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## Main Question or Discussion Point

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 :)

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 :)