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I often hear the term "coupling" when people speak of a potentially decaying dark matter (DM) particle. I don't understand what a (hypothetical) DM particle should couple to when we consider a decay? I though a particle can just decay without any interaction?

My understanding of "coupling" of two particles A and B is that in the Lagrangian (e.g. the one of the Standard Model) there appears a term in which A and B appear. How does this connect to a DM decay then?

rfl
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Welcome_Green
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    Why do you imagine decays would be different from say a scattering process? Both include couplings when making calculations. – Triatticus Dec 06 '22 at 08:07
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    See the pion decay Feynman diagram here https://physics.stackexchange.com/questions/418043/most-trivial-neutral-pion-decay and the wiki article https://en.wikipedia.org/wiki/Feynman_diagram – anna v Dec 06 '22 at 09:30

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This is best thought-of in terms of Feynman diagrams. You have something coming in on the left, something else going out on the right. In between, these somethings need to couple, i.e. you need to draw lines connecting them. @anna linked this nice example:

pion decay

As you can see, the pion needs to "couple" at the $g_s$ vertex to two Kaons, which then couple at the two electromagnetic vertizes to gammas. You could replace that triangle by an effective "coupling" of the pion to two gammas. Here's an example at tree level, muon decay:

enter image description here

Still, the muon needs to couple to other particles in order to decay, in this case directly to the W boson and the neutrino.

In your example, the dark matter particle too needs to couple to its decay products through some Feynman diagram. Often that involves a loop, e.g. for WIMPs with a box from a Z-boson, or perhaps some new gauge boson floating around.

rfl
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  • Okay, so in this article Fig. 4 (page 35): https://arxiv.org/pdf/2106.05913.pdf Is it correct to say that for example in Image a) we have a coupling between the sterile neutrino N, a SM neutrino v_1 and a Z Boson, and a coupling between two SM neutrinos and the Z boson? And, in the end these couplings lead to a decay. – Welcome_Green Dec 06 '22 at 13:02
  • figure 4.4. yes that is correct. – rfl Dec 06 '22 at 13:54