A Does the Z boson pole show up in the photon propagator?

[springbottom]

TL;DR Summary

Z and photon have same quantum numbers, how are their pole structures of the (interacting) propagator related?

If I look at the photon propagator <A_mu (x) A^nu(0) > in momentum space, as I understand it I am to compute this by summing up all the self-energy diagrams of the photon, which look like:

photon -> stuff -> photon

In particular, since the photon shares the same quantum numbers as the Z, you get a collection of diagrams that are:

photon -> stuff -> Z -> stuff -> Z -> stuff -> photon

(where the stuff connecting photon with Z could be a fermion loop for example). In this case, it would seem that the pole structure of the Z is inherted by the photon propagator? In particular, if there is some complex momenta value at which the Z boson has a pole, then the photon propagator should also have the same pole? Is this true?
[I may have messed something very basic up, I am still quite bad at basic QFT]

 

[malawi_glenn]

No, because of gauge symmetry (Ward identity)

 

[Vanadium 50]

Z and photon have same quantum numbers,

Why do you think that? The photon has odd parity. The Z doesn't even have parity.

 

[ohwilleke]

Why do you think that? The photon has odd parity. The Z doesn't even have parity.

I thought that the photon and Z both had helicity and not parity. Was I mistaken?

 

[Vanadium 50]

The weak interaction does not conserve parity. Parity is not a good quantum number when discussing the weak interaction.

 

[malawi_glenn]

For instance the Z boson couple to fermions via gamma5 (couple differently for left- and right-handed fermions), the photon does not care about such things.

this diagram does not contribute to the 1PI diagrams of the photons self-energy