# Quantum numbers of N/Deltas resonances

1. Jul 16, 2009

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 JP=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 L2I 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?

2. Jul 16, 2009

### clem

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.

3. Jul 16, 2009

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

4. Jul 16, 2009

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?

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.

5. Jul 16, 2009

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

6. Jul 16, 2009

Different internal symmetries (different wavefunctions).

I just might have answered my own question.

7. Jul 17, 2009

### clem

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.
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.

8. Jul 17, 2009

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

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?

Last edited: Jul 17, 2009
9. Jul 17, 2009

### clem

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.

10. Jul 17, 2009

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.

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.

11. Jul 17, 2009

### clem

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.