How can e-e+ possibly go to ZZ?

[AlanKirby]

Hi there, my question is the following.

If an electron and positron annihilate, how can they result in ZZ?

The issue I'm having is that due to charge conservation, the exchange particle can't be W- or W+.
It also can't be a photon since the Z's don't have electrical charge to couple to.
It also can't be a Z since the Z's don't have weak charge to couple to.

I'm reading in my notes that a photon or a Z boson can mediate this interaction. How is that possible?

Thanks for any replies.

 

[mfb]

It can work in the same way the annihilation to two photons works. No need to have the two Z interact with each other.
The first two diagrams here - the third is not possible in the SM. The diagrams are for quarks but leptons work the same way.

 

[Vanadium 50]

The process goes by a t-channel electron.