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

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Discussion Overview

The discussion centers on the relationship between the Z boson and the photon propagator in quantum field theory, specifically whether the pole structure of the Z boson appears in the photon propagator. The scope includes theoretical considerations and technical aspects of quantum electrodynamics and weak interactions.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that the photon propagator inherits the pole structure of the Z boson due to shared quantum numbers, proposing that if the Z boson has a pole at a complex momentum value, the photon propagator should reflect this.
  • Another participant counters this claim by invoking gauge symmetry and the Ward identity, implying that the relationship may not hold.
  • There is a discussion about the parity of the photon and Z boson, with some participants asserting that the photon has odd parity while the Z boson does not, leading to questions about the implications of this difference.
  • One participant notes that the weak interaction does not conserve parity, suggesting that parity may not be a relevant quantum number in this context.
  • Another participant points out that the Z boson couples to fermions differently than the photon, indicating that certain diagrams do not contribute to the photon’s self-energy.

Areas of Agreement / Disagreement

Participants express disagreement regarding the implications of shared quantum numbers and the role of parity in the context of the photon and Z boson. The discussion remains unresolved with multiple competing views on the relationship between the two particles.

Contextual Notes

Participants raise concerns about the implications of gauge symmetry and parity conservation in weak interactions, but these points remain open to interpretation and are not fully resolved within the discussion.

springbottom
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TL;DR
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]
 
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No, because of gauge symmetry (Ward identity)
 
springbottom said:
Z and photon have same quantum numbers,

Why do you think that? The photon has odd parity. The Z doesn't even have parity.
 
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Vanadium 50 said:
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?
 
The weak interaction does not conserve parity. Parity is not a good quantum number when discussing the weak interaction.
 
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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.

1657561494693.png

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