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?

Thanks in advance for the answers.

 

[fzero]

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.

 

[fzero]

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.

 

[Andrea M.]

Yes I've already read this but I still have some doubts, I will give him another chance.