Quantum numbers of N/Deltas resonances

[headbomb]

I've been working on something and I seem to have hit a noose.

The PDG lists many N/Delta resonances, but let's focus on four of them, each with J^P=3/2⁺:
*N(1720), P₁₃, http://pdg.lbl.gov/2009/listings/rpp2009-list-N-1720-P13.pdf
*Delta(1232), P₃₃, http://pdg.lbl.gov/2009/listings/rpp2009-list-Delta-1232.pdf
*Delta(1600), P₃₃, http://pdg.lbl.gov/2009/listings/rpp2009-list-Delta-1600.pdf
*Delta(1920), P₃₃, http://pdg.lbl.gov/2009/listings/rpp2009-list-Delta-1920.pdf

where spectroscopic state is noted L_{2I 2J}.

Now, if I want to identify the quantum numbers of these particles, J is given as 3/2, from P we know that L is 1, and thus S needs to be 1/2 (|J|=|L+S|, ..., |L-S| in integer steps). And now I'm left with only n to distinguish between a N and a Delta, which makes no sense. What am I doing wrong?

 

[Meir Achuz]

This spins of the N and the Delta are intrinsic spins. There is no L or S.
The parity refers to how they behave in decay to a pi N state.
Then the Delta(3/2) or the N(3/2) each decay to L_pi=1 and s_N=1/2.
They are distinguished by their Ispin.

 

[Vanadium 50]

N's have isospin 1/2. Deltas have isospin 3/2. That's the definition of the difference.

 

[headbomb]

This spins of the N and the Delta are intrinsic spins. There is no L or S.
The parity refers to how they behave in decay to a pi N state.
Then the Delta(3/2) or the N(3/2) each decay to L_pi=1 and s_N=1/2.
They are distinguished by their Ispin.

If there is no L, then why is L given (the P in P₁₃/P₃₃, see http://pdg.lbl.gov/2009/reviews/rpp2009-rev-n-delta-resonances.pdf). If there is no S, then why is J not equal to L?

N's have isospin 1/2. Deltas have isospin 3/2. That's the definition of the difference.

Isospin is not fundamental. I want the fundamental difference between the N(1720) and the Delta(1920)/Delta(1600) in terms of fundamental quantum numbers.

 

[Vanadium 50]

Isospin is not fundamental.

What do you mean it's not fundamental? Why then are the Lambda and Neutral Sigma different particles?

 

[headbomb]

Different internal symmetries (different wavefunctions).

I just might have answered my own question.

 

[Meir Achuz]

If there is no L, then why is L given (the P in P₁₃/P₃₃, see http://pdg.lbl.gov/2009/reviews/rpp2009-rev-n-delta-resonances.pdf). If there is no S, then why is J not equal to L?

As I said in my post, the L and S refer to the decay channel -->pi + N, or to the resonance channel in pi-N scattering.

Isospin is not fundamental. I want the fundamental difference between the N(1720) and the Delta(1920)/Delta(1600) in terms of fundamental quantum numbers.

Ispin is needed if quarks are not used. In the quark model, Ispin can be dispensed with,and the N and Delta difference is in their quark spin states. The same is true for the Lambda and Sigma.

 

[headbomb]

As I said in my post, the L and S refer to the decay channel -->pi + N, or to the resonance channel in pi-N scattering.

Any book or online refs I can check on that topic?

Ispin is needed if quarks are not used. In the quark model, Ispin can be dispensed with,and the N and Delta difference is in their quark spin states. The same is true for the Lambda and Sigma.

Yes, which then leads to the question, how would one write the analogous states for the equivalent \Sigma^- (dds) states? These would all be P₃₃ states [edit:I meant P₂₃, my bad]. Would mass be the only distinguisher?

 

[Meir Achuz]

Most older books on particle physics would discuss pi-N scattering.

There is a spin 1/2 Sigma-(dds) with the three quark spins adding up to 1/2.
The spin 3/2 dds state is now called the Y*. Its three quark spins add up to 3/2.
The Y* is not a P_33 state because its isospin is 1.

 

[headbomb]

Most older books on particle physics would discuss pi-N scattering.

Yes, but do you know of a book that specifically discuss these assignments of L with particular channels (instead of being a quantum number). Also, I've spoken with my teacher about this and he says that his impression is that L indeed is a quantum number. We are both quite puzzled by this.

There is a spin 1/2 Sigma-(dds) with the three quark spins adding up to 1/2.
The spin 3/2 dds state is now called the Y*. Its three quark spins add up to 3/2.
The Y* is not a P_33 state because its isospin is 1.

That doesn't make any sense. Spin three dds states are called \Sigma, just like the spin 1/2 dds states are called \Sigma. The only variation out there is to place a star in the decuplet Sigmas (\Sigma^*). If there's something called the Y* with the dds assignment, then it must've been a placeholder name for a resonance that will be changed into a \Sigma^ or \Sigma^* as soon as the dds assignment is confirmed.

And I meant P₂₃, my bad.

 

[Meir Achuz]

I'm sorry, Ihad the notation backwards. It was called the Y* years ago, but now is just listed in the pdg as Sigma, not even having the star for 3/2. Sigma- now refers to any quark model state dds of any J.

If you look at the summar tables for Sigmas, there are some with L>1 and J>3/2.
For instance, §(1775) D_15 is observed as a bump in pi-Sigma final states with angular distribution corresponding to L=2 and J=5/2.