Rho-meson mass due to angular momentum?

[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?

 

[malawi_glenn]

I believe 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.

 

[mormonator_rm]

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?

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.

 

[da_willem]

Right. thx!

 

[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.

 

[mormonator_rm]

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.

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.

 

[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.

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.

 

[Meir Achuz]

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.

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.

 

[mormonator_rm]

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

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.

 

[Meir Achuz]

I am most familiar with the bag model, though, since I have been using it heavily lately.

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

 

[mormonator_rm]

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

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?

 

[Meir Achuz]

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

 

[mormonator_rm]

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

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.

 

[humanino]

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

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.

 

[mormonator_rm]

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

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

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

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

 

[humanino]

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

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.

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

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

 

[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.

 

[humanino]

I just can't grasp the idea that particles can be stuck together with no force to bind them

I must admit that it is very disturbing indeed. Please keep in mind that all this is referring 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

 

[jal]

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

 

[mormonator_rm]

I must admit that it is very disturbing indeed. Please keep in mind that all this is referring only to light quarks and hadrons.

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

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.

Well, that's a little reassuring...

Another way to think about it, is that light hadrons might be bound merely by their quantum numbers.

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 propagate it. I like to keep an open mind just the same, so if you can explain this "quantum number only" binding, please speak up.

 

[humanino]

I would like to understand this better, but so far I really disagree with this conjecture and the articles that propagate it.

You should realize that I am not making this up. This approach was developped by Gribov, and is being propagated by Doksh_itzer. Those are major names in the field of QCD ! I think possibly nobody alive today would dare pretend having the depth of understanding in QCD Gribov had. He used to say "I'm not more clever, I just think longer".

For instance, when Hawking displayed his ideas about black-hole entropy and radiation, Gribov said he already had discussed that with Landau, and thought it was well-known. This keeps happening all the time : if all the treasures dispatched within the russian litterature were well-known to everybody, possibly physics would be much further advanced today.

For quarks confinement, the idea is that, the proton is lightest hadron and has nowhere to decay anyway. It is quite disturbing with regards to the classical picture of a binding potential but nevertheless, evidences are compelling. There are predictions in Gribov scenario, but those are not easy to test. It is unfair to say that merely quantum numbers bound quarks however. What lacks in the classical approach is a rigourous identification of the true vacuum state of QCD.

Say for instance you take the vacuum state to be all gluon fields (and quarks) to be zero. Then it is not difficult to show that, if the chromomagnetic part of the gluon field fluctuates, the energy density decreases. As a consequence, it is clear that the vacuum of QCD cannot be the absence of quark and gluons.

As we know indeed, there is a dynamical breaking of chiral symmetry by the quark condensate. Those do contain gluons, and the gluon condensate in the vacuum is non-vanishing as well. This hints towards a non-trivial vacuum very clearly.

If you go forward, you can picture the proton not as a bag whose energy comes from the inner potential, but more accurately as if the energy of the bag came from an outside pressure of the vacuum. If you will, the bag contains non-trivial quantum numbers which disturbates the outside vacuum.

 

[Voltage]

Very interesting, thanks humanino. I'll print and study offline.

 

[jambaugh]

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.

This brings up an issue I've been pondering. Can you get L excitations within a nucleon? In other words, are there actually translational degrees of freedom within the "bag". Does anyone recall whether resonances corresponding to orbital excitations occur?

The reason I wonder is that in researching quantum gravitation and unification it has occurred to me that some elements of a master symmetry group may play double duty depending on a phase change. Some would resolve as color degrees of freedom within the space-time-gauge phase of the nucleon interior but mixing with others to resolve as e.g. translational degrees of freedom once you cross the phase boundary outside the nucleon.

This then would help "explain" confinement and additionally give exact values to the coupling between color and space-time geometry hence predict masses of hadronic particles.

It would be good to find direct evidence for rejecting this hypothesis. (And even better to find the possibility of this evidence absent its actualization which would support the hypothesis.)

Regards,
James Baugh

 

[mormonator_rm]

This brings up an issue I've been pondering. Can you get L excitations within a nucleon? In other words, are there actually translational degrees of freedom within the "bag". Does anyone recall whether resonances corresponding to orbital excitations occur?

The reason I wonder is that in researching quantum gravitation and unification it has occurred to me that some elements of a master symmetry group may play double duty depending on a phase change. Some would resolve as color degrees of freedom within the space-time-gauge phase of the nucleon interior but mixing with others to resolve as e.g. translational degrees of freedom once you cross the phase boundary outside the nucleon.

This then would help "explain" confinement and additionally give exact values to the coupling between color and space-time geometry hence predict masses of hadronic particles.

It would be good to find direct evidence for rejecting this hypothesis. (And even better to find the possibility of this evidence absent its actualization which would support the hypothesis.)

Regards,
James Baugh

Why, yes, there are baryons and mesons with angular momentum excitations among their constituents, although I will refrain from describing them as being "confined" or in a "bag", considering the trouble I seem to have caused here earlier.

The PDG listings are full of such hadronic resonances that can be classed as having L-excitations.

 

[jambaugh]

Why, yes, there are baryons and mesons with angular momentum excitations among their constituents, although I will refrain from describing them as being "confined" or in a "bag", considering the trouble I seem to have caused here earlier.

The PDG listings are full of such hadronic resonances that can be classed as having L-excitations.

Well that (to some extent) undercuts my speculation. Thanks for the recollection.

 

[mormonator_rm]

You should realize that I am not making this up. This approach was developped by Gribov, and is being propagated by Doksh_itzer. Those are major names in the field of QCD ! I think possibly nobody alive today would dare pretend having the depth of understanding in QCD Gribov had. He used to say "I'm not more clever, I just think longer".

For instance, when Hawking displayed his ideas about black-hole entropy and radiation, Gribov said he already had discussed that with Landau, and thought it was well-known. This keeps happening all the time : if all the treasures dispatched within the russian litterature were well-known to everybody, possibly physics would be much further advanced today.

For quarks confinement, the idea is that, the proton is lightest hadron and has nowhere to decay anyway. It is quite disturbing with regards to the classical picture of a binding potential but nevertheless, evidences are compelling. There are predictions in Gribov scenario, but those are not easy to test. It is unfair to say that merely quantum numbers bound quarks however. What lacks in the classical approach is a rigourous identification of the true vacuum state of QCD.

Say for instance you take the vacuum state to be all gluon fields (and quarks) to be zero. Then it is not difficult to show that, if the chromomagnetic part of the gluon field fluctuates, the energy density decreases. As a consequence, it is clear that the vacuum of QCD cannot be the absence of quark and gluons.

As we know indeed, there is a dynamical breaking of chiral symmetry by the quark condensate. Those do contain gluons, and the gluon condensate in the vacuum is non-vanishing as well. This hints towards a non-trivial vacuum very clearly.

If you go forward, you can picture the proton not as a bag whose energy comes from the inner potential, but more accurately as if the energy of the bag came from an outside pressure of the vacuum. If you will, the bag contains non-trivial quantum numbers which disturbates the outside vacuum.

I'm sorry if I came across as a bit combative, its just that I've spent the last three and a half years working on a mixing model for the scalar mesons which involved standard meson states, tetraquark states, and a glueball state. I used the bag model heavily to calculate pure-state masses (for the tetraquark masses it was most important), and then I used a 5x5 mixing matrix to mix all of the I=0 states and 2x2's to mix the I=1 and I=1/2 states. It actually produced flavor amplitudes that were favorable to the experimental widths of the naturally occurring meson states below 2 GeV. I just presented my initial results at the CPS-AAPT Sprint Meeting 2007 at Penn State York this past March, and it was well received.

I felt that you were attacking my work and calling it worthless, in a sense. I am sorry that I became offended, and I hope I did not offend anyone else. I will, in future, refrain from posting here as I have caused many problems.

 

[humanino]

I felt that you were attacking my work and calling it worthless, in a sense. I am sorry that I became offended, and I hope I did not offend anyone else. I will, in future, refrain from posting here as I have caused many problems.

Dear mormonator_rm,

please do not take that personnaly. I was certainly not attacking your work, of which I am not aware. I am personnaly puzzled everyday by the powerful efficiency of chiral quark models : they do make an amazing job.

I think that Gribov's work is just very interesting, and I wanted to point to another possibility appart from growth of a potential : a phase transition between the "naked" vacuum and the true vacuum of QCD. This possibility is not ruled out so far.

I think PF is a great place to discuss and I have learned a lot here. I would be sorry to have pushed you out because I did not take enough care in my statements.