QCD scale and massless limit of u & d quarks

In summary, the conversation discusses the relationship between the QCD scale and the masses of u and d quarks and how it relates to the chiral symmetry of QCD. It is noted that the renormalization scale is unimportant and that the question is tricky due to the non-perturbative nature of QCD. The value of ~200MeV is often used in literature when discussing chiral symmetry, but it is not clear if this is accurate. The pion-decay constant, which is a measure of the strength of chiral symmetry breaking, is also mentioned. The conversation ends with a question about the relationship between quark masses and the pion decay constant.
  • #1
GIM
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Hello!
Could anybody help me?
My wondering seems so trivial, but I can't skip it.
They say that since u and d quarks are much lighter than QCD scale(~200MeV), in reality we can consider the QCD Lagrangian has an approximate global chiral symmetry with respect to these two flavors. At first, it sounded plausible, but now I wonder what relation between the QCD scale and the quark masses there is and how. Is this problem related to the renormalization scale?
 
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  • #2
Hello,

The renormalisation scale is unphysical, but appears as an artefact when we do perturbation theory only to a finite order. So I don't think that's important.

The question is a tricky one, since the light quarks are never free and are in bound hadrons where strong (non-perturbative) qcd effects are ever present... Maybe a lattice person would give a clearer answer.

On the other hand, what is the qcd scale? The value at which the strong coupling becomes non-perturbative. It's not clear to me at which scale this is (below a gev for sure).

For practical purposes, it seems like ignoring the u,d quark masses is reasonable. Even the strange could be considered massless. You can see how good/bad an approximation this is by comparing pion and kaon massed.
 
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  • #3
Having read the below thread. The quark review on the light quarks which vanhees posted is more informative!
 
  • #4
Thank you, @RGevo.
I just copied the value of ~200MeV from the literature. In many literatures(I've seen), which treat the chiral symmetry, most of them mention the similar statements. Is this really tricky?
 
  • #5
It's very tricky. A more pragmatic answer is that you can use chiral symmetry to build effective hadronic models. As it turns out, indeed chiral symmetry is a very good approximate symmetry of the strong interactions since the typical current-light-quark masses are small compared to the scale ##4 \pi f_{\pi} \simeq 1 \; \text{GeV}##, where ##f_{\pi} \simeq 92 \; \mathrm{MeV}## is the pion-decay constant that can be measured through the weak decay of the pions. Note that chiral symmetry is as good a symmetry of the strong interaction as is isospin symmetry (which is violated, because the ##u## and ##d## quark masses are not the same, and the difference is also a few MeV).
 
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  • #6
Thank you, @vanhees71.
What kind is the scale ##4\pi {f_\pi }##?
Now, you changed my question into the relation between quark masses and pion decay constant. Then, again, what reasoning makes me ignore the masses?
(For example, when I learned the pion decay, my professor used the formula ##\left\langle 0 \right|\bar u{\gamma ^5}d\left| {{\pi ^ - }} \right\rangle = \frac{{\sqrt 2 {f_\pi }m_\pi ^2}}{{\left( {{m_u} + {m_d}} \right)}}##. In this case, the massless limit gives "unacceptable result" and I think I have no hope to find the relation between the pion decay constant and the quark masses. I guess my example is beyond the main direction of my question and if so, then please ignore this. Thank you.)
 
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1. What is the QCD scale and why is it important?

The QCD scale, also known as the strong coupling scale, is a parameter that characterizes the strength of the strong nuclear force, which binds quarks together to form protons and neutrons. It is important because it determines the energy at which the dynamics of QCD, the theory of the strong force, changes from being perturbative (can be calculated using perturbation theory) to non-perturbative (requires other methods for calculation).

2. What is the massless limit of u and d quarks?

In the standard model of particle physics, the u and d quarks are considered to have zero mass. This is known as the massless limit since their masses are so small compared to other particles that they can be ignored in most calculations. This assumption is supported by experimental data, which shows that the masses of u and d quarks are several orders of magnitude smaller than other particles.

3. How is the massless limit of u and d quarks related to the QCD scale?

The massless limit of u and d quarks is closely related to the QCD scale because, in this limit, the QCD scale becomes the only relevant energy scale for the strong force. This means that at high energies, the strong force behaves differently than at low energies, which has important implications for particle interactions and the structure of matter.

4. Can the massless limit of u and d quarks be tested experimentally?

Yes, the massless limit of u and d quarks can be tested experimentally through the study of high-energy particle collisions. By measuring the behavior of the strong force at different energies, scientists can gather evidence for the existence of the QCD scale and the massless nature of u and d quarks.

5. What are the implications of the massless limit of u and d quarks for particle physics?

The massless limit of u and d quarks has significant implications for our understanding of the fundamental particles and forces that make up the universe. It helps explain why the strong force is so much stronger than the other fundamental forces and is essential for the development of the standard model of particle physics. It also plays a crucial role in theories of the early universe and the formation of matter after the Big Bang.

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