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I The spin-flavor wavefunction of Sigma+

  1. Jun 25, 2016 #1
    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?
     
  2. jcsd
  3. Jun 25, 2016 #2

    ChrisVer

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    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.
     
  4. Jun 25, 2016 #3
    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?
     
  5. Jun 26, 2016 #4
    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.
     
  6. Jun 26, 2016 #5

    ChrisVer

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    what is confusing?
     
  7. Jun 27, 2016 #6
    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...
     

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  8. Jun 27, 2016 #7

    ChrisVer

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    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.
     
  9. Jun 27, 2016 #8
    When determining ##X##?
     
  10. Jun 28, 2016 #9

    ChrisVer

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    when determining Phi...
    you should have a symmetric one (in the triplet I=1 combination) : [itex] uds + dus[/itex]
    and an antisymmetric one (in the singlet I=0 combination) : [itex] uds - dus [/itex]
    they both correspond to I3=0
     
  11. Jul 3, 2016 #10

    clem

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    Look at look at PR 172, 1807 for simple spin – flavor wave functions for baryons.
     
  12. Jul 3, 2016 #11
    What is PR?
     
  13. Jul 4, 2016 #12

    vanhees71

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