Understanding GUT Symmetry: Running Couplings

[indigojoker]

Hi, I'm very new to the field of GUT symmetry and would like to understand a passage in the book "Collider Physics"

the page reads:
All couplings evolve with the mass scale as discussed in chapter 7. Only particles with mass < mu contribute to the evolution at any given mass scale mu. Hence below the GUT scale, g3, g2 and g1 evolve independently according to the beta-functions of SU(3), SU(2) and U(1), respectively. The hope is that evolution from a common coupling at mu=Mx down to mu=Mw will bring these couplings into agreement with the experimentally measured strong and electroweak couplings. A complete analysis of this question should include two-loop contributions to the beta-functions and radiative corrections to the low-energy couplings.

I would really like to understand the following passage. I have no prior experience to symmetry but would just like to understand several questions.

"Only particles with mass < mu contribute to the evolution at any given mass scale mu."

what is mu? what is the evolution? what is the mass scale?

"Hence below the GUT scale, g3, g2 and g1 evolve independently according to the beta-functions of SU(3), SU(2) and U(1),"

what is the GUT scale g3 g2 g1? Why do they evolve? What are the beta-functions? What is SU(3), SU(2) and U(1)?

"The hope is that evolution from a common coupling at mu=Mx down to mu=Mw will bring these couplings into agreement with the experimentally measured strong and electroweak couplings."

What are couplings? What is "mu=Mx down to mu=Mw"?

"A complete analysis of this question should include two-loop contributions to the beta-functions and radiative corrections to the low-energy couplings."

what are two-loop contributions and radiative corrections to the low-energy couplings?


I am very curious about this field and am taking my first dive, but need a lot of help understanding, as shown by all my questions :)

 

[AndyW]

Hello and welcome to the field of GUT symmetry! I can understand that this passage may seem confusing if you are new to this field. Let me break it down for you:

1. "Only particles with mass < mu contribute to the evolution at any given mass scale mu."
- In this context, mu refers to the mass scale at which the couplings (strength of interactions between particles) are measured. The passage is stating that only particles with a mass less than the mu value will affect the evolution (changes) of the couplings at that specific mass scale.

2. "Hence below the GUT scale, g3, g2 and g1 evolve independently according to the beta-functions of SU(3), SU(2) and U(1)."
- The GUT scale refers to the energy scale at which the strong, weak, and electromagnetic forces are thought to be unified. G3, g2, and g1 are symbols representing the strengths of these forces (strong, weak, and electromagnetic). The passage is saying that at energy scales below the GUT scale, these forces evolve independently according to their respective beta-functions, which are equations that describe how a force changes with energy.

3. "The hope is that evolution from a common coupling at mu=Mx down to mu=Mw will bring these couplings into agreement with the experimentally measured strong and electroweak couplings."
- In this context, couplings refer to the strength of interactions between particles. The passage is saying that by evolving the couplings from a common value at a higher energy scale (mu=Mx) down to a lower energy scale (mu=Mw), they hope to bring these couplings in line with the experimentally measured strengths of the strong and electroweak forces.

4. "A complete analysis of this question should include two-loop contributions to the beta-functions and radiative corrections to the low-energy couplings."
- Two-loop contributions and radiative corrections are both ways of accounting for higher-order effects in calculations. In this case, they are referring to more complex calculations that take into account these effects in order to get a more accurate understanding of the evolution of the couplings at lower energy scales.

I hope this helps to clarify some of your questions. Please don't hesitate to ask for further clarification if needed. Good luck with your studies in GUT symmetry!

 

[Entropia]

Dear reader,

Thank you for your interest in understanding GUT symmetry and its application in collider physics. I will do my best to explain the passage you have shared and address your questions.

Firstly, mu refers to the mass scale, which is a fundamental parameter in particle physics that measures the energy level at which particles interact. In this context, it refers to the energy level at which the couplings (strength of interactions) between particles are measured.

The evolution mentioned in the passage refers to the change in the values of these couplings as the energy level or mass scale changes. This is a consequence of the fundamental theory of quantum field theory, which states that the strength of interactions between particles changes as the energy level changes.

The GUT scale is a theoretical energy level at which the three fundamental forces of nature (strong, weak, and electromagnetic) are believed to merge into one unified force. g3, g2, and g1 refer to the coupling constants of the strong, weak, and electromagnetic forces, respectively. These forces are described by the mathematical frameworks of SU(3), SU(2), and U(1) symmetries, which are fundamental symmetries in particle physics.

The evolution of these couplings at the GUT scale is significant because it is believed that at this energy level, all three forces have equal strength and can be described by a single unified theory. Therefore, the hope is that as the energy level decreases, the couplings will evolve in a way that brings them into agreement with the experimentally measured values of the strong and electroweak forces.

Couplings refer to the strength of interactions between particles. In this context, mu=Mx and mu=Mw refer to energy levels, where Mx is the GUT scale and Mw is the weak scale, which is the energy level at which the weak force is dominant.

Two-loop contributions and radiative corrections are terms used in quantum field theory to describe the effects of higher-order calculations on the values of couplings. These are important considerations in the analysis of the evolution of couplings at different energy levels.

I hope this explanation has helped you understand the passage and some of the concepts related to GUT symmetry and collider physics. It is a complex field, and it is normal to have many questions when first diving into it. I encourage you to continue learning and exploring this fascinating area of science. Best of luck on your journey!