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Quantum numbers of N/Deltas resonances

  1. Jul 16, 2009 #1
    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?
     
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  3. Jul 16, 2009 #2

    clem

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    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.
     
  4. Jul 16, 2009 #3

    Vanadium 50

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    N's have isospin 1/2. Deltas have isospin 3/2. That's the definition of the difference.
     
  5. Jul 16, 2009 #4
    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.
     
  6. Jul 16, 2009 #5

    Vanadium 50

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    What do you mean it's not fundamental? Why then are the Lambda and Neutral Sigma different particles?
     
  7. Jul 16, 2009 #6
    Different internal symmetries (different wavefunctions).

    I just might have answered my own question.
     
  8. Jul 17, 2009 #7

    clem

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    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.
     
  9. Jul 17, 2009 #8
    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 [tex]\Sigma^-[/tex] (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
  10. Jul 17, 2009 #9

    clem

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    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.
     
  11. Jul 17, 2009 #10
    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 [tex]\Sigma[/tex], just like the spin 1/2 dds states are called [tex]\Sigma[/tex]. The only variation out there is to place a star in the decuplet Sigmas ([tex]\Sigma^*[/tex]). 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 [tex]\Sigma^[/tex] or [tex]\Sigma^*[/tex] as soon as the dds assignment is confirmed.

    And I meant P23, my bad.
     
  12. Jul 17, 2009 #11

    clem

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    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.
     
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