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I am wondering if it is possible for a massless boson to change the particle interacting with it, into another type of particle. In other words, is it possible to have a pair production process (in S channel) similar to the diagram below:

enter image description here

where $\gamma’$ is a massless guage boson similar to photon, and $\chi$ and $\psi$ are both fermions (or scalars) of different mass. I know that it is allowed for a massive mediator (like W in the SM).

Do you have any arguments for or against this process?

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  • $\begingroup$ @CosmasZachos This kind of $\bar{\chi}\gamma^\mu\psi$ vertex appears in a dark matter model after mass splitting. I just want to make sure that this type of process is allowed where a particle is changed to another one through emitting a massless boson. I cannot see any problem with kinematics of the process. What do you think? $\endgroup$ – Ramtin Jun 28 at 1:21
  • $\begingroup$ @CosmasZachos My question is whether a massless boson can change the particle to another one with a different mass. $\endgroup$ – Ramtin Jun 28 at 8:20
  • $\begingroup$ If the answer is useful, you can click on the check mark. $\endgroup$ – Cosmas Zachos Jun 29 at 13:02
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I am not familiar with your models and their caveats, so I cannot speculate how your effective field theory imagines this vertex, $ie'A'_\mu\bar \chi \gamma^\mu \psi $ + c.c., exists for massless vectors which are not gauge bosons. The model should be non-renormalizable, but model-builders are pretty unscrupulous these days...

The Feynman diagram you have is meaningless Feynman-diagram-junk, as common in experimental talks with a Feynman-diagram fetish, in that it suborns the viewer into assuming it represents a term in an existing legitimate theory, of the "you-know, you-know" type.

Let me stress again what you must already know, namely that a massless gauge field $A'_\mu$ is completely out of the question, because it should couple to a conserved current, and your $\bar \chi \gamma^\mu \psi $ cannot be conserved unless χ and ψ have the same mass, so the fermions have a global U(1) symmetry before the introduction of such gauge fields.

I have little experience with non-gauge vector fields, against which the whole world of Lorentz consistency is arrayed, but that is a very different question I would not touch.

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