Is there a particular conservation principle that necessitates that the outcoming photon pair has the same frequencies as the incoming photon pair?
I'm thinking in particular of these Feynman-like diagrams. Is it only like A or can it be like B as well?
(The diagrams are $2$-dimensional and might suggest that the photons have different velocities, but that's not what I had in mind! What I do hope to convey is that the directions of the outgoing photons are different in A and B.)
If there is no such conservation principle at work, with which theory would one then be able to calculate the distribution of the amplitudes with respect to frequency-pairs?
I hope this makes sense. Otherwise please let me know.
Edit. I've added the diagrams with A', A'', and A''' below, just in case I got it wrong in A.