Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.
Sign up to join this community
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?
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.
