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Main Question or Discussion Point
Does anyone know the magnetic moments of the up and down quarks? I am interested only in the best experimental data, not theoretical estimates.
btw.: I checked the PDG and found ... nothingI guess identical for all elementary spin 1/2 particles; why do you expect a difference? QCD corrections?
Do you mean like an electron's magnetic moment? It's not possible to get an up or a down quark into that state, or any other quark into that state, as far as anyone knows. That's quark confinement. It takes too much energy to separate them by more than 10^{-15} m.Does anyone know the magnetic moments of the up and down quarks? I am interested only in the best experimental data, not theoretical estimates.
I just recently read that the mass of the three quarks is much smaller than the mass of the proton ... This is why certain theories suggest that there are more quarks in nucleons than just the three valance quarks
You guys should be careful when talking about a 'quark'.But one can easily estimate these quarks' magnetic moments when bound in nucleons.
... 1/sqrt(18) *
(2|u+u+d-> - |u+u-d+> - |u-u+d+> + 2|d-u+u+> - |d+u+u-> - |d+u-u+> + 2|u+d-u+> - |u-d+u+> - |u+d+u->)
One can easily find the magnetic moment:
mu_{u}/q_{u} = 2.78
mu_{d}/q_{d} = 2.92
False. The sum of the spins of the quarks is 1/2. The spin of the nucleon is 1/2.They are related by the Bjorken Sum rule, which says that the sum of the spin of the quarks is equal to the spin of the nucleon. Experiment proved this to be not true.
False again.I assume the spin crisis relates to the magnetic moment of the quarks being different from what theory predicted, which are the numbers Ipetrich posted.
Well, I don't think there was a spin crisis, just muddy thinking. But the people who went around advertising it would not agree with your description of it. It's just wrong.If the spin of a quark is 1/2 and the spin of a nucleon is 1/2, then there is no "Nucleon Spin Crisis".
you talk about an assumption only. What is this assumption exactly? Where does it come from?They are related by the Bjorken Sum rule, which says that the sum of the spin of the quarks is equal to the spin of the nucleon. Experiment proved this to be not true. I assume the spin crisis relates to the magnetic moment of the quarks being different from what theory predicted, which are the numbers Ipetrich posted.
No; we did not give you experimental data but just commented on wrong ideas; there are Terrabytes of experimental data* There's no experimental data.
There are theoretical estimates; all what we were saying ways that quark or bag model estimates are too naive and are not suitable for an explanation (a theory that explains 50% of the data but fails to explain the other 50% is not really helpful - even if your interest is in the first 50%)* There's no theoretical estimate either.
There is only one theory today - QCD - and in QCD there are no such ambiguities. Explaining the spin structures based on (non-rel.) quark models is like explaining black holes based on Newtonian gravity... it is controversial depending on the definition of a quark and what specific theory we are using
There is a clear relation and I just quoted the correct formula using the g-factor; what I was saying is that I can't see how the quark magnetic moment and the nucleon spin are related; it was your claim that this should be the case, and therefore expected some explanation, reference, whatever* Spins and magnetic moments have no relation to each other.
Yes, I think I used that formula, but I can't see how it may help; you either explain the nucleon magnetic moment in terms of its spin (which you can't as long as you can't explain the spin), or you explain the quark magnetic moment in terms of its spin which is trivial and not the subject of the 'spin crisis'.* There is, however, an equation that relates them directly: "magnetic moment is defined as μ = g (q/2m) s = g q/4m with s = 1/2"
No, g = 2 + QED corrections, m for 'up'and 'down' is a few MeV; and you can find a lot of data for quark masses at the particle data group; but this is (afaik) irrelevant for the nuclon spin* In regards to the above equations, g and m are unknowns for quarks.
I don't think it's muddy thinking. The problem is that all naive models fail to explain the spin, and that even in QCD not everything is well-understood.How can it be even after over 25 years, that no one noticed that this is just muddy thinking?
... One can easily find the magnetic moment:
mu_{p} = (4*mu_{u} - mu_{d})/3
mu_{n} = (4*mu_{d} - mu_{u})/3
With
mu_{p} = 2.79
mu_{n} = -1.81
in nuclear magnetons,
mu_{u} = 1.85
mu_{d} = -0.97
Dividing by the quark charges,
mu_{u}/q_{u} = 2.78
mu_{d}/q_{d} = 2.92
A 5% discrepancy.
I spent some time looking for bag-model and lattice-QCD estimates, but I couldn't find very much.
If you cannot detect quarks by themselves, what logic is used to experimentally detect an amount of spin or a magnetic moment to the quarks?... It's about the results of deep-inelastic-scattering experiments. At typical DIS-experiment momenta, only about 30% of a nucleon's spin is carried in the valence quarks.