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I just read https://en.wikipedia.org/wiki/Annihilation#Examples and there is the popular $ e^+e^- \to \gamma \gamma $ reaction described.

Is it always possible to produce a $ \gamma $? A photon does not have mass (but momentum and thus energy and then, somehow, in return, mass finally) so is there any energy threshold for a photon?

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There is no threshold because photons can have arbitrarily small energy (and arbitrarily small momentum).

Their invariant mass is zero so thinking that “then, somehow, in return, mass finally” is a bad idea. If you learned about the obsolete concept of “relativistic mass”, it’s just the energy, up to factors of $c$, and does not warrant a confusing name.

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  • $\begingroup$ But $ E=mc^2 $ is valid for photons as well? $\endgroup$ – Ben Aug 20 '19 at 16:38
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    $\begingroup$ No, it is not, because for a photon $E$ is nonzero but $m$ is zero. The general formula that applies to all particles is $E^2-(pc)^2=(mc^2)^2$. For a photon this becomes $E=pc$. Remember the general formula and forget about $E=mc^2$. $\endgroup$ – G. Smith Aug 20 '19 at 16:40

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