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

• A
• springbottom
In summary, the photon propagator <A_mu (x) A^nu(0) > in momentum space can be computed by summing up all the self-energy diagrams of the photon, which include contributions from the Z boson. However, due to gauge symmetry (Ward identity), the photon and Z do not have the same parity. This means that the pole structure of the Z is not inherited by the photon propagator. Additionally, the weak interaction does not conserve parity, making it not a good quantum number for discussing the weak interaction. Finally, the diagram connecting the photon and Z does not contribute to the 1PI diagrams of the photon's self-energy.
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]

ohwilleke
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.

vanhees71 and protonsarecool
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.

vanhees71, ohwilleke and 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

Last edited by a moderator:
vanhees71

## 1. What is the Z boson pole and how does it relate to the photon propagator?

The Z boson pole is a point in the complex plane where the propagator for the Z boson has a singularity. This singularity is related to the coupling of the Z boson to other particles, including the photon. The presence of the Z boson pole in the photon propagator indicates that the photon can interact with the Z boson and other particles through the weak interaction.

## 2. How is the Z boson pole detected in experiments?

The Z boson pole can be detected in experiments by studying the decay products of the Z boson. By analyzing the energy and momentum of these decay products, scientists can determine the presence of the Z boson pole and its properties, such as its mass and coupling strengths.

## 3. What is the significance of the Z boson pole in particle physics?

The Z boson pole is significant because it is a manifestation of the weak interaction, one of the four fundamental forces of nature. It allows for the exchange of particles such as the Z boson and the photon, which play crucial roles in many physical processes, including radioactive decay and nuclear reactions.

## 4. Can the Z boson pole show up in the photon propagator in all energy scales?

No, the Z boson pole only shows up in the photon propagator at energy scales close to the mass of the Z boson. At higher energy scales, the Z boson propagator becomes negligible and the electromagnetic interaction dominates, leading to a different behavior of the photon propagator.

## 5. How does the presence of the Z boson pole affect the behavior of the photon propagator?

The presence of the Z boson pole in the photon propagator leads to a modification of the photon's behavior at energy scales close to the Z boson mass. This can be seen in various physical processes, such as the scattering of electrons and positrons, where the presence of the Z boson pole affects the cross-section and angular distribution of the scattered particles.

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