Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Baryon singlet representation for SU(3) flavour symmetry

  1. Oct 23, 2008 #1
    Hi there!

    As most people already might know, we can decompose the 27 dimensional representation for the baryons under SU(3) flavour symmetry as 27 = 10 + 8 + 8 + 1. I can find a lot of information about the particles that lie in the decuplet and in the octet, but nothing about which particle is associated to the singlet representation. Can anyone give me some information about this? :)

    Thanks in advance!
     
  2. jcsd
  3. Oct 23, 2008 #2
    the singlet particle is uds (lambda) and it does not exist in the ground state (angular momentum zero) due to Fermi statistics.
     
  4. Oct 23, 2008 #3

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2015 Award

    Hamster is right that the SU(3) baryon flavor singlet is an isospin 0 uds combination. He's also right that it doesn't exist: however, it still possesses (or would possess) angular momentum of 1/2, because the three quarks each have spin 1/2. I think he means there is no orbital angular momentum.

    There is an excited SU(3) singlet. It must have T=0, J=3/2, and a quick look in the PDG suggests to me that the best candidate is the Lambda(1890).
     
  5. Oct 24, 2008 #4

    clem

    User Avatar
    Science Advisor

    There is a uds spin 1/2 state that is the Lambda particle of the baryon octet.
    It does exist in the octet ground state.
     
  6. May 20, 2010 #5
    Could you explain to me why it doesn't exist? I've also been wondering about this question.
     
  7. May 20, 2010 #6

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2015 Award

    It's a fermion so it's total wave function has to be antisymmetric. If I make it symmetric in color, under SU(3) and spatially, it's total wave function isn't antisymmetric.
     
  8. May 21, 2010 #7

    clem

    User Avatar
    Science Advisor

    The spin addition 1/2+1/2+1/2=1/2 leads to a spin state of mixed symmetry (not completely symmetric or antisymmetric). This means the flavor state must also be mixed, which requires a flavor octet, and not a singlet.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Baryon singlet representation for SU(3) flavour symmetry
  1. SU(3) symmetry of QCD (Replies: 20)

  2. SU(3) symmetry (Replies: 12)

Loading...