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Imagine a positive and negative pion, their only interaction between each other would be due to electromagnetism and the weak force, right? It is not like these two pions can form neutral pions due to the strong force. Otherwise it would mean the pions have emitted "gluonic" radiation due to the difference in binding energies which is obviously impossible.

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Do pions not interact with other pions via the strong force

Pions are bound states of quark anti quark that have a small lifetime, so pion pion scattering experiments are note easy to design. The forces that would enter in any calculation are the strong, the weak, and the electromagnetic, the strong by definition being the strongest. The hypothesis that the only forces are the weak and electromagnetic is wrong.

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