The Mystery of the W and Z Bosons' Mass Difference

In summary: The phrase "The W and Z ate the goldstone bosons" refers to the 3 unphysical goldstone boson degrees of freedom appearing as the W and Z longitudinal polarization.In other words, you have the Higgs field belonging to (2,1) representation of SU(2)xU(1) (is a doublet under SU(2) and singlet under U(1) ). That means that you have 2 scalar complex fields (upper lower component in SU(2) doublet) which give you four degrees of freedom. The physical degrees of freedom though are 1, because the other 3 can be gauged out by choosing gauge.The procedure of SSB leads to 3 massive/1
  • #1
ChrisVer
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Because I am a little tired to think...
For where does the mass difference between the W and Z bosons come from?
 
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  • #2
MW = ½ v g
MZ = ½ v (g2 + g'2)1/2

so the difference basically comes from the weak mixing angle,

MW/MZ = cos θW
 
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  • #3
would that mean that it's because the Z -as chargeless- gets contributions from more interactions? because it gets the g' of U1
 
  • #4
would that mean that it's because the Z -as chargeless- gets contributions from more interactions? because it gets the g' of U1

Unlike the charged components of the [itex]W[/itex] [itex]SU(2)[/itex] Triplet, The Neutral component mixes with the Hypercharge gauge boson ( [itex]B[/itex] ) to give two mass eigenstates, the [itex]Z[/itex] and the photon. This Hypercharge gauge boson component is the origin of the contribution to the [itex]Z[/itex] mass which is proportional to [itex]g^{'}[/itex]
 
  • #5
While we are on this topic, I have a question.

Layman explanation of W and Z masses are that they "ate" Goldstone bosons produced by electroweak symmetry breaking.
What is meant by "eating" here? Thats not a scientific term for sure :D
 
  • #6
Layman explanation of W and Z masses are that they "ate" Goldstone bosons produced by electroweak symmetry breaking

A full understanding of this would require a thorough study of spontaneously broken gauge theories.

However, in short:

In General when a theory has a spontaneously broken continues symmetry (Are you familiar with the concept?) it has massless particle which is called a goldstone boson ( see http://en.wikipedia.org/wiki/Goldstone_boson )

Masses for the W and Z require the gauge symmetry of the standard model to be spontaneously broken. This breaking would naively introduce goldstone bosons to theory. However, It turns out the theory can be written without any reference to these goldstone bosons, i.e. , they are not physical. This happens because the symmetry is a gauge symmetry and not a global symmetry.

On the other handed When massless spin 1 particle becomes massive it has in addition a longitudinal polarization ( Where the spin's projection on its momentum is zero). Therefore there are 3 additional degrees of freedom after the symmetry is broken.

The phrase "The W and Z ate the goldstone bosons" refers to the 3 unphysical goldstone boson degrees of freedom appearing as the W and Z longitudinal polarization.
 
  • #7
In other words, you have the Higgs field belonging to (2,1) representation of SU(2)xU(1) (is a doublet under SU(2) and singlet under U(1) ). That means that you have 2 scalar complex fields (upper lower component in SU(2) doublet) which give you four degrees of freedom. The physical degrees of freedom though are 1, because the other 3 can be gauged out by choosing gauge.
The procedure of SSB leads to 3 massive/1 massless spin-1 particles from 4 massless... the extra degree of freedoms (3) came from the gauged out fields of the Higgs doublet - the Goldstone bosons were those fields...They were "eaten"/disappeared by 3 gauge bosons and the 3 became massive (or acquired longitudial dof).

Wouldn't it be correct to see the Goldstone boson as a ghost field?
I mean the initial gauge bosons, massless, would have to be represented by a state:
[itex]|Ψ>= |T> + |S-L> [/itex]
(T: transverse, L: longitudia, S:scalar , and the + is not the "normal" sum sign).
The norm of the second space is 0, while the other's is positive definite.
In that case I could say that the Goldstone bosons should belong to some scalar
[itex] |Φ> = |S> [/itex]
in order to kill out the (negatively normed S states and leave L untouched).
I am not so keen in Ghosts that's why I am making this question. To see how well I understand it :)
 

1. What are W and Z bosons?

W and Z bosons are subatomic particles that are responsible for carrying the weak nuclear force, one of the four fundamental forces of nature. They were first discovered in the 1980s through experiments at the Large Hadron Collider.

2. What is the mass difference between W and Z bosons?

The mass difference between W and Z bosons is approximately 84 GeV (gigaelectronvolts). This means that the Z boson is about 84 times heavier than the W boson.

3. Why is the mass difference between W and Z bosons important?

The mass difference between W and Z bosons is important because it provides insight into the nature of the weak nuclear force and its role in the universe. It also helps scientists understand the fundamental particles and their interactions.

4. How was the mass difference between W and Z bosons measured?

The mass difference between W and Z bosons was measured using particle accelerators, specifically the Large Electron-Positron Collider and the Large Hadron Collider. By colliding particles at high energies, scientists were able to observe the decay products and calculate the mass difference between the two bosons.

5. What does the mass difference between W and Z bosons tell us about the Standard Model of particle physics?

The mass difference between W and Z bosons is consistent with the predictions of the Standard Model of particle physics, which describes the fundamental particles and their interactions. This provides further evidence for the validity of the Standard Model and its ability to explain the behavior of subatomic particles.

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