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Higgs boson, though electrically neutral, can decay to produce a pair of photons i.e., have electromagnetic interactions. See the answer here. Therefore, it appears that making dark matter electrically uncharged is not enough to prevent its decay into photons. For example, @marmot points out that axions can decay into photons. However, dark matter models usually also involve $\mathbb{Z}_2$ symmetries to prevent the decay of dark matter particles. Then how is it possible that the dark matter, like the axion, can still decay?

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  • $\begingroup$ same story with Z-boson. This is because Z and Higgs are electroweak multiplets, or parts of multiplets. Photon is also part of EW multiplet. $\endgroup$ – Kosm Jun 14 '18 at 12:18
  • $\begingroup$ @marmot You mean $\mathbb{Z}_2$ type symmetry would forbid its decay into photons? My question is this. While building a model for dark matter, is it enough to consider the dark matter to be uncharged in order to prevent its decay into photons? $\endgroup$ – SRS Jun 14 '18 at 12:35
  • $\begingroup$ In many models decay of dark matter to photons is forbidden by giving it some conserved exotic quantum number, see for example Wikipedia on the LSP. $\endgroup$ – Sebastian Riese Jun 14 '18 at 12:45
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    $\begingroup$ No, I did not read your question carefully. DM can decay into photons. An example is the axion, whose decay rate is hover tiniest. $\endgroup$ – user178876 Jun 14 '18 at 12:54
  • $\begingroup$ @marmot Not your fault. I edited the question. $\endgroup$ – SRS Jun 14 '18 at 13:11
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Both Higgs and (hypothetically) axions do not decay directly into photons, but indirectly through "virtual loops" involving other particles.

(Have a look also here.)

So, yes, if something doesn't carry electric charge then it cannot directly "touch" photons :)

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