The spin-flavor wavefunction of Sigma+

[Xico Sim]

Hi, guys.

If I want to write the spin-flavor wavefunction of $\Sigma_+$ starting only from knowing that the quark content of the proton is $uud$, how can I procced?
I started by applying the ladder operators in order to get the baryon octet vertexes. I am now having problems with:

1. determining the flavor wavefunction for the center octet states (including $\Sigma_+$).
2. determining the spin wavefunction for $\Sigma_+$. Even if I suppose that the its spin state is $|1/2,1/2\rangle$, there is more than one way for this to happen when we combine 3 spin 1/2 quarks...

Does anyone know a text where I can find something like this done in a comprehensive and detailed way? Or, alternatively, can you tell me a way to do it?

 

[ChrisVer]

Aren't sigma baryons strange ones? Are you using an SU(3) flavor symmetry?
As for the quarks they would be uus ? If you have more than 1 combination then you write them all, as you did for the proton [when you had the mixed symmetric states].
the flavor states can be obtained in a similar way by combining u,u and s.

 

[Xico Sim]

The problem is that I did not understand the derivation of the proton wavefunction also: I found Griffiths, and for that matter every other text I found on the subject, quite confusing. Do you happen to know a place where it is clearly and thoroughly explained?

 

[Xico Sim]

Using Thomson's book I understood the derivation of the proton spin-flavour wavefunction. I will try to apply what I learned to this case.

 

[ChrisVer]

what is confusing?

 

[Xico Sim]

what is confusing?

To make myself clear, I posted my attempt. I arrived at the correct wavefunction, but I have a problem with it: even though it seems symmetric, I would expect it to be only mixed symmetric (only symmetric in 1,2), since $X$ is only symmetric in 1,2 and $\phi$ is completely symmetric...

 

[ChrisVer]

Why is phi symmetric? aren't you using a uds? I am sorry but I don't see why you wouldn't consider the antisymmetric singlet.

 

[Xico Sim]

I am sorry but I don't see why you wouldn't consider the antisymmetric singlet.

When determining $X$?

 

[ChrisVer]

when determining Phi...
you should have a symmetric one (in the triplet I=1 combination) : uds + dus
and an antisymmetric one (in the singlet I=0 combination) : uds - dus
they both correspond to I3=0

 

[Meir Achuz]

Look at look at PR 172, 1807 for simple spin – flavor wave functions for baryons.

 

[Xico Sim]

Look at look at PR 172, 1807 for simple spin – flavor wave functions for baryons.

What is PR?

 

[vanhees71]

That's HEP slang ;-)). The correct citation is

Jerrold Franklin, Phys. Rev. 172, 1807 (1968)
http://dx.doi.org/10.1103/PhysRev.172.1807