# Nucleon spin

1. Jun 29, 2004

### humanino

How well are we certain that nucleon have spin one half ?
I see several experimental answers. I would like to have theoretical arguments, considering the fact that nucleons are not fundamental particles. How well can one apply lorentz symmetry to the free neutron wich is not stable ?

2. Jul 2, 2004

### humanino

Perhaps should I reformulate more precisely.

It can easily be infered from experimental data that nucleons have spin one-half. One can consider the H atom, which is so well described. One can also consider massive nuclei whose spectra can be accuratly modelled using 1/2 spin constituent. It is even possible to find stronger arguments. OK guys, I seriously have no doubt, we all agree.

But I am trying to understand what spin really is. Maybe one among you has an opinion ! See, the Noether's theorem is easy in the case of internal symmetries (gauge) but these are not real symmetries. Just a convenient way to describe the system. However, external (spacetime) symmetries are tricky to deal with. Deriving the energy-momentum tensor from Noether's theorem is not that straightforward (to me ) As for deriving a conservation of spin : I just can't find how to do it anywhere.
So the appearance of spin seems to me to be due to the structure of the Lorentz group SO(1,3) which decompose in two SU(2). But I can't find anything else ! I mean : spinors appear in the description of particles because of Dirac equation. So if I ask a question such as "Can the nucleon have a spin 0.5+0.000001" theoreticians would laugh and reply "Absurd ! It is EXACTLY 0.5 because of highest weight of SU(2)"

Is there someone to help me out ? :shy:

3. Jul 2, 2004

### arivero

On the other hand, we have *hadrons* with different spin states.

4. Jul 2, 2004

Staff Emeritus
Hadrons are composite particles, made up of quarks. All quarks are fermions, with spin 1/2.

5. Jul 2, 2004

### arivero

Exactly. The point is that nucleons are a very particular kind of hadrons. The question about the "spin" of nucleons is really a question about its total angular momentum. Of course, every angular momentum is quantised too. One must remember that 1/2 is just the natural unit way to say h/2.

6. Jul 2, 2004

### hellfire

First of all I have to say that my knowledge of this subject is poor, but I think I can give a hint (may be already well known by you, humanino): AFAIK to make possible a spin with different values than half-integer or integer ones, it would not be enough to take the double covering group of the generator of rotations, but the triple or quadruple (and so on) covering groups would be needed. I think these are not possible within four space-time dimensions. Well, honestly, I am not sure to have understood your question...

Regards.

Last edited: Jul 2, 2004
7. Jul 6, 2004

### humanino

Fundamental particle must have an integer or half integer spin, OK, that's fine. But why should a hadron, which is a real soup of quarks and gluons, have a well-defined spin. The wave function for the hadron is doubtlessly the superposition of multiquark states (not just two or three (or five :surprise: ) quarks), and mutligluons as well. My question would be : how come that in the end of the day, we observe only well defined quantum numbers for hadrons ?

That is to say : how come this naive picture of the quark-constituent model works so well when it comes to quantum numbers, but fail when dynamical questions come into play ?

Let me illustrate : the proton for example could be pictured as :
|p->) = ( { uud } * { -> -> <- } * [ rgb ] ) = 1/sqrt(18) * ((2u->u->d<-) - (u->u<-d->) - (u<-u->d->) + permut)
flavor * spin * color
with {symetrization} and [antisymetrization]
OK, in this case, the proton spin is clearly understood : it comes from the valence quarks.
But we know that this picture is really wrong, we know that the quark spins contribute only up to 30% to the proton spin. As for the nucleon mass, which should be computed either using constituent quark mass(~300 MeV), or current quark mass (~ few MeV) in the context of which about 10% of the baryon mass comes from Higgs contribution, the remaining 90% coming from the gluon field around the valence state.

8. Jul 12, 2004

### humanino

It is amazing to me that angular momentum rules from elementary quantum mechanics apply in the Deep regime, where one is able to contemplate hundreds of partons fluctuating around. How can this system organize itself to respect ordinary quantum mechanics ? If one goes deep enough, the proton is seen as a huge bag containing thousand partons. Are the partons far appart causaly linked ? They should be in order to build this formidable conspiracy ! Think of the gap between the picture of three valence quarks, and the soup corresponding to the observation of a 1000-partons state !

9. Jul 12, 2004

Staff Emeritus
"Hundreds" of partons? Only three partons in the nucleons. Hundreds or skillions of gluons, maybe, but they are bosons.

10. Jul 12, 2004

### drachman

I guess that the formal solution to your spin problem is this: If the spin operator commutes with the Hamiltonian, then spin is conserved, and you don't need to worry about the complicated structure of the "nucleon'. The question remains: what is the form of the Hamiltonian? And the other question about how many quarks can be in the nucleon--virtual pairs of quark and anti-quark can add indefinitely to the three basic ones.

11. Jul 12, 2004

### humanino

but what about quark pairs fluctuations ?
shall one consider them only as part of the dressed gluon propagators, not as real constituents ?