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Is the decay of a neutral rho meson into a neutral pi meson and a photon forbidden? It doesn´t look like parity conservation or charge conservation is violated but I haven´t found this decay is possible on the Internet.

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In fact, the decay is not forbidden, even though it is a rare decay as you could check on PDG. If you're interested you can check this (and many others) article:

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    $\begingroup$ Right. Being electromagnetic, it is suppressed wrt to the strong one by four orders of magnitude. Spot on. $\endgroup$ Commented Aug 23, 2020 at 11:50

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