QCD Questions Answered by Experts

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In summary, the conversation discusses various topics related to quantum chromodynamics (QCD) and the parton model. Some key points include the universality of the strong coupling constant and the quantization of color charge, the relationship between quark pole mass and MS-bar quark mass, and the role of the renormalized gluon-gluon splitting function in QCD calculations. The conversation also touches on the concept of energy nonconservation in the parton model and the role of probability functions in describing the repartition of energy among partons. Ultimately, the conversation highlights the complexity and challenges involved in studying QCD and the parton model.
  • #1
hagi
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Hi @ all,

during tmy exam preparation I stumbled upon some facts that I couldn't explain to myself.

1. Strong coupling constant [tex]g_s[/tex] is universal -> colour charge is quantised

2. The MS_bar quark mass [tex]\bar{m} = m_0 + \delta \bar{m}[/tex] can be given as a function of the quark pole mass [tex]m = m_0 + \delta m[/tex],
[tex]\bar{m}(m^2) = \frac{m}{1 + 2\alpha_s}[/tex],
but neither can be measured because of confinement. What is the purpose of giving such an equation? Is any relevance therein?

3. The renormalized gluon-gluon splitting function contains a term proportional to [tex]N_F P_{qg}[/tex]. Is this just a consequence of the collinear and soft poles of the unrenormalized gluon-gluon splitting function? Whence does the flavour factor comes?

4. Does anybody know something about parton cascade/parton branching/probability picture and why 3-momentum is conserved, but energy not? (This topic showed up during the heuristic justification of the parton model.)

Thanks in advance to everyone answering!

Cheers

Andreas
 
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  • #2
4) If it is about deep inelastic scattering, then the energy is "not conserved" in the sense that its part goes to the "internal" energy of the reaction products (breaking a target in pieces takes some energy). The momentum is always conserved.

Bob_for_short.
 
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  • #3
I think it is not a specific DIS question. The energy nonconservation should imho be a trick but that's exactly my problem, why this trick is allowed. The problem is that I had to ask the prof so much things that I couldn't ask everything and his notes are not selfexplaining.

He called the whole thing "probability picture" and his conclusion was that in the parton model (infinite momentum frame) the life time for partons with
Bjorken 0<x<1 is much longer than for partons with x<0 or x>1 corresponding to a backward directed motion of a daugher parton.
 
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  • #4
hagi said:
He called the whole thing "probability picture" and his conclusion was that in the parton model (infinite momentum frame) the life time for partons with
Bjorken 0<x<1 is much longer than for partons with x<0 or x>1 corresponding to a backward directed motion of a daugher parton.

I am not good at it but I remember that the energy is somewhat distributed between partons and this repartition is described with a probability function.
 
  • #5
Thanks but I solved question 4 now. The energy nonconservation is just due to an approximation of a square root, to be able to compute the answer but it has nothing to do with the parton branching as such. Quigg helped me here.
 

1. What is QCD and why is it important in physics?

QCD (Quantum Chromodynamics) is a theory that describes the strong nuclear force, one of the four fundamental forces in nature. It explains how quarks and gluons interact to form protons, neutrons, and other hadrons. QCD is important because it helps us understand the behavior of matter at a fundamental level and is essential for explaining the structure and behavior of the universe.

2. How does QCD differ from other theories of fundamental forces?

QCD differs from other theories, such as electromagnetism and gravity, because it describes a force that is confined to a very short range and becomes stronger as particles move further apart. This is known as the "strong" force, and it is responsible for holding quarks together to form larger particles. QCD also introduces the concept of color charge, which is a property of quarks and gluons that allows them to interact with each other.

3. What are the main challenges in studying QCD?

One of the main challenges in studying QCD is that it is a non-perturbative theory, meaning that traditional mathematical methods cannot be used to solve it. This makes it difficult to make precise predictions and calculations in certain situations. Another challenge is that QCD involves many different particles and interactions, making it a complex theory to understand and analyze.

4. How has our understanding of QCD evolved over time?

Our understanding of QCD has evolved significantly since its development in the 1960s. Initially, it was thought to be a theory of just three quarks, but as more experimental evidence was gathered, it became clear that there are many more quarks and gluons involved in the strong force. Additionally, advancements in computing power have allowed for more accurate calculations and simulations, leading to a deeper understanding of the theory.

5. What are some current research topics in QCD?

Some current research topics in QCD include studying the properties of quark-gluon plasma, a state of matter that existed in the early universe and can be recreated in high-energy particle collisions. Other areas of research include exploring the structure of hadrons, such as protons and neutrons, and investigating the behavior of particles in extreme conditions, such as in the cores of neutron stars. Researchers are also working to develop new mathematical tools and techniques to better understand and solve the non-perturbative aspects of QCD.

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