the book image. It probably was published before the existence of quarks was suspected, and was correct for the time it happend. Now the lower diagram is used ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QCD/… .it is a d quark that plays ball $\endgroup$ – anna v Jul 17 '18 at 11:16
  • $\begingroup$ sorry, the image is from physnet.org/modules/pdf_modules/m279.pdf it seems quarks where known when this was published $\endgroup$ – Joel Linn Jul 17 '18 at 11:45
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    $\begingroup$ Your quark diagram is incomplete. You skipped the vertex $\pi^0 \bar{u} u$ involving a pion resolving to this virtual pair of quarks, and ending up with the type of triangle diagram similar to the old-fashioned one involving virtual Ks or ps. Remarkably, when you include all u and d quarks of all colors, you get roughly the same rate in the hadron triangle calculation, as in the quark triangle calculation. $\endgroup$ – Cosmas Zachos Jul 17 '18 at 13:38
  • $\begingroup$ Do the hadronic processes contribute/exist or are they just of historic meaning? $\endgroup$ – Joel Linn Jul 18 '18 at 20:39
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    $\begingroup$ The hadronic processes are not used anymore, and , as such, they are historical vestiges, superceded by the quark calculations. Nevertheless, as an effective low energy calculational technique, they never had their death certified: lots of alternative techniques can live side-by-side in complementarity. The states in the triangles are virtual, so "exist" is a charged and evanescent fighting word! $\endgroup$ – Cosmas Zachos Jul 19 '18 at 14:31
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To describe the uncharged pion in the initial state you will have to project the open $u$ or $d$ quarks onto the mesonic spin zero wavefunction carrying quantum numbers of the $\pi^0$. At the Feynman diagram level, as mentioned in the comments, you obtain the famous triangle diagrams via Yukawa interaction describing the decay, driven by the well known chiral anomaly.

The hadronic mediating diagrams can be viewed as a 'course-graining' or effective description of the underlying quark resolved diagrams. The pion decay rate is independent of the description used under the so called anomaly matching condition, but that is a detail.

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