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Baryon effective Lagrangian

  1. Sep 28, 2015 #1
    I'm trying to understand how to construct effective lagrangians for the hadrons. I understand the procedure for the mesons but I get stuck on baryons. In particular I don't understand how the baryons should transform under a chiral transformation. I mean for the mesons it was easy because they could be interpreted as the Goldston bosons of the theory, but for baryons?

    Thanks in advance for the answers.
     
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  3. Sep 28, 2015 #2

    fzero

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    Are you working from a specific reference? In the linear sigma model, for example, the nucleon is introduced as a Dirac spinor. The chiral symmetry is manifest as ##SU(2)_L\times SU(2)_R##, where the factors act independently on the chiral components of the spinor.
     
  4. Sep 29, 2015 #3
    I'd like to understand how the octet of baryons ##B## transforms under ##SU(3)_L\times SU(3)_R##. The only thing I know is that it must transforms as the eight dimensional representation of the unbroken symmetry ##SU(3)_V## but I don't get why it should transform like
    $$
    B\to h(\phi,g)Bh^{\dagger}(\phi,g)
    $$
    where ##\phi## are Goldstone bosons fields, ##g## is a ##SU(3)_L\times SU(3)_R## transformation and ##h## is a ##SU(3)_V## transformation as claimed for example in Pich, A. & de Rafael, E., 1991. Strong CP violation in an effective chiral Lagrangian approach. Nucl. Phys., B367(2), pp.313–333.
     
  5. Sep 29, 2015 #4

    fzero

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    I am not that familiar with specific nonlinear realizations, but there is a draft version of Georgi's book available at www.people.fas.harvard.edu/~hgeorgi/weak.pdf. This representation is discussed in Ch. 6, but you will need to refer to the discussion of mesons in Ch. 5 to figure out the notation.
     
  6. Sep 29, 2015 #5
    Yes I've already read this but I still have some doubts, I will give him another chance.
     
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