Baryon quantum numbers from partons

[Physics Monkey]

Hi everyone,

I have a perhaps slightly vague question for all the QCD experts out there.

The simplest description of hadron quantum numbers comes from the parton picture where I attempt to simply add up the quantum numbers of a few partons that are supposed to make up the hadron. However, in reality I know that the weakly interacting parton picture is very far from the truth. A relevant example here would be attempting to quantitatively decompose the proton's spin in terms of various "components" like quark spin and gluon orbital angular momentum etc. I am aware that there are issues associated with gauge invariance in precisely defining all these components.

My question is this: do we have an understanding why the weakly coupled parton description seems to work for some qualitative questions (to the extent that it does) despite failing quantitatively?

Put more simply, why can I get away with computing the proton's quantum numbers as if it were three non-interacting quarks even though its most certainly not?

 

[tom.stoer]

why can I get away with computing the proton's quantum numbers as if it were three non-interacting quarks even though its most certainly not?

We know how SU(N) flavor symmetry works and we know its representations theory. This symmetry is not destroyed by the strong color interaction, so SU(N) flavor operators still commute with SU(3) color operators such that the algebraic relations for SU(N)*SU(3) remain valid for the representations even when taking color intercation, renormalization and non-perturbative effects into account. There is no "flavor anomaly".

Of course this what we expect from a consistent quantum field theory and what we observe in nature, but unfortunately this is not what mathematics tells us; I think we are far away from being able to prove this b/c this requires the existence of a mathematically consistent formulation of an interacting QFT - which we do not have.

All what one can do is to show that this holds in perturbation theory - which is of course not sufficient for bound states.

 

[Physics Monkey]

Thanks for your reply, tom.

I'm ok with the presence of flavor symmetry. If that symmetry is not broken in the ground state of the theory then the excited states will form representations of the symmetry group, even if we don't have a simple picture in terms of partons.

I'm particularly interested in the angular momentum structure of hadrons in light of the experiments that are interpreted as saying "valence quarks" contribute only a small-ish fraction of the total angular momentum of the proton, nevertheless, we seem to be able to use the "valence quark" quantum numbers to compute proton spin. I'd like to learn more about this issue in particular.

 

[tom.stoer]

I'm ok with the presence of flavor symmetry. If that symmetry is not broken in the ground state of the theory then the excited states will form representations of the symmetry group, even if we don't have a simple picture in terms of partons.

The dynamics of QCD does not break flavor symmetry. Unfortunately it is explicitly broken by the different quark masses which means that SU(2) with u and d is nearly perfect, SU(3) with a additonal s is OK, from SU(4) with c, ... it becomes less reasonable to use this as asymptotic or approximate symmetry. For SU(3) and classification of multiplets it's OK.

I'm particularly interested in the angular momentum structure of hadrons in light of the experiments that are interpreted as saying "valence quarks" contribute only a small-ish fraction of the total angular momentum of the proton, nevertheless, we seem to be able to use the "valence quark" quantum numbers to compute proton spin. I'd like to learn more about this issue in particular.

Unfortunately the valence quark model fails completely for the nucleon spin. Polarized deep inelastic scattering experiments showed that the proton spin must have a large contribution not coming from valence quarks.

I am not involved in recent discussions, therefore I do not have a sound review article at hand. I guess googling for "spin structure function" and "HERMES" should be OK.

 

[Physics Monkey]

The dynamics of QCD does not break flavor symmetry. Unfortunately it is explicitly broken by the different quark masses which means that SU(2) with u and d is nearly perfect, SU(3) with a additonal s is OK, from SU(4) with c, ... it becomes less reasonable to use this as asymptotic or approximate symmetry. For SU(3) and classification of multiplets it's OK.

Sure, I agree.

Unfortunately the valence quark model fails completely for the nucleon spin. Polarized deep inelastic scattering experiments showed that the proton spin must have a large contribution not coming from valence quarks.

I am not involved in recent discussions, therefore I do not have a sound review article at hand. I guess googling for "spin structure function" and "HERMES" should be OK.

Yes, perhaps what I'm looking for is a coherent discussion of the notion of valence quarks and their role in determining hadron quantum numbers. For example, the proton is spin 1/2 and has all the other quantum numbers as would be predicted by the parton model, yet the partons do not qualitatively account for the angular momentum as you say. If I try to put things more precisely, we do some group theory using parton angular momentum, then we turn on interactions that do not leave the parton angular momentum separately conserved, yet the group theory seems to keep working?

I wonder if there is some weakly interacting limit, adiabatically connected to real world, where the parton picture is more qualitatively accurate?