Annihilation and production of bosons

[Arcturus7]

I am confused about the production of bosons in annihilation processes.

If we have a positron and an electron coming together and annihilating, we can always find a frame in which the net momentum is zero, which would suggest that a single photon can never be produced in such an interaction (but a massive boson such as a Z could be).

However, in a question asked by my prof. in lectures the other week, she said that future electron/positron colliders may operate at energies sufficient to produce top-antitop pairs. How would this occur? And also, how would Feynman diagram for this process look?

I had imagined that the initial annihilation would simply produce a boson which would then decay into the top/antitop pair, however thinking about it, I feel as though the boson should be massive, and therefore not be a photon. Is this correct, or does the fact that the photon is virtual allow it to occur?

 

[mfb]

or does the fact that the photon is virtual allow it to occur?

Exactly. The (main) process would happen via a virtual photon/Z boson.
As they are virtual, you cannot even say "this was produced via a photon" or "via a Z boson" - their amplitudes add, you cannot distinguish between the processes. The Higgs leads to a much smaller contribution as well, and there are loop processes contributing a little bit.

 

[Arcturus7]

Ah I see - that's great! Thanks for clearing that up :)