Why was is it needed to include the Z boson along with the W's?

In summary, the inclusion of the Z boson along with the W bosons was necessary to have a renormalizable theory with U(1) x SU(2) gauge invariance. Without it, the theory would not have gauge symmetry and could not be made renormalizable. Additionally, the inclusion of the Z boson also helped address the issue of unitarity in the Fermi theory at high energies.
  • #1
happy42er
2
0
Why was is it needed to include the Z boson along with the W's... is the theory nonrenoramalizable without it?
 
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  • #2
happy42er said:
Why was is it needed to include the Z boson along with the W's... is the theory nonrenoramalizable without it?

Right. To have a renormalizable theory, one must have a U(1) x SU(2) gauge invariance. After spontaneous symmetry breaking, two of the gauge fields of the SU(2) symmetry as well as one linear combination of the U(1) generator and tau_3 generator acquire a mass..Those are the Z,W+,W-. The other, orthogonal, linear combination of the generators give the massless photon. If one simply throws in a W+ and W-, there is no gauge symmetry and the theory can't be made renormalizable.
 
  • #3
http://nobelprize.org/nobel_prizes/physics/laureates/1979/glashow-lecture.pdf
 
  • #4
arivero said:
http://nobelprize.org/nobel_prizes/physics/laureates/1979/glashow-lecture.pdf

very interesting reference. Thanks!
 
  • #5
happy42er said:
Why was is it needed to include the Z boson along with the W's... is the theory nonrenoramalizable without it?

I thought though that the reason why the Z and W bosons where included was because without them the theory violated unitarity.

Isn't that so?
 
  • #6
I'm not sure about unitarity or renormalizability but one way to think about it was if the theory was SU(2) the theory has no mutually commuting generators so it's can describe theory of electromagnetism.
 
  • #7
You can describe low-energy limit of weak interaction without intermediate bosons, that's called Fermi theory, but it is not renormalizable. A theory with spontaneously broken SU(2) x U(1) symmetry group nicely describes everything, and SU(2) x U(1) just happens to have 4 generators, which become a photon and three new gauge bosons.

I don't think that unitarity enters in any way.
 
  • #8
hamster143 said:
You can describe low-energy limit of weak interaction without intermediate bosons, that's called Fermi theory, but it is not renormalizable. A theory with spontaneously broken SU(2) x U(1) symmetry group nicely describes everything, and SU(2) x U(1) just happens to have 4 generators, which become a photon and three new gauge bosons.

I don't think that unitarity enters in any way.

When I referred to unitarity I meant that in the Fermi theory there are cross sections that grow with the energy.

For example:

[tex]\sigma(e \nu \rightarrow e \nu) \propto {G_F}^2 s[/tex]

Since cross sections express the likelihood of interaction between particles, what happens is that at sufficient high energies the probability of some process happening is greater than 1. In the Fermi theory this energies are around [tex]\sqrt{s}[/tex]=300 GeV.

That's why I thought that there was a problem with unitarity.

After looking into it now I'd say that the theory had both problems, it wasn't renormalizable and it violated unitarity.
 

FAQ: Why was is it needed to include the Z boson along with the W's?

Why was it needed to include the Z boson along with the W's?

The inclusion of the Z boson was necessary in order to complete the theory of electroweak interactions, which describes the unification of the electromagnetic and weak nuclear forces.

What is the role of the Z boson in electroweak interactions?

The Z boson is responsible for mediating the weak nuclear force, which is involved in processes such as radioactive decay and nuclear reactions.

How does the Z boson differ from the W boson?

The Z boson and the W boson are both gauge bosons that mediate the weak nuclear force, but they differ in their electric charge and weak isospin values. The Z boson has zero electric charge and a neutral weak isospin, while the W boson has either a positive or negative electric charge and a non-zero weak isospin.

What evidence supports the existence of the Z boson?

The Z boson was first observed in experiments at the Super Proton Synchrotron (SPS) at CERN in 1983. This discovery was later confirmed by experiments at the Large Electron-Positron (LEP) collider and the Tevatron collider, providing strong evidence for the existence of the Z boson.

What are the implications of the inclusion of the Z boson in the electroweak theory?

The inclusion of the Z boson in the electroweak theory not only completes our understanding of the unification of forces, but it also provides a more comprehensive explanation of the fundamental interactions in the universe and has led to further developments in particle physics and the Standard Model.

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