What is the 't Hooft Model and Equation in QCD?

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In summary, the conversation revolved around the topic of meson decays and the use of the 't Hooft Model, which involves using one spatial and one temporal dimension and an infinite number of colors in QCD. The main question was about obtaining more information on the 't Hooft model and equation, specifically on how to use it. Some recommended resources were 't Hooft's original paper, Sidney Coleman's lectures, and a set of notes available online. The conversation ended with the person thanking those who provided helpful responses.
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silmaril89
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Hello Everyone,

I'm doing some research on meson decays, I was going to be attempting to use the 't Hooft Model. It's a model in which we use only 1 spatial and 1 temporal dimension, and we have the number of colors in QCD go towards infinity (or just very large).

It's my understanding that the 't Hooft equation can be used to solve for a wave function of a meson. Does anyone know where I can get some more information on the 't Hooft model and the 't Hooft equation? I'm specifically looking for a more basic understanding of it, and it'd be great if I could find a good explanation or example on how to use the 't Hooft equation.

Thank you to anyone that replies.
 
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't Hooft's original paper "A two-dimensional model for mesons" is worth looking at, and you might want to look at "A planar diagram theory for strong interactions" as a primer. If you can't find them, let me know and I'll dig out the references for you. There's also a published volume of lectures by Sidney Coleman in the book "Aspects of Symmetry" which treats it well if you can get hold of a copy. Finally, a good set of notes on http://arxiv.org/abs/hep-ph/9802419" .
 
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I have read "A two-dimensional model for mesons" and it was helpful, but a little advanced for me. I was able to find "A planar diagram theory for strong interactions", I'm going to give that a shot, and the paper on Large N QCD. I'll also check out the library for the Sidney Coleman book.

Thanks for responding.
 

1. What is the 't Hooft Model in QCD?

The 't Hooft Model in QCD (Quantum Chromodynamics) is a theoretical model proposed by Dutch physicist Gerard 't Hooft in the 1970s to study the behavior of subatomic particles called quarks and gluons, which make up the protons and neutrons in the nucleus of an atom.

2. How does the 't Hooft Model differ from other models in QCD?

The 't Hooft Model is unique in that it introduces a new parameter called the 't Hooft coupling, which describes the strength of the interaction between quarks and gluons. This coupling is essential for understanding the confinement of quarks and the formation of hadrons (particles made of quarks) in QCD.

3. What is the significance of the 't Hooft Model in QCD?

The 't Hooft Model has greatly contributed to our understanding of the strong nuclear force, which is one of the four fundamental forces of nature. It also provides a framework for studying the phenomenon of confinement, where quarks are bound together within hadrons and cannot be observed as individual particles.

4. What are some applications of the 't Hooft Model in QCD?

The 't Hooft Model has been used to study a wide range of phenomena in particle physics, such as the behavior of quark-gluon plasma (a state of matter that existed in the early universe), the production of heavy quarks in high-energy collisions, and the properties of exotic hadrons containing more than three quarks.

5. What are the current challenges in the study of the 't Hooft Model in QCD?

One of the major challenges in the 't Hooft Model is finding ways to solve it analytically, as the equations governing the interactions of quarks and gluons become increasingly difficult to solve at higher energies. Another challenge is to reconcile the model with experimental data and observations from particle accelerators, which can provide valuable insight into the behavior of subatomic particles.

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