Questions about the baryon octet and decuplet?

[jeebs]

Hi,
I have been looking at the baryon decuplet for spin 3/2 baryons, and the octet for spin 1/2 baryons. Here is a picture of the baryon decuplet:
http://schools-wikipedia.org/images/392/39222.png
Here is a picture of the baryon octet:
http://upload.wikimedia.org/wikipedi...-small.svg.png

As I understand it, the spin of the baryon is determined by the spins of its constituent quarks, ie. you can either have all 3 quark spins aligned, giving spin 1/2 + 1/2 + 1/2 = 3/2,
or you can have 2 of the spins in one direction and the other in the opposite direction, giving spin 1/2 + 1/2 - 1/2 = 1/2.

The differences between the decuplet and the octet appear to be that the quarks are on the decuplet but not the octet, and the octet has the quark but the decuplet does not.

Also, the proton and neutron on the octet are the same quark combination as the do on the decuplet, but for some reason they are called different names depending on which diagram you look at.

Why do we have different names for particles with exactly the same quark content?
I thought the answer to this might be to do with the spin of the baryon, but the octet and the decuplet both include the quarks, with the same name and quark content. What's going on here?

My other question is why should there be ten particles in the decuplet but only eight in the octet? By that I mean, take the quark that appears on the decuplet only. It has quark content ddd. Clearly if it only appears in the decuplet diagram, the ddd combination cannot form a spin 1/2 baryon.
What is the reason why these quarks ARE able align so that the baryon they form has a spin 3/2, but are NOT able to align so that they form a baryon with spin 1/2?

Or, to put it more simply, why are there 10 quarks in the one diagram but not the other?

Thanks.

 

[Meir Achuz]

You have t add the spins quantum mechanically. Then you would see that the decuplet has a different spin function than the octet.

 

[jeebs]

You have t add the spins quantum mechanically. Then you would see that the decuplet has a different spin function than the octet.

could you elaborate please?

 

[humanino]

A good review, as usual, is in the PDG, QM
Basically, you have to think about (14.23)
3 x 3 x 3 = 10 + 8 + 8 + 1
There is a lot to say to fully describe this seemingly simple model. A good introductory textbook is (for instance) Close's "An introduction to quarks and partons", or available online, this (2.92)

 

[Vanadium 50]

What is the reason why these quarks ARE able align so that the baryon they form has a spin 3/2, but are NOT able to align so that they form a baryon with spin 1/2?

Because the total wavefunction has to be antisymmetric. If I have the same flavors of quarks, I can put them in a spin-3/2 state, because the state is antisymmetric in color and symmetric in spin. If I try and put them in a spin-1/2 state, it's still antisymmetric in color but now it's also antisymmetric in spin, so it doesn't work.