Baryon effective Lagrangian

Andrea M.
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?

Homework Helper
Gold Member
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.

Andrea M.
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.