Electroweak asymptotic freedom

  • Context: High School 
  • Thread starter Thread starter star apple
  • Start date Start date
  • Tags Tags
    Electroweak
Click For Summary

Discussion Overview

The discussion revolves around the concept of asymptotic freedom in the context of the electroweak theory, specifically examining the properties of the gauge group SU(2)xU(1) and its implications for the coupling constants of the electroweak interactions. Participants explore theoretical aspects and implications of asymptotic freedom, particularly in relation to the U(1) component and its behavior in different dimensions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the electroweak SU(2)xU(1) is asymptotically free, noting that U(1) is not asymptotically free and suggesting that this may affect the overall behavior of the electroweak theory.
  • One participant expresses skepticism about the asymptotic freedom of SU(2)xU(1), arguing that in (3+1) dimensions, the U(1) coupling should grow in the ultraviolet (UV) regime.
  • Another participant references Peter Woit's book, discussing the implications of the symmetry groups in the electroweak theory and questioning the consistency of the theory given the non-asymptotic freedom of U(1).
  • A later reply asserts that the Glashow-Salam-Weinberg theory is not asymptotically free due to the presence of the U(1) component and the Higgs mechanism, suggesting that models with Higgsed local gauge symmetries generally do not exhibit asymptotic freedom.

Areas of Agreement / Disagreement

Participants express disagreement regarding the asymptotic freedom of SU(2)xU(1), with some arguing for its asymptotic freedom and others asserting that it is not asymptotically free due to the U(1) component. The discussion remains unresolved with competing views on the topic.

Contextual Notes

Participants reference specific theoretical frameworks and literature, indicating that the discussion is influenced by various interpretations of asymptotic freedom and the role of the Higgs mechanism in gauge theories. There are unresolved assumptions regarding the behavior of coupling constants in different dimensions.

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?
 
Physics news on Phys.org
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.
 
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.
 
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
 
  • Like
Likes   Reactions: star apple

Similar threads

Graduate Beta function of electroweak theory
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Why do the proton and electron have equal and opposite electric charge?
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Intuition behind asymptotic freedom/slavery
  • · Replies 1 ·
Replies
1
Views
1K
Graduate The "electroweak eta meson"
  • · Replies 8 ·
Replies
8
Views
1K
Graduate Spinor indices on Yukawa coupling terms in electroweak sector
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why EM and weak interaction are unified
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Color confinement in high-energy quark knockout
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad QCD: Asymptotic not-exactly freedom?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate The Electroweak Symmetry: What Happens When It Breaks?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Counting degrees of freedom for Goldstone bosons
  • · Replies 10 ·
Replies
10
Views
5K