# Pair production through massless gauge mediator

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:

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?

• @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? – Ramtin Jun 28 at 1:21
• @CosmasZachos My question is whether a massless boson can change the particle to another one with a different mass. – Ramtin Jun 28 at 8:20
• If the answer is useful, you can click on the check mark. – Cosmas Zachos Jun 29 at 13:02

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...
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.