given truncated chiral Lagrangian. On the other hand they may be analyzed systematically in a $1/N_c$ expansion. A matching of the two results leads to a correlation of the low-energy parameters of the chiral Lagrangian formulated with the baryon octet and decuplet fields. We use here the conventions for the various low-energy parameters as introduced previously in [@Semke:2011ez].

For the reader’s convenience all terms relevant for our study are recalled explicitly in this chapter. The applied conventions are illustrated at the hand of the kinetic terms $$\begin{aligned}
&& \mathcal{L}^{(1)} =
\mathrm{tr}\, \Big\{ \bar B\, (i\, \Dslash\, - M_{[8]})\, B \Big\}  +
 \mathrm{tr}\, \Big\{ \bar B_\mu \cdot \big((i\,\Dslash\, - M_{[10]})\,g^{\mu\nu} 
\nonumber\\ 
&& \qquad \qquad \qquad  -\,i\,(\gamma^\mu D^\nu + \gamma^\nu D^\mu) + \gamma^\mu(i\,\Dslash + M_{[10]})\gamma^\nu \big)\, B_\nu \Big\}\,,
\nonumber\\
&&\Gamma_\mu ={\textstyle{1\over 2}}\,u^\dagger \,\big[\partial_\mu -i\,(v_\mu + a_\mu) \big] \,u
+{\textstyle{1\over 2}}\, u \,
\big[\partial_\mu -i\,(v_\mu - a_\mu)\big] \,u^\dagger\,,  
\nonumber\\
&&  D_\mu \, B \;\,= \partial_\mu B +  \Gamma_{\mu}\, B -
B\,\Gamma_{\mu} \,, \qquad \qquad \qquad
 u = e^{i\,\frac{\Phi}{2\,f}}  \,,
\label{def-L1}\end{aligned}$$ for the baryon spin 1/2 and 3/2 fields $B$ and $B_\mu$. Here we encounter the covariant derivative $D_\mu$ which involves the vector and axial vector source fields $v_\mu$ and $a_\mu$. The SU(3) matrix 