The chiral Lagrangian with three flavors and large-$N_c$ sum rules

We reconsider the chiral Lagrangian with three-flavor baryon fields. A systematic analysis of all low-energy constants (LEC) that contribute to the axial-vector and pseudoscalar currents in the baryon octet and decuplet fields at next-to-leading order in the inverse number of colors ($N_c$ ) of QCD is performed. We study the correlation function consisting of axial-vector and scalar currents as well. While there are 4 LEC relevant at leading chiral order, the number of relevant LEC at subleading order is 23. For those a leading order large-N_cN c​ analysis predicts 3 and 18 sum rules respectively. At the next accuracy level the number of sum rules is reduced to 2 and 8. Our results are illustrated by a tree-level analysis of available axial-vector coupling constants and strong decay widths of the baryon decuplet states