Electroweak asymptotic freedom

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In summary, the strong force's coupling constant can be calculated, but this does not necessarily mean the same is true for the electroweak force. Additionally, while U(1) is not asymptotically free, the combination of SU(2) and U(1) in the electroweak theory is. Peter Woit's book "Not Even Wrong" raises questions about the origin and values of the symmetry groups in the electroweak theory, particularly the value of the fine structure constant. The statement about the U(1) part of the gauge theory not being asymptotically free may refer to the Glashow-Salam-Weinberg theory, which includes a Higgsed U(1)
  • #1
star apple
First, the coupling constant of the strong force can be computed.. does it mean it should also (ought to be) for the electroweak?

Also U(1) is not asymptotically free but electroweak SU(2)xU(1) is asymptotically free.. why is SU(2)xU(1) asymptotically free?
 
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  • #2
star apple said:
why is SU(2)xU(1) asymptotically free?

I don't believe that it is. In (3+1) dimensions, the U(1) coupling should grow in the UV.
 
  • #3
king vitamin said:
I don't believe that it is. In (3+1) dimensions, the U(1) coupling should grow in the UV.

I queried this as a result of reading Peter Woit book "Not Even Wrong".. he quoted:

"Why SU(3)xSU(2)xU(1)? A truly fundamental theory should explain where this precise set of symmetry groups is coming from. In addition, whereas QCD (the SU(3) part of this) has the beautiful property of having no free parameters, introducing the two other groups SU(2) and U(1)) introduces two free parameters and one would like some explanation of why they have the values they do. One of these is the fine structure constant a, and the question of where this number comes from goes back to the earliest days of QED. Another related concern is that the U(1) part of the gauge theory is not asymptotically free, and as a result it may not be completely mathematical consistent."

I thought he meant that SU(2)xU(1) was asymptotically free.. if not.. why did he mentioned that "Another related concern is that the U(1) part of the gauge theory is not asymptotically free, and as a result it may not be completely mathematical consistent"? This statement implied SU(2)xU(1) was asymptotically free.
 
  • #4
The Glashow-Salam-Weinberg theory is not asymptotically free. There's a U(1) in the gauge group and also it's Higgsed. I'm not certain anymore, what's the precise statement but if I remember right, one can show that for a wide range of Higgsed local gauge symmetries the resulting models are not asymptotically free, even if there are no U(1)'s are in the gauge group:

Higgs phenomena in asymptotically free gauge theories
T. P. Cheng, E. Eichten, and Ling-Fong Li
https://doi.org/10.1103/PhysRevD.9.2259
 
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Related to Electroweak asymptotic freedom

1. What is electroweak asymptotic freedom?

Electroweak asymptotic freedom is a fundamental property of the electroweak force, one of the four fundamental forces in nature. It describes the behavior of this force at extremely high energies, where the particles involved are close together and the force between them is very strong.

2. How does electroweak asymptotic freedom differ from other types of asymptotic freedom?

Electroweak asymptotic freedom is unique because it describes the behavior of two forces, the electromagnetic and weak forces, at high energies. Other types of asymptotic freedom, such as quantum chromodynamics (QCD), only describe the behavior of a single force.

3. What is the significance of electroweak asymptotic freedom?

Electroweak asymptotic freedom is significant because it allows for the unification of the electromagnetic and weak forces at high energies, providing a more complete understanding of the fundamental forces of nature. It also helps to explain the behavior of particles at extreme energies, such as those found in particle accelerators.

4. Can you provide an example of electroweak asymptotic freedom in action?

One example of electroweak asymptotic freedom can be seen in the behavior of quarks, the fundamental particles that make up protons and neutrons. At high energies, the strong force between quarks becomes weaker, allowing them to move more freely and interact with other particles. This behavior is described by QCD, which exhibits asymptotic freedom.

5. Are there any current research efforts related to electroweak asymptotic freedom?

Yes, there are ongoing research efforts to further understand and explore electroweak asymptotic freedom. One area of interest is in the development of new mathematical models and theoretical frameworks to better describe the behavior of the electroweak force at high energies. Additionally, experiments are being conducted at particle accelerators to test and validate predictions made by the theory of electroweak asymptotic freedom.

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