# Rho-meson mass due to angular momentum?

1. May 18, 2007

### da_willem

I just read that the rho mesons have the same quark content as pions, but with one net unit angular momentum. Is their higher energy due to the energy associated with their angular momentum?

(A short 'rigid rotor' calculation indicated a size of the order 10^-15m to 10^-11m depending on whether using the mass of a u/d quark or half the pion mass, which seems reasonable)

PS: I saw delta+ and delta 0 particles have the same quark content as the proton and the neutron, are these also excited states?

2. May 18, 2007

### malawi_glenn

I belive it is Spinn angular momentum, the two quarks in the roh meson have parallel spin, and we have S-S coupling that "gives extra mass".

Also the delta particles have spinn parallel for all three quarks.

3. May 18, 2007

### mormonator_rm

It is not "angular momentum" as in the quantum number "L", but rather "spin momentum" as in the quantum number "S" that gives them mass above that of the pion.

PS... Yes, the Delta baryons are the spin excitation of the nucleons.

The rho meson has Jpc = 1--, L = 0, and S = 1. Its mass falls at about 770 MeV.

The lightest meson with an L = 1 excitation is the axial-vector meson h1(1170). Its quantum numbers are Jpc = 1+-, L = 1, ans S = 0. Its mass falls at about 1170 MeV. Its mass excitation above the pion is entirely due to angular excitation.

4. May 18, 2007

### da_willem

Right. thx!

5. May 21, 2007

### Meir Achuz

There is a $${\vec s}_1\cdot{\vec s}_2$$ interaction between quarks. It is similar to the hyperfine interaction between the nuclear and electron spins in atomic physics, and is called "the color hyperfine interaction".
It is repulsive in the spin one state of a quark and antiquark.
It is attactive and three times stronger in the spin zero state.

6. May 21, 2007

### mormonator_rm

This is indeed borne out in the mathematics of the Bag Model. The color-magnetic interaction term is shown to be $$({\vec s}_i\cdot{\vec s}_j)\times(\vec{\lambda}_i\cdot\vec{\lambda}_j)$$ where the first term is the spin coupling and the second is for the color matrices. This gives the spin-1 mesons a higher mass than the spin-0 mesons since the color-hyperfine interaction is repulsive for the spin-1 state.

7. May 21, 2007

### mormonator_rm

That should read $$({\vec s}_i\cdot{\vec s}_j)\times(\vec{\lambda}_i\cdot\vec{\lambda}_j)$$, but has not updated since I edited it.

8. May 22, 2007

### Meir Achuz

When you edit a tex file, you don't see your correction if you use the back operation. You have to click on the forum again.

The energy difference between the two spin states is true in any model, not just the bag model.

9. May 30, 2007

### mormonator_rm

This is true, the same thing happens in vector-gluon exchange model and all the other models. I am most familiar with the bag model, though, since I have been using it heavily lately.

10. May 31, 2007

### Meir Achuz

Why do you do that? It has been known for many years that the quark distributions are not bag-like.

11. Jun 7, 2007

### mormonator_rm

What do you mean? If the bag model is known to be incorrect, then how can objects like tetraquarks and pentaquarks now be justified in any way?

12. Jun 7, 2007

### Meir Achuz

They just don't have to be in a bag.

13. Jun 7, 2007

### mormonator_rm

Well, bag or not, they must have a potential model that causes them to be confined, such as the Cornell potential model or something else.

14. Jun 7, 2007

### humanino

The bag model is incorrect and as of today, tetraquarks and pentaquarks are just abstract conscruction without any real conterpart. Sorry

Confinement needs not to be the consequence of a rising potential or "bag". It can be something else.

15. Jun 8, 2007

### mormonator_rm

So I guess all of Jaffe's work is out...

What "something else" is there? If you don't have any potential holding these things together, then what IS holding them together?

16. Jun 8, 2007

### humanino

Don't take it personnaly
Bag and potential models are very interesting by themselves but they are not the end of the story, that's it. For instance, they very poorly represent chiral symmetry breaking, which trivially occurs at the edges of the bag and nowhere inside.
A potential is something properly defined when you have one (only one) meson exchange. In QED for instance this works very well because of the smallness of the coupling and the possibility to do perturbation calculations. So the classical pictures usually work rather well. In QCD however, classical analogies might be very misleading. If you take lattice calculations of the "string" potential between quarks, you will find that the potential between quarks should exceed the pion mass as soon as 0.26 fm separation. If you insist on twice the pion mass, you will find 0.4 fm, but those configurations can last at most for a short time equal to the inverse of the pion mass. How are we to reconcile these numbers with the fact that the hadrons have a size at least of 1 fm ?

Meanwhile, if you do calculate gluons configurations on the lattice, you will find very complicated fluctuations all over the place. But once you "cool down" those ensembles, by averaging them, what you end up with are only the large lumps, identified as instantons, and seemingly able to reproduce density-density quark correlations inside the nucleon, so possibly confinement (without rising potential). Check out Instantons and baryon dynamics for instance. Instantons are manifestations of tunneling between different vacuum states with different topological numbers. They have no classical analogues, and are inherently non-perturbative.

I find even more interesting the Gribov conception of quark confinement, so let me try to summarize it here. It has to do with the correct identification of the vacuum. First let us proceed by analogy and discuss QED. Let us simplify and imagine that the nucleus of the atom is pointlike. Take the QED coupling constant to be equal to 1/137. Then consider the possibility that the nucleus contains more than 137 protons. What happens in that case !!? Perturbation calculations must have failed at this point. When you investigate this situation you find a sort of phase transition. An electron/positron pair goes from virtual in the vacuum to real, the electron falls in the nucleus and the positron escapes to infinity. You have some kind of confinement of nucleus charge larger than 137. Now in real life, the coupling is not exactly 1/137 and most importantly the nucleus has a finite size, so proceeding to a more careful evaluation you will find that this so-called supercritical biding occurs around 180 protons (I don't remember exactly, it does not matter). Somehow it is energetically favorable to create fermions pairs, a sort of condensation if you will although I am not talking about the dual-abelian Higgs model of confinement (which is mainly string confinement in fact). Now what about QCD ? Gribov argues that for colored charge, this supercritical biding occurs as early as 1 color charge (due to the large QCD coupling). Once again it is non-perturbative. He proceeded to the full fledged Dyson-Schwinger propagation of quarks within this scheme. It is unfortunate that Gribov died too early, leaving us with extremely stimulating but unfinished physical insights. See for instance Gribov program of understanding confinement

17. Jun 11, 2007

### mormonator_rm

I'll have to look deeper into this when I get a chance. I just can't grasp the idea that particles can be stuck together with no force to bind them right now, but I will check out the sources you have posted here. Thankyou for the input.

18. Jun 11, 2007

### humanino

I must admit that it is very disturbing indeed. Please keep in mind that all this is refering only to light quarks and hadrons. Heavy quarks, no doubt about it, are certainly confined by the rising of the potential, or if you will, the flux tube. But this does not seem to be relevant for light quarks. Another way to think about it, is that light hadrons might be bound merely by their quantum numbers.

You can find a nice lecture by Doksh_itzer where he discusses this : QCD Phenomenology, and in particular, starting from "is the proton really bound" in section 2.3

19. Jun 11, 2007

### jal

Thanks! humanino!
Your links gave me a better understanding of what is in the nucleons.
jal

20. Jun 12, 2007

### mormonator_rm

Yes, truly disturbing, because it comes across as saying that they are bound by "choice" and not by "force".

Well, that's a little reassuring...

Wait a minute. The arrangement of objects in "bound states" as allowed by quantum numbers still requires a force between the bound particles, as in the Cooper Pair effect for electrons that group together in energy states according to the Pauli Exclusion Principle. Quarks, I know, are similar except that the color degree of freedom allows for three members to be in a bound state without violating the Pauli Exclusion Principle. I really dislike the idea that the quantum numbers alone bind the quarks together: that's like saying that the quarks do not follow any ordered force or potential, but instead choose to group into hadrons the way they do. There is little or no predictability or guidance involved there.

I would like to understand this better, but so far I really disagree with this conjecture and the articles that propogate it. I like to keep an open mind just the same, so if you can explain this "quantum number only" binding, please speak up.